Introductory Statistics Using SPSS 2nd Edition Knapp Solutions Manual

Type:

Solution Manual

Introductory Statistics Using Resource: SPSS Edition:

2nd Edition

Author(s):

Herschel Knapp

1

Chapter 1 Research Principles Solutions to All Exercises

Exercise

Page

1.1 ..................... 2 1.2 ..................... 3 1.3 ..................... 4 1.4 ..................... 5 1.5 ..................... 6 1.6 ..................... 7 1.7 ..................... 8 1.8 ..................... 9 1.9 ................... 10 1.10 ................. 11

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 NOTE: It is not expected that your answers will match the solutions below verbatim or that your methods will be identical, but they should concur conceptually.

Exercise 1.1 (a) Will 30 minutes of square dancing, 5 days a week, help reduce pediatric weight? (b) This would be a two-group study: The control group would have recess as usual with no structured activities; the kids can do whatever they want (except participate in the square dancing). The treatment group would participate in the square dancing. (c) The briefing sheet that would be distributed to teachers would instruct each teacher to go through their roll list, and flip a coin one time for each student: Heads assigns the student to the square dancing, tails assigns the student to have regular recess. (d) H0: Aerobic square dancing 30 minutes a day, 5 days a week, facilitates no weight loss among elementary school students.

H1: Aerobic square dancing 30 minutes a day, 5 days a week, facilitates weight loss among elementary school students. (e) At the conclusion of the study, the school nurse will weigh each student. The statistician will compare the weights of those who participated in the aerobic square dancing against those who had regular recess. If there is no statistically significant difference between the weights of these two groups, then we would accept H 0, otherwise, we would reject H0 in favor of H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 Exercise 1.2 (a) Does pet therapy for 30 minutes per day with certified therapy dogs help reduce depression among nursing home residents? (b) This nursing home has the hours of 2:00 p.m. to 4:00 p.m. daily designated as open time. Those who are in the treatment group will be taken to the patio from 2:30 p.m. to 3:00 p.m. to participate in the pet therapy program. Those in the control group will be free to utilize that 2-hour block of time any way they choose (except for pet therapy). (c) I would assign residents who were born on an even date to the control group, and those born on an odd date would be assigned to the treatment (pet therapy) group. (d) H0: Pet therapy for 30 minutes per day has no impact on nursing home residents’ level of depression.

H1: Pet therapy for 30 minutes per day reduces nursing home residents’ level of depression. (e) After pet therapy, our team will ask each resident in both groups to rate their mood (1 = feeling very depressed, 10 = feeling very happy). We will process the scores; if there is no statistically significant difference between the scores of the two groups, then I would not reject H0 and reject H1. If the treatment group has a statistically significantly lower score than the control group, then I would reject H0 and not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 Exercise 1.3 (a) Will placing a security camera on cashiers reduce cash shortages? (b) This will be a two-group study: The control group will have no cameras installed. The treatment group will have a camera installed focused on each cashier, and all cashiers in the treatment group will be notified that their actions are now being recorded. (c) The name of each of the 10 stores will be written on a chip and placed into a bag. The bag will be sealed, shaken, and then opened; a staff member will reach into the bag and without looking, withdraw five chips. The stores indicated on these five chips will constitute the treatment group; the other five stores will constitute the control group.

NOTE: Since this is a two-group design, one could have simply used the coin-flip method; the chip selection is one potential alternative to consider when there are more than two groups, as will be the case in Chapter 6 (“ANOVA and KruskalWallis Test”). (d) H0: Video recording will have no effect on cashier balances.

H1: Video recording will reduce cashier losses. (e) The statistician will gather data from all 10 stores and compare cash register losses from the stores with no cameras to the stores with cameras. If there is no statistically significant difference between the cash losses of these two groups, then we would accept H0, otherwise, we would reject H0 in favor of H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 Exercise 1.4 (a) Will implementing a neighborhood watch program reduce vandalism in Anytown? (b) Anytown consists of 20 demographically equivalent square blocks. The town will be split in half (north side and south side). The neighborhood watch program will be implemented on one side of town, which will constitute the treatment group. The other side of town will get no neighborhood watch program—there’ll be no “Neighborhood Watch” signs posted. (c) A coin flip will be used: Heads will assign the north side of the town to the treatment group; tails will assign the south side of town to the treatment group. (d) H0: Neighborhood watch program does not significantly reduce the number of vandalisms in Anytown.

H1: Neighborhood watch program significantly reduces the number of vandalisms in Anytown. (e) After 30 days, we would contact the police department and ask them to provide us with the number of reported vandalisms for the month along with their addresses. We would then compare the number of vandalisms committed on the north side of town to the south side of town. If there is no statistically significant difference between the two groups, then I would not reject H0, but would reject H1. If there were statistically significantly fewer vandalisms in the zone where the neighborhood watch was implemented, then I would reject H0, and not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 1.5 (a) Will entering on-time employees in a weekly “get out of Friday free” lottery reduce morning lateness? (b) Two of the four buildings should participate in the “get out of Friday free” lottery, these sites will serve as the treatment groups, and two should continue business as usual, serving as the control groups. (c) A staff member writes the name or address of each of the four buildings on four identical cards, and places them in a box. Without looking, the staff member draws two cards out of the box, one at a time. These two cards will constitute the treatment groups; the other two will serve as the control groups. (d) H0: Rewarding on-time arrivals with the chance to win a free day off will have no effect on lateness.

H1: Rewarding on-time arrivals with the chance to win a free day off will reduce lateness. (e) After running this lottery program for a month, the statistician will gather and analyze the time cards from each of the four buildings and compare the minutes late from those in the two buildings that had no day-off lottery (in the control groups), to those who did participate in the day-off lottery (in the treatment group). If there is no significant difference in the minutes late, comparing the employees in the control group to those in the treatment group, then we would accept H0, otherwise we would reject H0, in favor of H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 Exercise 1.6 (a) Does drinking Acme Herbal Tea actually help people relax? (b) The members of the control group would get a regular cup of generic herbal tea; those in the treatment group would get the Acme Herbal Tea. (c) As each participant shows up at their appointed time, I would flip a coin and let heads assign the participant to the control group and tails would assign the participant to the treatment group. (d) H0: Herbal tea has no effect in terms of relaxation level.

H1: Acme Herbal Tea makes people more relaxed than generic herbal tea. (e) We will measure relaxation by pulse rate (lower pulse rates suggests more relaxed). If there is no statistically significant difference in the pulse rates of the two groups, then we would not reject H0 and reject H1. If the pulse rate of the treatment group is significantly lower than those in the control group, then I would reject H 0 and not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 Exercise 1.7 (a) Does singing 1 hour a day improve memory? (b) Members in the control group will sit quietly for an hour, and then take a memory test.

Those in the treatment group will sing well known songs for 1 hour (karaoke style) and then take the memory test. (c) Professor Madrigal will recruit 60 participants for this experiment. Prior to the arrival of the first participant, the professor flipped a coin (heads for control group, tails for treatment group)—the coin flip rendered tails, hence, the first participant who shows up will be assigned to the treatment group. Each remaining subject would be assigned to the control/treatment group on an alternating basis, upon arrival, thereby keeping the groups balanced. (d) H0: Singing has no effect on memory.

H1: Singing enhances memory. (e) Upon the departure of the last subject, the professor compares the memory test scores of those in the control group to those in the treatment group. If there is no statistically significant difference in the scores, then this supports H0, otherwise, the professor would reject H0 in that the data supports H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 Exercise 1.8 (a) Does providing various colored pens to students help them write longer essays? (b) The control group will write with a black ink pen. The treatment group will be issued a pen equipped with multiple colors. (c) The instructor will stand at the classroom door—upon entry, each student will be handed a black pen or a multicolored pen on an alternating basis and instructed not to exchange with anyone. (d) H0: Students equipped with the multicolor pens do not write longer essays than those who use single color pens.

H1: Students equipped with the multicolor pens write statistically significantly longer essays than those who use single color pens. (e) After the class, the teaching assistant would gather the essays and count the words of each. If there is no statistically significant difference in essay length between the control group and the treatment group, then I would accept H0 and reject H1. If students wrote statistically significantly longer essays with the multicolored pens, compared to those who wrote with the black pens, then I would reject H0 and not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 1.9 (a) Do flash cards help students memorize the multiplication table? (b) Members in the treatment group will each be issued a set of 100 flash cards (1 x 1 through 10 x 10), and will be instructed to work with them for 30 minutes a day for 1 month. Members in the control group will use the usual multiplication teaching method (no flash cards). Members of both groups will be tested once a week; they will be given 10 minutes to answer 100 multiplication problems (1 x 1 = ___ through 10 x 10 = ___). (c) Ms. Fractal calls each student to the front of the room one at a time; she holds up a coin and asks the student to guess heads or tails. She then flips a coin; if the student guessed correctly, then that student is assigned to the treatment group, and given a set of multiplication flash cards, otherwise the student is assigned to the control group, and receives no flash cards. (d) H0: Flashcards do not help students learn the multiplication table.

H1: Flashcards help students learn the multiplication table. (e) Ms. Fractal will grade the tests. If the treatment group’s overall score is statistically significantly higher than the control group’s score, then she would reject the null hypothesis (H0), in favor of the alternative hypothesis (H1), otherwise, the findings suggest support for the null hypothesis (H0).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 Exercise 1.10 (a) Will running a classic movie on a big screen with the sound muted help increase the number of calls processed per hour at the Acme Call Center? (b) The Acme Call Center consists of two rooms with 40 staff members assigned to each room. One room will be equipped to play movies at the front of the room—this will be the treatment group, the other room will not—this will be the control group. (c) A coin flip will be used to select which room (Room A or Room B) will get the movie— heads for Room A, tails for Room B. (d) H0: Showing a movie with the sound muted will have no effect on the number of calls processed.

H1: Showing a movie with the sound muted will increase the number of calls processed. (e) If there is no statistically significant difference in calls processed between Room A and Room B, then I would not reject H0 and would reject H1. If the movie room processed more calls than the nonmovie room, then I would reject H0 and not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 2 Sampling Solutions to All Exercises

Exercise

Page

2.1 ..................... 2 2.2 ..................... 3 2.3 ..................... 4 2.4 ..................... 5 2.5 ..................... 6 2.6 ..................... 7 2.7 ..................... 8 2.8 ..................... 9 2.9 ................... 10 2.10 ................. 11

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 NOTE: It is not expected that your answers will match the solutions below verbatim or that your methods will be identical, but they should concur conceptually.

Exercise 2.1 (a) In terms of time, gathering a sample of an entire population could take weeks, months, or possibly years depending on the size of the population, geographical area involved, and the complexity of the data to be gathered. The point of research is to get the answer to a meaningful question, presumably, to solve a problem or improve a situation.

Such answers can be expedited by sampling, as opposed to gathering data on the entire population. Attempting to sample the entire population would be so timeconsuming that by the time you had acquired your full data set, the nature of the initial problem may have changed substantially, thereby making your findings virtually irrelevant. (b) No matter what method of gathering data one uses (e.g., in-person surveys, phone surveys, postal/e-mail contact, tests), costs are involved. When it comes to data collection, subject participation fees are customary, data collection teams need to be paid, additionally, there are administrative costs involved (photocopying, office space, equipment, office supplies, etc.). Considering the volume of individuals that would be involved in studying an entire population, the costs would be prohibitive. (c) Beyond the lengthy time and exorbitant costs that would be involved in studying an entire population, it is seldom feasible to gather data on so many people. The population may span a broad geographical region, requiring lengthy travel among the research staff. Within a population, one would likely encounter a variety of languages; it may not be possible to translate verbal/written instructions to engage everyone in the population. Additionally, some studies may involve experiments that can only be administered at a special facility; it would be impossible to arrange to round-tripcommute every member of a population to that facility to participate. (d) Extrapolation involves working diligently to gather a representative sample in sufficient quantities to facilitate stable statistical processing. If the data gathered constitute a representative sample, then one could confidently extrapolate the findings, in order to (better) comprehend the overall population that it was drawn from; this is also known as external validity.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 Exercise 2.2 (a) The population is the largest possible realm of sampling. For example, if we are studying instructors in the school district, the population would be the full list of every single instructor in the school district. (b) The sample frame is the available list of the population that could potentially be sampled. For example, the sample frame of instructors would consist of only those included on this list, but the list may not consist of the entire population—there may be omissions (e.g., does not include substitutes, does not include those who opt not to be on the list, does not include instructors who recently joined the school district or those who are suspended or on sabbatical). (c) The sample is the portion of instructors that will be selected from the sample frame. For example, you may decide to randomly select 100 instructors or some percentage of the instructors to study. (d) A representative sample is a sample that is proportionally equivalent to the larger population that it was drawn from. For example, if there are 40% men and 60% women in the population, then the sample should consist of those same proportions. Also, the sample shouldn’t all be drawn from any single school—the sample should be evenly drawn from across the school district.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 Exercise 2.3 (a) The population is the entire student body currently enrolled (e.g., 22,000 students). (b) The sample frame is the available list of students currently enrolled (e.g., 16,000 students). (c) Fortunately, the list of participants in the sample frame were already numbered from 1 to 16,000. I would want to gather data on 2% of the sample frame (16,000 x .02 = 320); I would use SPSS to generate 320 random numbers between 1 and 16,000—this list would indicate which students on the sample frame to recruit. Actually, I would probably generate more than 320 random numbers just in case SPSS produces some duplicates. (d) I would build (and test) an online survey. Next, I would send an e-mail to each of the 320 students in the sample set; the e-mail would concisely explain the nature of the study, and courteously request that they voluntarily click on the link to the online survey.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 Exercise 2.4 (a) The population is every single subscriber of this Internet service. (b) The sample frame is the list of subscribers who have agreed to be on their customer contact list (they checked a box in their user profile that says “Yes, you may contact me to engage in customer satisfaction surveys”). (c) Suppose the list consists of 500,000 subscribers and I want to sample 1,000 subscribers. I would begin by dividing the population size by the sample size to derive the k (skip) term (500,000 ÷ 1,000 = 500). Next, I’d have the computer generate a random number between 1 and 500; this number would be the start point (let’s say that number is 42). The sample would then consist of the subscribers on the list who are at positions 42, 542, 1,042, 1,542, 2,042, etc. (start at 42 and keep adding 500 to generate the sample list). (d) First, I would build the survey using an online survey system, and test it (myself) to make sure that it’s operating properly. Then I would send individual e-mails to each recipient. Sending individual e-mails would preserve the anonymity among the participants (nobody could see the e-mail addresses of the other participants). In the body of the e-mail, I’d explain the nature of the research, explain that their participation is voluntary (and appreciated), and provide the link to the survey website.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 2.5 (a) The population is all of the people who enter the library. (b) The sample frame consists of those who enter the reference section. (c) I would approach each person in the reference section and ask if they would be willing to spend a few minutes answering some simple questions about how they use the library. In order to satisfy the strata (children/adult), the first question would be “How old are you?” or “Are you 18 or older?” I’d want to get at least 30 in each stratum (at least 30 children, and at least 30 adults). (d) I would use a clipboard with a prepared questionnaire. Regarding the children, I would presume that children at a library would be accompanied by an adult. It would be a good idea to interview the adult with the child together to gather more complete information and to make sure that the adult (parent) is okay with their child participating in the survey process.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 Exercise 2.6 (a) The population is every single person who lives within the 300 blocks of Cityville. (b) The sample frame would be the (partial) list of all of those who reside in Cityville, but that list may not exist or not be accessible. (c) To use area sampling, first we would need to label the 300 blocks (1-300). Next, we would select some percentage of the blocks to sample; for example, 10%, which would require selecting 30 blocks (300 x .10 = 30). We would randomly select the 30 blocks using a random number generator generating numbers contained within 1 and 300.

Next, suppose that we’ve decided to survey five households per block, we’d need to gather all of the addresses on each of those blocks and randomly select five of them to survey. (d) Next we would assemble the list of targeted addresses (five per specified block) and send out our survey teams to administer the survey(s).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 Exercise 2.7 (a) I wouldn’t want to bother people who are walking someplace, or who are engaged in conversations with friends/family, so I would approach people waiting in line (for food or an attraction) since they’d probably be a bit bored just waiting in line. (b) I would greet them and tell them my name, just to be friendly, and then tell them that I work for Acme Research Firm (I’d point to my badge) and tell them that I’m gathering some information about how much money they intend to spend today and ask them if they wouldn’t mind estimating that amount for me. Whether they choose to respond or not, I’d thank them.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 Exercise 2.8 (a) With the permission of the administration of a local school, I would stand at the exit of the school at the end of the day and hand out flyers that says “If you have dyslexia, you may be eligible to partake in our (paid) survey”—the flyer would include contact information. After I completed the survey procedure with each participant, I would ask if he or she knows of anyone else with dyslexia who might be interested in being in this study. I would also approach the school administration to ask them if they would be willing to offer the survey recruitment flyer to any students that have been identified as dyslexic. (b) I would schedule each potential participant individually and begin with a dyslexic diagnostic test. If the participant meets the criteria for dyslexia, then I would administer the survey.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 2.9 (a) I would ride the bus starting at 8:00 a.m. At first I’d approach anyone. If they consented to talk to me, I would begin by asking them their age. Once I’d hit my quota for a group (50 minors, 100 adults), I’d stop approaching that group and proceed with the other group. When I’d gathered all 150 surveys, I’d stop the sampling process completely, and move on to the analysis (off the bus). (b) I would approach potential participants, identify myself as a staff member of the Acme Bus Company (I’d point to my badge), and ask the person if I could ask them a few questions about their impressions of their bus riding experience(s). I would record their responses on a clipboard, which would contain the printed survey. The first question I would ask is “What is your age?” which I would record on the survey form; if they didn’t want to tell me their age, I would ask “Are you 18 or over?” unless it was obvious that the person was clearly either a child or an adult. This way I could keep a running count of how many minors and how many adults I had surveyed. To adhere to ethical standards, if a child is with an adult, I would ask the adult if I could ask them (the adult) a few questions about their bus riding experience, and then after they knew what the questions were, I would ask the adult if I could ask the same question to their child. If a child is alone on the bus, I wouldn’t approach them, since there would be no adult present who could authorize the child’s participation in this survey. If anyone, especially a child, is resistant to talking with me, I’d just thank them and courteously end the conversation—I wouldn’t pursue the questioning.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 Exercise 2.10 (a) I would coordinate with the local school district to distribute flyers to all students who are enrolled in the specified school district. The flyer would be addressed to the parents and say: “If you have a child who is under 18 years old who would like to participate in a community tutoring program 3 days a week from 3:30 p.m. to 5:00 p.m., please call or text us at (555) 555-5555 or e-mail us FreeTutor@AcmeSchool.edu.” (b) I would ask students to provide copies of their report cards so we could track (changes in) grades over the course of the tutoring program.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 3 Working in SPSS Solutions to All Exercises

Exercise

Page

3.1 ..................... 2 3.2 ..................... 3 3.3 ..................... 4 3.4 ..................... 5 3.5 ..................... 6 3.6 ..................... 8 3.7 ................... 10 3.8 ................... 12 3.9 ................... 13 3.10 ................. 14

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 3.1 enrolled Value Standard Attributes

Valid Values

Position

Count

Percent

1

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2

Yes No

4 1

units Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

2 <none> Numeric F8 Scale Input 5 0 9.20 6.261 6.00 12.00 12.00

grade Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8 Scale Input 5 0 81.40 10.550 72.00 81.00 91.00

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

80.0% 20.0%

3 Exercise 3.2 id Value Standard Attributes

Valid Values

Count

Percent

AL331

1

20.0%

DD987

1

20.0%

JW105

1

20.0%

QF732

1

20.0%

RK122

1

20.0%

Position

1

Label

<none>

Type

String

Format

A8

Measurement

Nominal

Role

Input

volunteer_hours Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8.2 Scale Input 5 0 2.2000 1.35093 1.5000 2.0000 3.0000

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 Exercise 3.3 degree Value Standard Attributes

Valid Values

Position

Count

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Ordinal

Role

Input

1 2 3 4

Associate’s Bachelor’s Master’s Doctorate

1 2 2 0

pretest Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8 Scale Input 5 0 27.20 3.701 25.00 28.00 30.00

posttest Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8 Scale Input 5 0 39.00 8.000 34.00 38.00 46.00

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20.0% 40.0% 40.0% .0%

5 Exercise 3.4 employ Value Standard Attributes

Valid Values

Count

Position

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Ordinal

Role

Input

1 2 3 4

Unemployed Temporary Part-time Full-time

1 1 1 2

work_hours Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8 Scale Input 5 0 24.20 18.390 16.00 20.00 40.00

sleep_hours Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8.2 Scale Input 5 0 8.3000 1.20416 7.5000 8.0000 9.0000

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20.0% 20.0% 20.0% 40.0%

6 Exercise 3.5 first_initial Value Standard Attributes

Valid Values

Position

Count

Percent

2

Label

<none>

Type

String

Format

A1

Measurement

Nominal

Role

Input

D

1

20.0%

J

1

20.0%

P

1

20.0%

T

1

20.0%

V

1

20.0%

last_name Value Standard Attributes

Valid Values

Position

Count

Percent

3

Label

<none>

Type

String

Format

A20

Measurement

Nominal

Role

Input

Freeman

1

20.0%

Gower

1

20.0%

Jones

1

20.0%

Rexx

1

20.0%

Smith

1

20.0%

siblings Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8 Scale Input 5 0 1.60 1.140 1.00 2.00 2.00

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7

adopted Value Standard Attributes

Valid Values

Position

Count

Percent

5

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2

Yes No

1 4

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20.0% 80.0%

8 Exercise 3.6 patient_ID Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

2 <none> Numeric F8 Scale Input 5 0 5.27E9 3.006E9 2.14E9 5.83E9 8.05E9

age Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8 Scale Input 5 0 43.60 24.337 24.00 38.00 53.00

temp Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8.2 Scale Input 5 0 99.7600 1.33903 98.8000 99.0000 100.9000

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9

flu_shot Value Standard Attributes

Valid Values

Count

Position

Percent

5

Label

<none>

Type

Numeric

Format

F20

Measurement

Nominal

Role

Input

1 2

Yes No, and I don’t want one Not yet, but I’d like one

3

3 1

60.0% 20.0%

1

20.0%

rx Value Standard Attributes

Position Label

<none>

Type

String

Format

A20

Measurement

Nominal

Role

Input

Valid Values

Count

Percent

6

3

60.0%

Multivitamin

1

20.0%

Xamine, Tutsocol

1

20.0%

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 3.7 passport Value Standard Attributes

Valid Values

Position

Count

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2 3

Yes No Decline to answer

2 3 0

40.0% 60.0% .0%

fired Value Standard Attributes

Valid Values

Position

Count

Percent

3

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2 3

Yes No Decline to answer

1 3 1

20.0% 60.0% 20.0%

er Value Standard Attributes

Valid Values

Position

Count

Percent

4

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2 3

Yes No Decline to answer

2 3 0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40.0% 60.0% .0%

11

dob Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

5 <none> Numeric ADATE10 Scale Input 5 0 8/21/1965 280683:12:0 7.445 1/23/1936 6/07/1974 3/01/1987

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 Exercise 3.8 dogs Value Standard Attributes

Valid Values

Position

Count

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Ordinal

Role

Input

1

Strongly disagree Disagree Neutral Agree Strongly agree

2 3 4 5

0

.0%

0 1 1 3

.0% 20.0% 20.0% 60.0%

cats Value Standard Attributes

Valid Values

Position Label

<none>

Type

Numeric

Format

F8

Measurement

Ordinal

Role

Input

1

Strongly disagree Disagree Neutral Agree Strongly agree

2 3 4 5

Count

Percent

3

1

20.0%

1 1 0 2

20.0% 20.0% .0% 40.0%

pets Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8 Scale Input 5 0 1.20 1.304 .00 1.00 2.00

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 Exercise 3.9 blood_type Value Standard Attributes

Valid Values

Count

Position

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2 3 4 5 6 7 8 9

AA+ BB+ ABAB+ OO+ Don’t know

1 0 0 1 0 1 1 0 1

20.0% .0% .0% 20.0% .0% 20.0% 20.0% .0% 20.0%

gender Value Standard Attributes

Valid Values

Position

Count

Percent

3

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2

Female Male

2 3

40.0% 60.0%

prior_donor Value Standard Attributes

Valid Values

Position

Count

Percent

4

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2

Yes No

2 3

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40.0% 60.0%

14 Exercise 3.10 entree_food Value Standard Attributes

Valid Values

Position

Count

Percent

2

Label

<none>

Type

Numeric

Format

F8

Measurement

Nominal

Role

Input

1 2 3 4

Fish Chicken Beef Vegetarian

4 0 1 0

entree_quality Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

3 <none> Numeric F8 Scale Input 5 0 8.60 1.140 8.00 9.00 9.00

dessert_quality Value Standard Attributes

N Central Tendency and Dispersion

Position Label Type Format Measurement Role Valid Missing Mean Standard Deviation Percentile 25 Percentile 50 Percentile 75

4 <none> Numeric F8 Scale Input 5 0 8.80 1.304 8.00 9.00 10.00

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

80.0% .0% 20.0% .0%

1

Chapter 4 Descriptive Statistics Solutions to All Exercises

Exercise

Page

4.1 ..................... 2 4.2 ..................... 6 4.3 ................... 10 4.4 ................... 14 4.5 ................... 18 4.6 ................... 23 4.7 ................... 28 4.8 ................... 33 4.9 ................... 37 4.10 ................. 41

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 4.1 (a) Statistics siblings N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

41 0 1.54 1.00 1 .951 .905 4 0 4

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 (b) class

Valid

Prof. Lamm Prof. Milner Total

Frequency 20 21 41

Percent 48.8 51.2 100.0

Valid Percent 48.8 51.2 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 48.8 100.0

4 (c) Statistics siblings N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

20 0 1.34 1.38 0 .708 .502 3 0 3

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 (d) Statistics siblings N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

21 0 1.72 1.62 3 .993 .986 4 0 4

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 4.2 (a) Statistics donated N Valid 17 Missing 0 Mean 3.88 Median 4.00 Mode 2a Std. Deviation 2.315 Variance 5.360 Range 9 Minimum 0 Maximum 9 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 (b) Statistics gender N Valid Missing

17 0 gender

Valid

Female Male Total

Frequency 9 8 17

Percent 52.9 47.1 100.0

Valid Percent 52.9 47.1 100.0

Cumulative Percent 52.9 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 (c) Statistics donated N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

9 0 4.00 4.00 5 2.872 8.250 9 0 9

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 (d) Statistics donated N Valid 8 Missing 0 Mean 3.75 Median 3.50 Mode 2a Std. Deviation 1.669 Variance 2.786 Range 5 Minimum 2 Maximum 7 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 4.3 (a) Statistics spelling N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

22 0 16.23 16.00 16 2.308 5.327 8 12 20

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 (b) Statistics looker N

Valid Missing

22 0 looker

Valid

Looks at keyboard Doesn’t look at keyboard Total

Frequency 15 7 22

Percent 68.2 31.8 100.0

Valid Percent 68.2 31.8 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 68.2 100.0

12 (c) Statistics spelling N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

15 0 15.60 16.00 16 1.765 3.114 6 12 18

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 (d) Statistics spelling N Valid 7 Missing 0 Mean 17.57 Median 19.00 Mode 19a Std. Deviation 2.878 Variance 8.286 Range 7 Minimum 13 Maximum 20 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 4.4 (a) Statistics atmsec N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

20 0 152.35 153.00 142 35.154 1235.818 125 95 220

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 (b) Statistics gender N Valid Missing

20 0 gender

Valid

Female Male Total

Frequency 11 9 20

Percent 55.0 45.0 100.0

Valid Percent 55.0 45.0 100.0

Cumulative Percent 55.0 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 (c) Statistics atmsec N Valid 11 Missing 0 Mean 161.18 Median 163.00 Mode 107a Std. Deviation 38.081 Variance 1450.164 Range 113 Minimum 107 Maximum 220 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

17 (d) Statistics atmsec N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

9 0 141.56 142.00 142 29.733 884.028 90 95 185

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Exercise 4.5 (a) Statistics units N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

40 0 11.85 12.00 12 2.348 5.515 9 6 15

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

19 (b) degree

Valid

Bachelors Masters Doctorate Total

Frequency 31 7 2 40

Percent 77.5 17.5 5.0 100.0

Valid Percent 77.5 17.5 5.0 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 77.5 95.0 100.0

20 (c) Statistics units N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

31 0 12.10 12.00 12 2.119 4.490 6 9 15

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

21 (d) Statistics units N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

7 0 10.29 9.00 9 2.928 8.571 9 6 15

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

22 (e) Statistics units N

Valid Missing

2 0 Mean 13.50 Median 13.50 Mode 12a Std. Deviation 2.121 Variance 4.500 Range 3 Minimum 12 Maximum 15 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 Exercise 4.6 (a) Statistics bill N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

100 0 6.5403 6.6050 6.70 .67939 .462 3.23 5.06 8.29

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24 (b) Statistics profrole N Valid Missing

100 0 profrole

Valid

Nurse Doctor Other Total

Frequency 39 38 23 100

Percent 39.0 38.0 23.0 100.0

Valid Percent 39.0 38.0 23.0 100.0

Cumulative Percent 39.0 77.0 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

25 (c) Statistics bill N

Valid Missing

39 0 Mean 6.5577 Median 6.6800 Mode 5.72a Std. Deviation .75645 Variance .572 Range 3.04 Minimum 5.25 Maximum 8.29 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 (d) Statistics bill N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

38 0 6.5524 6.5350 6.70 .65319 .427 2.82 5.06 7.88

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

27 (e)

Statistics bill Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

0 6.4909 6.5300 6.34 .60643 .368 2.16 5.46 7.62

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

28 Exercise 4.7 (a) Statistics emails N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

173 0 169.77 168.00 170 33.078 1094.164 166 109 275

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

29 (b) employ

Valid

Full-time Part-time Unemployed Total

Frequency 85 39 49 173

Percent 49.1 22.5 28.3 100.0

Valid Percent 49.1 22.5 28.3 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 49.1 71.7 100.0

30 (c) Statistics emails N

Valid Missing

85 0 Mean 153.71 Median 153.00 Mode 137a Std. Deviation 23.294 Variance 542.615 Range 91 Minimum 109 Maximum 200 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

31 (d) Statistics emails N

Valid Missing

39 0 Mean 166.77 Median 168.00 Mode 129a Std. Deviation 24.330 Variance 591.972 Range 89 Minimum 129 Maximum 218 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

32 (e) Statistics emails N

Valid Missing

49 0 Mean 200.04 Median 204.00 Mode 175a Std. Deviation 33.209 Variance 1102.832 Range 139 Minimum 136 Maximum 275 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

33 Exercise 4.8 (a) Statistics minwalked N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

53 0 47.85 46.00 46 7.754 60.131 30 34 64

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 (b) Statistics musickey N Valid Missing

53 0 musickey

Valid

Major Minor Total

Frequency 25 28 53

Percent 47.2 52.8 100.0

Valid Percent 47.2 52.8 100.0

Cumulative Percent 47.2 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

35 (c) Statistics minwalked N Valid 25 Missing 0 Mean 54.28 Median 55.00 Mode 46a Std. Deviation 5.631 Variance 31.710 Range 18 Minimum 46 Maximum 64 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

36 (d) Statistics minwalked N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

28 0 42.11 43.00 43 3.891 15.136 16 34 50

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

37 Exercise 4.9 (a) Statistics nsatisfy N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

336 0 72.78 74.00 82 11.154 124.421 56 42 98

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 (b) ward

Valid

2 patients per nurse 4 patients per nurse Total

Frequency 162 174 336

Percent 48.2 51.8 100.0

Valid Percent 48.2 51.8 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 48.2 100.0

39 (c) Statistics nsatisfy N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum

162 0 79.84 80.00 82 7.049 49.688 35 63 98

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40 (d) Statistics nsatisfy N Valid 174 Missing 0 Mean 66.21 Median 66.00 Mode 65a Std. Deviation 10.229 Variance 104.642 Range 46 Minimum 42 Maximum 88 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

41 Exercise 4.10 (a) Statistics ahss N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

100 0 21.77 22.00 26 4.399 19.351 19 11 30

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

42 (b) Statistics dance N

Valid Missing

100 0 dance

Valid

Dancer Nondancer Total

Frequency 50 50 100

Percent 50.0 50.0 100.0

Valid Percent 50.0 50.0 100.0

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Cumulative Percent 50.0 100.0

43 (c) Statistics ahss N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

50 0 24.64 25.00 26 3.082 9.500 12 18 30

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

44 (d) Statistics ahss N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

50 0 18.90 19.00 18 3.576 12.786 15 11 26

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 5 t Test and Mann-Whitney U Test Solutions to All Exercises

Exercise

Page

Exercise

Page

5.1A....................2

5.6A ................. 32

5.1B....................5

5.6B ................. 35

5.2A....................8

5.7A ................. 38

5.2B..................11

5.7B ................. 41

5.3A..................14

5.8A ................. 44

5.3B..................17

5.8B ................. 47

5.4A..................20

5.9A ................. 50

5.4B..................23

5.9B ................. 53

5.5A..................26

5.10A ............... 56

5.5B..................29

5.10B ............... 59

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 5.1, Data Set A (a) H0: Practicing meditation for 30 minutes a day, 3 days a week has no effect on resting pulse rate.

H1: Practicing meditation for 30 minutes a day, 3 days a week for 2 weeks affects resting pulse rate. (b) Histograms with normal curve plots show a normal distribution of pulse for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for pulse in Group 1 (No meditation)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 Normal distribution for pulse in Group 2 (Meditated 30 minutes a day, 3 days per week)

Test of Homogeneity of Variances pulse Levene Statistic df1 df2 Sig. .089 1 68 .766

The homogeneity of variance score shows a significance (p) of .766; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is 35 for each group; since the ns are greater than 30, this criterion passes also.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 (c) The t test revealed the following: Descriptives pulse

No meditation Meditates 30 minutes Total

N 35 35 70

Mean 97.40 92.20 94.80

Std. Deviation 6.826 7.287 7.483

Std. Error 1.154 1.232 .894

95% Confidence Interval for Mean Lower Bound Upper Bound 95.06 99.74 89.70 94.70 93.02 96.58

Minimum 84 78 78

ANOVA pulse Between Groups Within Groups Total

Sum of Squares 473.200 3390.000 3863.200

df 1 68

Mean Square 473.200 49.853

F 9.492

Sig. .003

69

The mean pulse rate for Group 1 (No meditation) is 97.40, whereas the mean pulse rate for Group 2 (Meditated 30 minutes, 3 days per week) is 92.20. This 5.2-point difference is statistically significant since the significance (p) is .003 (which is less than the .05  level). (d) This study analyzed the effects that meditation had on resting pulse rates. The subjects were randomly assigned to one of two groups; the group that did not meditate, and the other group that meditated for 30 minute on Monday, Wednesday and Friday for 2 weeks. Results revealed a mean resting pulse rate of 97.40 for those who did not meditate, and 92.20 for those who did meditate. Using a .05  level, the p value of .003 suggests that meditation does facilitate a significant reduction in resting pulse rate, hence, we reject H0. These findings suggest support for H1, specifically, that practicing meditation for 30 minutes a day, 3 days a week for 2 weeks affected the mean resting pulse rate among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Maximum 109 105 109

5 Exercise 5.1, Data Set B (a) H0: Practicing meditation for 30 minutes a day, 3 days a week has no effect on resting pulse rate.

H1: Practicing meditation for 30 minutes a day, 3 days a week for 2 weeks affects resting pulse rate. (b) Histograms with normal curve plots show a normal distribution of pulse for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for pulse in Group 1 (No meditation)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Normal distribution for pulse in Group 2 (Meditated 30 minutes a day, 3 days per week)

Test of Homogeneity of Variances pulse Levene Statistic df1 df2 Sig. .317 1 66 .576

The homogeneity of variance score for pulse shows a significance (p) of .576; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n criterion is satisfied as both groups have an n of more than 30 (see Descriptives table below).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 (c) The t test revealed the following: Descriptives pulse

No meditation Meditates 30 minutes Total

N 33 35 68

Mean 95.15 93.54 94.32

Std. Deviation 5.901 6.797 6.382

Std. Error 1.027 1.149 .774

95% Confidence Interval for Mean Lower Bound Upper Bound 93.06 97.24 91.21 95.88 92.78 95.87

Minimum 80 79 79

ANOVA pulse Between Groups Within Groups Total

Sum of Squares 43.954 2684.928 2728.882

df 1 66

Mean Square 43.954 40.681

F 1.080

Sig. .302

67

The mean pulse rate for Group 1 (No meditation) is 95.15, whereas the mean pulse rate for Group 2 (Meditated 30 minutes, 3 days per week) is 93.54. Even though the mean pulse rate for the meditation group is 1.61 points lower than the control group, this difference is not considered to be statistically significant since the significance (p) is .302 (which is greater than the .05  level). (d) This study analyzed the effects that meditation had on resting pulse rates. The subjects were randomly assigned to two groups; those that did not meditate, and those that meditated for 30 minutes on Monday, Wednesday and Friday for 2 weeks. Results revealed a mean resting pulse rate of 95.15 for those who did not meditate, and 93.54 for those who did meditate. This study showed a 1.61 reduction in the pulse rate of those who meditated; however, since the p value of .302 is greater than the .05  level, we would conclude that this difference is not statistically significant, hence, we do not reject H0. For the subjects studied, meditation did not significantly affect resting pulse rate.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Maximum 105 107 107

8 Exercise 5.2, Data Set A (a) H0: Pairing incoming freshmen with a sophomore for mentorship will have no effect on freshman’s overall term grade.

H1: Pairing incoming freshmen with a sophomore for mentorship will increase the freshman’s overall term grade. (b) Since the n for each group is low (only 25 each), and the histogram for grade in Group 1 (No mentor) is negatively skewed, this means that there are two violations of the pretest conditions for the t test. For these reasons, I would use the Mann-Whitney U test instead of the t test.

Group 1—No mentor

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 Group 2—With mentor

(c) The Mann-Whitney U test revealed the following: Ranks group grade

N

No mentor In-person mentor Total

25 25 50

Mean Rank 25.78 25.22

Sum of Ranks 644.50 630.50

Test Statisticsa grade Mann-Whitney U 305.500 Wilcoxon W 630.500 Z -.136 Asymp. Sig. (2-tailed) .892 a. Grouping Variable: group

The mean term grade for Group 1 (No mentor) is 68.84, whereas the mean term grade for Group 2 (With mentor) is 69.12. This .028-point difference is not statistically significant since the significance (p) is .892 (which is greater than the .05  level).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 (d) This study analyzed the effects that peer mentoring from a sophomore had on incoming freshmen’s term grades. The freshmen were randomly assigned to one of two groups: a group that did not have a mentor and the other group that was assigned to a mentor.

Results revealed a mean term grade of 68.84 for those who did not have a mentor and 69.12 for those who did have a mentor. Using a .05  level, the p value of .892 suggests that this type of mentorship does not facilitate a significant increase in freshman term grade; hence, we do not reject H0. These findings do not suggest support for H1— specifically, that providing sophomore mentors to incoming freshman enhances freshman term grade among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 Exercise 5.2, Data Set B (a) H0: Pairing incoming freshmen with a sophomore for mentorship will have no effect on freshman’s term grade.

H1: Pairing incoming freshmen with a sophomore for mentorship will increase the freshman’s term grade. (b) Histograms with normal curve plots show a normal distribution of term grade for both groups as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No mentor

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 Group 2—With mentor

Test of Homogeneity of Variances grade Levene Statistic df1 df2 Sig. .188 1 48 .666

The homogeneity of variance score shows a significance (p) of .666; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 25 for each group; the t test becomes more robust when the ns are at least 30, but we’ll proceed with the 25 per group.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 (c) The t test revealed the following: Descriptives grade

No mentor In-person mentor Total

N 25 25 50

Mean 63.56 69.40 66.48

Std. Deviation 7.042 7.539 7.799

Std. Error 1.408 1.508 1.103

95% Confidence Interval for Mean Lower Upper Bound Bound 60.65 66.47 66.29 72.51 64.26 68.70

Minimum 48 54 48

Maximum 77 83 83

ANOVA grade Between Groups Within Groups Total

Sum of Squares 426.320 2554.160 2980.480

df 1 48

Mean Square 426.320 53.212

F 8.012

Sig. .007

49

The mean term grade for Group 1 (No mentor) is 63.56, whereas the mean term grade for Group 2 (With mentor) is 69.40. This 5.84-point difference is statistically significant since the significance (p) is .007 (which is less than the .05  level). (d) This study analyzed the effects that peer mentoring from a sophomore had on incoming freshmen’s term grades. The freshmen were randomly assigned to one of two groups: a group that did not have a mentors and the other group that was assigned to mentors.

Results revealed a mean term grade of 63.56 for those who did not have a mentor and 69.40 for those who did have a mentor. Using a .05  level, the p value of .007 suggests that this type of mentorship facilitates a significant increase in freshman term grade; hence, we reject H0. These findings suggest support for H1—specifically, that providing sophomore mentors to incoming freshman enhances freshman term grade among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 5.3, Data Set A (a) H0: Tending to a plant has no effect on depressive mood.

H1: Tending to a plant reduces depressive mood. (b) Despite the few low score outliers shown in the histogram for Group 2, the Histograms with normal curve plots show a normal distribution of the depress variable for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for depress in Group 1 (No plant)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 Normal distribution for depress in Group 2 (Bamboo)

Test of Homogeneity of Variances depress Levene Statistic df1 df2 Sig. 3.615 1 118 .060

The homogeneity of variance score for mood shows a significance (p) of .060; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group is 60 (see Descriptives table below), which satisfies the 30 per group minimum criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 (c) The t test revealed the following: Descriptives depress

No plant Bamboo Total

N 60 60 120

Mean 19.60 18.05 18.83

Std. Deviation 2.701 2.500 2.706

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .349 18.90 20.30 .323 17.40 18.70 .247 18.34 19.31

Minimum 15 8 8

Maximum 25 24 25

ANOVA depress Between Groups Within Groups Total

Sum of Squares 72.075 799.250 871.325

df 1 118

Mean Square 72.075 6.773

F 10.641

Sig. .001

119

The mean depression level for those in the control group (No plant) is 19.60, whereas those in the treatment group (Bamboo) had a mean depression level of 18.05. Since the significance (p) is .001 (which is less than the .05  level), the 1.55-point improvement in those who were given plants is considered to be statistically significant. As such, we would reject H0 in favor of H1. (d) We hypothesized that empowering nursing home residents with an opportunity to provide nurturance would help reduce depression. To test this hypothesis, 120 residents were randomly assigned to one of two groups: The 60 people in the treatment group were each given a small bamboo plant to tend to along with a card providing care instructions; the 60 members of the control group were given no plant. After 90 days, we administered the Acme Depression Scale (1 = Low depression, 100 = High depression) to members of both groups. We found that those who were given the bamboo plant scored an average of 18.05; their depression level was 1.55 points lower than those in the control group, who had an average depression score of 19.60. This improvement in depression, though small, produced a statistically significant p value of .001, using a .05  level, hence, we rejected H0. For those involved in this study, it appears that having a plant reduced depression, thereby supporting H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

17 Exercise 5.3, Data Set B (a) H0: Tending to a plant has no effect on depressive mood.

H1: Tending to a plant reduces depressive mood. (b) The Histograms with normal curve plots show a normal distribution of the depress variable for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for depress in Group 1 (No plant)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Normal distribution for depress in Group 2 (Bamboo)

Test of Homogeneity of Variances depress Levene Statistic df1 df2 Sig. 2.039 1 107 .156

The homogeneity of variance score for mood shows a significance (p) of .156; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for the No plant group is 58, and the n for the Bamboo group is 51 (see Descriptives table below). These ns exceed the 30 per group minimum criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

19 (c) The t test revealed the following: Descriptives depress N No plant Bamboo Total

58 51 109

Mean 15.69 16.37 16.01

Std. Deviation 4.210 3.521 3.900

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .553 14.58 16.80 .493 15.38 17.36 .374 15.27 16.75

Minimum 8 10 8

Maximum 26 25 26

ANOVA depress Between Groups Within Groups Total

Sum of Squares 12.655 1630.335 1642.991

df 1 107

Mean Square 12.655 15.237

F .831

Sig. .364

108

The mean depression level for those in the control group (No plant) is 15.69, whereas those in the treatment group (Bamboo) had a mean depression level of 16.37. Even though the mean depression score for those who received the bamboo plant was .68 points higher than those in the control group, ultimately, this difference is not statistically significant since the significance (p) is .364 (which is greater than the .05  level). As such, we would not reject H0. (d) We hypothesized that empowering nursing home residents with an opportunity to provide nurturance would help reduce depression. To test this hypothesis, 109 residents were randomly assigned to one of two groups: 51 of the residents were given a small bamboo plant to tend to along with a card providing care instructions; the remaining 58 residents received no plant. After 90 days, we administered the Acme Depression Scale (1 = Low depression, 100 = High depression) to members of both groups. We found that on average, those who were given no plant were less depressed (15.69) than those who were given the bamboo plant (16.37), however, in light of the p value of .364, using a .05  level, this .68-point difference in the average depression scores is not considered to be statistically significant. Accordingly, we did not reject H0.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20 Exercise 5.4, Data Set A (a) H0: Eating chocolate does not enhance mood.

H1: Eating chocolate enhances mood. (b) Histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No chocolate

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

21 Group 2—Chocolate with breakfast, lunch and dinner

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. .026 1 48 .872

The homogeneity of variance score shows a significance (p) of .872; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 25 for each group; the t test becomes more robust when the ns are at least 30, but we’ll proceed with the 25 per group.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

22 (c) The t test revealed the following: Descriptives mood

No chocolate Chocolate (1 per meal) Total

N Mean Std. Deviation 25 73.00 5.148 25 76.68 4.488 50 74.84 5.128

Std. Error 1.030 .898 .725

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 70.88 75.12 60 82 74.83 78.53 67 83 73.38 76.30 60 83

ANOVA mood Between Groups Within Groups Total

Sum of Squares 169.280 1119.440 1288.720

df 1 48

Mean Square 169.280 23.322

F 7.258

Sig. .010

49

The mean mood for Group 1 (No chocolate) is 73.00, whereas the mean mood for Group 2 (Chocolate 3 times per day) is 76.68. This 3.68-point difference is statistically significant since the significance (p) is .010 (which is less than the .05  level). Hence, I would reject H0 and not reject H1. (d) This study analyzed the effects that chocolate (three times per day) has on mood. The participants were randomly assigned to one of two groups: a group that ate their regular meals (with no chocolate), and a group that ate chocolate after breakfast, lunch, and dinner. Results revealed a mean mood score of 73.00 on the Acme Mood Scale for those who did not have chocolate and 76.68 for those who did have chocolate. Using a .05  level, the p value of .010 suggests that eating chocolate facilitates a significant increase in mood; hence, we reject H0. These findings suggest support for H1— specifically, that eating chocolate after breakfast, lunch and dinner enhances mood among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 Exercise 5.4, Data Set B (a) H0: Eating chocolate does not enhance mood.

H1: Eating chocolate enhances mood. (b) Histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No chocolate

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24 Group 2—Chocolate with breakfast, lunch and dinner

Test of Homogeneity of Variances Mood Levene Statistic df1 df2 Sig. .790 1 49 .378

The homogeneity of variance score shows a significance (p) of .378; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 28 for the nochocolate group and 23 for the chocolate group; the t test becomes more robust when the ns are at least 30, but we’ll proceed with the data analysis.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

25 (c) The t test revealed the following: Descriptives mood

No chocolate Chocolate (1 per meal) Total

N Mean 28 78.82 23 79.17 51 78.98

Std. Deviation 8.667 7.075 7.913

Std. Error 1.638 1.475 1.108

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 75.46 82.18 63 98 76.11 82.23 67 96 76.75 81.21 63 98

ANOVA mood Between Groups Within Groups Total

Sum of Squares 1.569 3129.411 3130.980

df 1 49

Mean Square 1.569 63.866

F .025

Sig. .876

50

The mean mood for Group 1 (No chocolate) is 78.82, whereas the mean mood for Group 2 (Chocolate 3 times per day) is 79.17. This .35-point difference is not statistically significant since the significance (p) is .876 (which is greater than the .05  level). (d) This study analyzed the effects that chocolate (three times per day) has on mood. The participants were randomly assigned to one of two groups: a group that ate their regular meals (with no chocolate), and a group that ate chocolate after breakfast, lunch, and dinner. Results revealed a mean mood score of 78.82 on the Acme Mood Scale for those who did not have chocolate and 79.17 for those who did have chocolate. Using a .05  level, the p value of .876 suggests that eating chocolate does not facilitate a significant increase in mood; hence, we do not reject H0. These findings do not suggest support for H1—specifically, that eating chocolate after breakfast, lunch and dinner enhances mood among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 Exercise 5.5, Data Set A (a) H0: Providing a flu shot information pamphlet has no impact on flu shot receptivity.

H1: Providing a flu shot information pamphlet has a positive impact on flu shot receptivity. (b) The histograms (below) for both groups show normal distributions of flu shots, hence the pretest criterion of normality is satisfied.

Group 1—No flu shot information pamphlet

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

27 Group 2—Flu shot information pamphlet

Test of Homogeneity of Variances shots Levene Statistic df1 df2 Sig. .010 1 78 .920

The homogeneity of variance score shows a significance (p) of .920; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is greater than 30; the n quotas are satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

28 (c) The t test revealed the following: Descriptives shots

Nothing Flu shot pamphlet Total

N Mean 40 16.52 40 16.55 80 16.54

Std. Deviation 4.151 3.651 3.884

Std. Error .656 .577 .434

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 15.20 17.85 7 25 15.38 17.72 9 23 15.67 17.40 7 25

ANOVA shots Between Groups Within Groups Total

Sum of Squares .013 1191.875 1191.887

df 1 78

Mean Square .013 15.280

F .001

Sig. .977

79

The mean daily flu shot count for Group 1 (No flu shot information pamphlet) is 16.52, whereas the mean flu shot count for Group 2 (Received a flu shot pamphlet) is 16.55.

This .03-point difference is not statistically significant since the significance (p) is .977 (which is greater than the .05  level). (d) This study analyzed the effects that providing a flu shot information pamphlet to patients in a walk-in clinic during flu season may have on patient receptivity to having a flu shot.

The participants were randomly assigned to one of two groups: those who had drawn an odd-numbered service ticket were given a flu shot information pamphlet; those who drew an even-numbered ticket were not given any such literature. Results revealed that those who were given no pamphlet rendered a mean of 16.52 flu shots per day, compared to a mean of 16.55 among those who were issued a pamphlet. Using a .05  level, the p value of .977 suggests that the flu shot pamphlet did not facilitate a significant increase in flu shot receptivity; hence, we do not reject H0. These findings do not suggest support for H1—specifically, that providing a flu shot pamphlet increases receptivity to having a flu shot during flu season among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

29 Exercise 5.5, Data Set B (a) H0: Providing a flu shot information pamphlet has no impact on flu shot receptivity.

H1: Providing a flu shot information pamphlet has a positive impact on flu shot receptivity. (b) The histograms (below) for both groups show normal distributions of flu shots, hence the pretest criterion of normality is satisfied.

Group 1—No flu shot information pamphlet

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

30 Group 2—Flu shot information pamphlet

Test of Homogeneity of Variances Shots Levene Statistic df1 df2 Sig. 2.235 1 118 .138

The homogeneity of variance score shows a significance (p) of .138; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is greater than 30; the n quotas are satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

31 (c) The t test revealed the following: Descriptives shots

Nothing Flu shot pamphlet Total

N Mean Std. Deviation 60 29.70 10.179 60 33.97 8.326 120 31.83 9.504

Std. Error 1.314 1.075 .868

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 27.07 32.33 9 48 31.82 36.12 16 53 30.12 33.55 9 53

ANOVA shots Between Groups Within Groups Total

Sum of Squares 546.133 10202.533 10748.667

df 1 118

Mean Square 546.133 86.462

F 6.316

Sig. .013

119

The mean daily flu shot count for Group 1 (No flu shot information pamphlet) is 29.70, whereas the mean flu shot count for Group 2 (Received a flu shot pamphlet) is 33.97.

This 4.27-point difference is statistically significant since the significance (p) is .013 (which is less than the .05  level). (d) This study analyzed the effects that providing a flu shot information pamphlet to patients in a walk-in clinic during flu season may have on patient receptivity to having a flu shot.

The participants were randomly assigned to one of two groups: those who had drawn an odd-numbered service ticket were given a flu shot information pamphlet; those who drew an even-numbered ticket were not given any such literature. Results revealed that those who were given no pamphlet rendered a mean of 29.70 flu shots per day, compared to a mean of 33.97 among those who were issued a pamphlet. Using a .05  level, the p value of .013 suggests that the flu shot pamphlet facilitated a significant increase in flu shot receptivity; hence, we reject H0. These findings suggest support for H1—specifically, that providing a flu shot pamphlet increases receptivity to having a flu shot during flu season among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

32 Exercise 5.6, Data Set A (a) H0: A laugh track on a comedy video does not enhance viewer enjoyment.

H1: A laugh track on a comedy video enhances viewer enjoyment. (b) Histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No laugh track

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

33 Group 2—Laugh track

Test of Homogeneity of Variances enjoy Levene Statistic df1 df2 Sig. .946 1 63 .335

The homogeneity of variance score shows a significance (p) of .335; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is greater than 30; the n quotas are satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 (c) The t test revealed the following: Descriptives enjoy

No laugh track Laugh track 50 Total

N Mean Std. Deviation 32 3.47 1.646 33 4.21 1.364 65 3.85 1.543

Std. Error .291 .237 .191

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 2.88 4.06 1 8 3.73 4.70 2 7 3.46 4.23 1 8

ANOVA enjoy Between Groups Within Groups Total

Sum of Squares 8.978 143.484 152.462

df 1 63

Mean Square 8.978 2.278

F 3.942

Sig. .051

64

The mean enjoyment level for Group 1 (No laugh track) is 3.47, whereas the mean enjoyment level for Group 2 (With the laugh track) is 4.21. This .35-point difference is not statistically significant since the significance (p) is .051 (which is greater than the .05  level). (d) This study analyzed the effects that a laugh track has on viewer enjoyment of a comedy video. The participants were randomly assigned to one of two groups: a group that watched a comedy video with no laugh track, and a group that watched the same video with the laughter of a 50 member audience. Results revealed an enjoyment level of 3.47 (on a 5-point scale) for those who watched without the laugh track, and 4.21 for those who watch with the laugh track. Using a .05  level, the p value of .051 suggests that the laugh track does not facilitate a significant increase in enjoyment; hence, we do not reject H0. These findings do not suggest support for H1—specifically, that including a laugh track enhances viewer enjoyment among these participants. Considering how close the p level is to .05, it may be worth repeating this experiment.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

35 Exercise 5.6, Data Set B (a) H0: A laugh track on a comedy video does not enhance viewer enjoyment.

H1: A laugh track on a comedy video enhances viewer enjoyment. (b) Histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No laugh track

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

36 Group 2—Laugh track

Test of Homogeneity of Variances enjoy Levene Statistic df1 df2 Sig. .465 1 59 .498

The homogeneity of variance score shows a significance (p) of .498; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

One of the ns, as shown in the Descriptives table is 35, the other is 26. The t test becomes more robust when each of the ns are 30 or greater, but we’ll proceed with these figures.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

37 (c) The t test revealed the following: Descriptives enjoy

No laugh track Laugh track 50 Total

N Mean Std. Deviation 35 2.49 .853 26 2.62 1.098 61 2.54 .959

Std. Error .144 .215 .123

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 2.19 2.78 1 4 2.17 3.06 1 6 2.30 2.79 1 6

ANOVA enjoy Between Groups Within Groups Total

Sum of Squares .251 54.897 55.148

df 1 59

Mean Square .251 .930

F .270

Sig. .606

60

The mean enjoyment level for Group 1 (No laugh track) is 2.49, whereas the mean enjoyment level for Group 2 (With the laugh track) is 2.62. This .13-point difference is not statistically significant since the significance (p) is .606 (which is greater than the .05  level). (d) This study analyzed the effects that a laugh track has on viewer enjoyment of a comedy video. The participants were randomly assigned to one of two groups: a group that watched a comedy video with no laugh track, and a group that watched the same video with the laughter of a 50 member audience. Results revealed an enjoyment level of 2.49 (on a 5-point scale) for those who watched without the laugh track, and 2.62 for those who watch with the laugh track. Using a .05  level, the p value of .606 suggests that the laugh track does not facilitate a significant increase in enjoyment; hence, we do not reject H0. These findings do not suggest support for H1—specifically, that including a laugh track enhances viewer enjoyment among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 Exercise 5.7, Data Set A (a) H0: Light therapy has no effect on depression.

H1: Light therapy is effective in reducing depression. (b) Histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for mood in Group 1 (No light therapy)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

39 Normal distribution for mood in Group 2 (Light therapy: even days)

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. 1.700 1 158 .194

The homogeneity of variance score for mood shows a significance (p) of .194; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group is 80 in each group, which satisfies the 30 per group minimum criterion (see Descriptives table below).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40 (c) The t test revealed the following: Descriptives mood N No light therapy Light therapy: even days Total

80 80 160

Std. Deviation 8.299 7.077 7.811

Mean 59.13 61.88 60.50

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .928 57.28 60.97 .791 60.30 63.45 .617 59.28 61.72

Minimum 42 46 42

ANOVA mood Between Groups Within Groups Total

Sum of Squares 302.500 9397.500 9700.000

df 1 158

Mean Square 302.500 59.478

F 5.086

Sig. .025

159

The mean mood level for those in the Light therapy group was 61.88, which is 2.75 points higher than the mean score of those in the control group (59.13). In light of the significance (p) score of .025 (which is less than the .05  level) this difference is considered to be statistically significant. (d) In order to determine if light therapy is a viable supplement to treating depression, 160 subjects diagnosed with depression were randomly assigned to one of two groups: Half received 1 hour of light therapy every other day for a month; the other half received no light therapy. After 30 days, all participants completed the Acme Mood Scale, a 10 question survey that renders a score from 1 to 100 (1 = Extremely bad mood, 100 = Extremely good mood). Those who received light therapy showed a small but statistically significant improvement in mood; light therapy participants had an average mood score of 61.88; 2.75 points higher than those who did not have the light therapy who scored an average of 59.13 on the mood test. Using a .05  level, the p value of .025 suggests that this difference is statistically significant, hence, we reject H 0. For those tested, it appears that light therapy provided some relief from depressive symptoms, hence supporting H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Maximum 77 79 79

41 Exercise 5.7, Data Set B (a) H0: Light therapy has no effect on depression.

H1: Light therapy is effective in reducing depression. (b) Despite the spike in the histogram for the No light therapy group (the tall bar at around 42), the histograms with normal curve plots show a normal distribution of mood for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for mood in Group 1 (No light therapy)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

42 Normal distribution for mood in Group 2 (Light therapy: even days)

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. .119 1 102 .731

The homogeneity of variance score for mood shows a significance (p) of .731; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for the groups are 48 and 56 (see Descriptives table below); these figures exceed the 30 per group minimum criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

43 (c) The t test revealed the following: Descriptives Mood

No light therapy Light therapy: even days Total

N 48 56 104

Mean 45.44 44.86 45.13

Std. Deviation 3.631 3.806 3.720

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .524 44.38 46.49 .509 43.84 45.88 .365 44.40 45.85

Minimum 38 37 37

ANOVA Mood Between Groups Within Groups Total

Sum of Squares 8.705 1416.670 1425.375

df 1 102

Mean Square 8.705 13.889

F .627

Sig. .430

103

The mean mood level for those in the control group (No light therapy) is 45.44, whereas those in the treatment group (Light therapy: even days) had a mean mood level of 44.86. Unexpectedly, the mood for those who received no light therapy was .58 points higher than those who did, however, since the significance (p) is .430 (which is greater than the .05  level), this difference is not considered to be statistically significant. (d) In order to determine if light therapy is a viable supplement to treating depressed individuals, 104 participants with a diagnosis of depression were randomly assigned to one of two groups: In addition to their regular care, 56 subjects received light therapy for 1 hour every other day; the other 48 participants received none. After 30 days, all participants completed the Acme Mood Scale, a 10 question survey that renders a score from 1 to 100 (1 = Extremely bad mood, 100 = Extremely good mood). Contrary to expectations, on the average, those in the Light therapy group scored 44.86; about a half point (.58) lower than those who had no light therapy, who had an average mood score of 45.44. Using a .05  level, the p value of .430 suggests that this difference is not statistically significant, hence, we do not reject H0. For those tested, it appears that light therapy did not have a significant impact on their mood.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Maximum 53 53 53

44 Exercise 5.8, Data Set A (a) H0: Walking 30 minutes in the morning will have no effect on energy.

H1: Walking 30 minutes in the morning will enhance energy. (b) Although the histogram for Group 1 (below) shows some low outliers, the majority of the data forms a normal curve for energy. The histogram for Group 2 appears normally distributed. I’d say the pretest criterion of normality is sufficiently satisfied.

Group 1—No walking

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

45 Group 2—Walked 30 minutes each morning

Test of Homogeneity of Variances energy Levene Statistic df1 df2 Sig. 1.662 1 254 .198

The homogeneity of variance score shows a significance (p) of .198; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is greater than 30; the n quotas are satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

46 (c) The t test revealed the following: Descriptives energy

No walking Walking: 30 min.

Total

N Mean 132 81.23 124 82.60 256 81.90

Std. Deviation 4.328 4.320 4.370

Std. Error .377 .388 .273

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 80.49 81.98 61 88 81.84 83.37 73 93 81.36 82.44 61 93

ANOVA energy Between Groups Within Groups Total

Sum of Squares 120.003 4749.357 4869.359

df 1 254

Mean Square 120.003 18.698

F 6.418

Sig. .012

255

The mean energy level for Group 1 (No morning walking) is 81.23, whereas the mean energy level for Group 2 (30 minute morning walk each day) is 82.60. This 1.37-point difference is statistically significant since the significance (p) is .012 (which is less than the .05  level). (d) This study analyzed the effects that walking 30 minutes each morning has on energy levels. The participants were randomly assigned to one of two groups: a group that did no morning walking and a group that walked for 30 minutes each morning. Results revealed an end-of-the-day energy level of 81.23 (on a 100-point scale) for those who did not walk, and 82.60 for those who walked. Using a .05  level, the p value of .012 suggests that the walking exercise facilitated a significant increase in energy as measured at the end of the day; hence, we reject H0. These findings suggest support for H1—specifically, that walking for 30 minutes per day enhances energy among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

47 Exercise 5.8, Data Set B (a) H0: Walking 30 minutes in the morning will have no effect on energy.

H1: Walking 30 minutes in the morning will enhance energy. (b) The normal curve on the histograms for each of the two groups show normal distributions, hence the pretest criterion of normality is satisfied.

Group 1—No walking

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

48 Group 2—Walked 30 minutes each morning

Test of Homogeneity of Variances Energy Levene Statistic df1 df2 Sig. 1.538 1 178 .217

The homogeneity of variance score shows a significance (p) of .217; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is greater than 30; the n quotas are satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

49 (c) The t test revealed the following: Descriptives energy

No walking Walking: 30 min.

Total

N Mean Std. Deviation 90 54.22 10.994 90 55.43 9.971 180 54.83 10.483

Std. Error 1.159 1.051 .781

95% Confidence Interval for Mean Lower Bound Upper Bound 51.92 56.52 53.34 57.52 53.29 56.37

Minimum Maximum 32 77 35 77 32 77

ANOVA energy Between Groups Within Groups Total

Sum of Squares 66.006 19605.656 19671.661

df 1 178

Mean Square 66.006 110.144

F .599

Sig. .440

179

The mean energy level for Group 1 (No morning walking) is 54.22, whereas the mean energy level for Group 2 (30 minute morning walk each day) is 55.43. This 1.21-point difference is not statistically significant since the significance (p) is .440 (which is greater than the .05  level). (d) This study analyzed the effects that walking 30 minutes each morning has on energy levels. The participants were randomly assigned to one of two groups: a group that did no morning walking and a group that walked for 30 minutes each day. Results revealed an end-of-the-day energy level of 54.22 (on a 100-point scale) for those who did not walk, and 55.43 for those who walked. Using a .05  level, the p value of .440 suggests that the walking exercise did not facilitate a significant increase in energy as measured at the end of the day; hence, we do not reject H0. These findings do not suggest support for H1—specifically, that walking for 30 minutes per day enhances energy among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

50 Exercise 5.9, Data Set A (a) H0: The Acme reading lamp is no different from regular room lighting when it comes to reading speed.

H1: The Acme reading lamp facilitates faster reading speed than regular room lighting. (b) Histograms with normal curve plots show a normal distribution of seconds for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (Room lighting)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

51 Normal distribution for seconds in Group 2 (Acme reading lamp)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. .217 1 51 .643

The homogeneity of variance score for seconds shows a significance (p) of .643; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The Room lighting group had an n of 25, and the Acme lamp group had an n of 28 (see Descriptives table below); these figures are close to the minimal quota of 30 per group.

The findings of the t test would be more robust if the ns were slightly higher for these groups.

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52 (c) The t test revealed the following: Descriptives seconds N Room lighting Acme lamp Total

25 28 53

Mean 435.86 405.93 420.05

Std. Deviation 38.422 31.184 37.601

Std. Error 7.684 5.893 5.165

95% Confidence Interval for Mean Lower Bound Upper Bound 420.00 451.72 393.84 418.02 409.68 430.41

Minimum 374 357 357

Maximum 509 455 509

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 11835.678 61685.335 73521.012

df 1 51

Mean Square 11835.678 1209.516

F 9.785

Sig. .003

52

The mean reading time for Group 1 (Room lighting) is 436 seconds (rounded), whereas the mean reading time for Group 2 (Acme reading lamp) is 406 seconds (rounded). This 30-second difference is statistically significant since the significance (p) is .003 (which is less than the .05  level). (d) This study analyzed the effects that the Acme reading lamp had on reading speed. The 53 subjects were randomly assigned to one of two groups; one group read a 1,000 word essay using regular room lighting, and the other group read the same essay using the new Acme reading lamp. Results revealed that on the average, those who read using the Acme reading lamp completed the essay 30 seconds earlier than those who used regular room lighting to read the essay (406 seconds vs. 436 seconds, respectively).

Using a .05  level, the p value of .003 suggests that the Acme reading lamp facilitates prompter reading speeds; hence, we reject H0. These findings suggest support for H1; specifically, that the Acme reading lamp enhances reading rates.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

53 Exercise 5.9, Data Set B (a) H0: The Acme reading lamp is no different from regular room lighting when it comes to reading speed.

H1: The Acme reading lamp facilitates faster reading speed than regular room lighting. (b) Histograms with normal curve plots show a normal distribution of seconds for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (Room lighting)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

54 Normal distribution for seconds in Group 2 (Acme reading lamp)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. .785 1 48 .380

The homogeneity of variance score for seconds shows a significance (p) of .380; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group is 25 (see Descriptives table below), which is close to the minimal quota of 30 per group. The findings of the t test would be more robust if the ns were slightly higher.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

55 (c) The t test revealed the following: Descriptives seconds

Room lighting Acme lamp Total

N 25 25 50

Mean 416.44 415.60 416.02

Std. Deviation 33.904 38.045 35.667

Std. Error 6.781 7.609 5.044

95% Confidence Interval for Mean Lower Bound Upper Bound 402.44 430.44 399.90 431.30 405.88 426.16

Minimum 331 344 331

Maximum 489 481 489

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 8.820 62326.160 62334.980

df 1 48

Mean Square 8.820 1298.462

F .007

Sig. .935

49

The mean reading time for Group 1 (Room lighting) is 416.44 seconds, whereas the mean reading time for Group 2 (Acme reading lamp) is 415.60 seconds. This .84second difference is statistically insignificant since the significance (p) is .935 (which is less than the .05  level). (d) This study analyzed the effects that the Acme reading lamp had on reading speed. The 50 subjects were randomly assigned to one of two groups; half read a 1,000 word essay using regular room lighting, and the other half read the same essay using the new Acme reading lamp. Results revealed that, on average, those who read using the Acme reading lamp completed the essay about 1 second (.86 seconds) earlier than those who used regular room lighting read the essay (415.60 seconds vs. 416.44 seconds respectively). Using a .05  level, the p value of .935 suggests that the Acme reading lamp does not facilitate significantly prompter reading speeds; hence, we do not reject H0. The claim that the Acme Company made, that this lamp increases reading speed, is not supported by these findings.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

56 Exercise 5.10, Data Set A (a) H0: Classical music has no effect on problem-solving skills.

H1: Classical music enhances problem-solving skills. (b) Histograms with normal curve plots show a normal distribution of seconds for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (No music)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

57 Normal distribution for seconds in Group 2 (Music at 30 dB)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 2.861 1 78 .095

The homogeneity of variance score for seconds shows a significance (p) of .095; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group is 40 (see Descriptives table below), which satisfies the 30 per group minimum criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

58 (c) The t test revealed the following: Descriptives seconds

No music Music at 30 dB Total

N 40 40 80

Mean 619.55 593.95 606.75

Std. Deviation 35.380 47.862 43.758

Std. Error 5.594 7.568 4.892

95% Confidence Interval for Mean Lower Bound Upper Bound 608.23 630.86 578.64 609.26 597.01 616.49

Minimum 541 497 497

Maximum 690 707 707

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 13105.152 138161.213 151266.366

df 1 78

Mean Square 13105.152 1771.298

F 7.399

Sig. .008

79

The mean puzzle completion time for Group 1 (No music) is 620 seconds (rounded), whereas the subjects in Group 2 (Music at 30 dB) had a mean completion of 540 seconds (rounded). This 80-second difference is statistically significant since the significance (p) is .008 (which is less than the .05  level). (d) This experiment was designed to determine if classical music facilitates problem solving. We recruited 80 subjects; half were randomly assigned to solve a 100-piece jigsaw puzzle in a silent room, the other half solved the same puzzle in a room with soft classical music playing (at 30 dB). Those in the music group solved the puzzle an average of 80 seconds faster than those who worked in silence (540 seconds vs. 620 seconds). Using a .05  level, the p value of .008 suggests that this is a statistically significant difference; hence, we reject H0. These findings support H1—that classical music facilitates problem solving.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

59 Exercise 5.10, Data Set B (a) H0: Classical music has no effect on problem-solving skills.

H1: Classical music enhances problem-solving skills. (b) Histograms with normal curve plots show a normal distribution of seconds for both groups as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (No music)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

60 Normal distribution for seconds in Group 2 (Music at 30 dB)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 1.430 1 80 .235

The homogeneity of variance score for seconds shows a significance (p) of .235; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the two groups, hence, this pretest criterion passes.

The n for each group is over 30: 43 for No music group, and 39 for Music at 30 dB group (see Descriptives table below), which satisfies the 30 per group minimum criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

61 (c) The t test revealed the following: Descriptives seconds

No music Music at 30 dB Total

N 43 39 82

Mean 608.93 606.33 607.70

Std. Deviation 11.194 12.461 11.812

Std. Error 1.707 1.995 1.304

95% Confidence Interval for Mean Lower Bound Upper Bound 605.49 612.38 602.29 610.37 605.10 610.29

Minimum 588 585 585

Maximum 635 637 637

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 137.921 11163.457 11301.378

df 1 80

Mean Square 137.921 139.543

F .988

Sig. .323

81

The mean puzzle completion time for Group 1 (No music) is 609 seconds (rounded), whereas the subjects in Group 2 (Music at 30 dB) had a mean puzzle completion time of 606 seconds (rounded). This difference is statistically insignificant since the significance (p) is .323 (which is greater than the .05  level). (d) This experiment was designed to determine if classical music aides in problem solving.

We recruited 82 participants and randomly assigned them to one of two groups: Those who assembled a 100-piece jigsaw puzzle in a silent room, and those who assembled the same puzzle in a room with soft classical music playing (at 30 dB). On average, participants in the music group completed the puzzle 2.6 seconds faster than those who worked in silence (606.33 seconds vs. 608.93 seconds), however, using a .05  level, the p value of .323 suggests that this difference is not statistically significant; hence, we do not reject H0. For those tested, it appears that classical music is not a substantial factor when it comes to problem solving.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 6 ANOVA and Kruskal-Wallis Test Solutions to All Exercises

Exercise

Page

Exercise

Page

6.1A....................2

6.6A ................. 42

6.1B....................6

6.6B ................. 46

6.2A..................10

6.7A ................. 50

6.2B..................14

6.7B ................. 54

6.3A..................18

6.8A ................. 58

6.3B..................22

6.8B ................. 62

6.4A..................26

6.9A ................. 66

6.4B..................30

6.9B ................. 71

6.5A..................34

6.10A ............... 76

6.5B..................38

6.10B ............... 81

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 6.1, Data Set A (a) H0: Practicing meditation has no effect on resting pulse rate.

H1: Practicing meditation reduces resting pulse rate. (b) Histograms with normal curve plots show a normal distribution of pulse for the groups as shown in the three figures below, hence, the pretest criteria of normality is satisfied.

Normal distribution for pulse in Group 1 (No meditation)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 Normal distribution for pulse in Group 2 (meditated 30 minutes a day, 3 days per week)

Normal distribution for pulse in Group 3 (meditated 30 minutes a day, 6 days per week)

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4

Test of Homogeneity of Variances pulse Levene Statistic df1 df2 Sig. .083 2 102 .920

The homogeneity of variance score shows a significance (p) of .920; since this is greater than the  level of .05, this suggests that there is no statistically significant difference among the variances of the three groups, hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below is 35 for each group; since the ns are greater than 30, this criterion passes also. (c) The ANOVA revealed the following: Descriptives pulse

No meditation Meditates 3 days Meditates 6 days Total

N 35 35 35 105

Mean 97.40 92.20 91.40 93.67

Std. Deviation 6.826 7.287 6.779 7.400

Std. Error 1.154 1.232 1.146 .722

95% Confidence Interval for Mean Lower Bound Upper Bound 95.06 99.74 89.70 94.70 89.07 93.73 92.23 95.10

Minimum 84 78 77 77

Maximum 109 105 106 109

ANOVA pulse Between Groups Within Groups Total

Sum of Squares 742.933 4952.400 5695.333

df 2 102

Mean Square 371.467 48.553

F 7.651

Sig. .001

104 Multiple Comparisons

pulse Tukey HSD (I) group

(J) group

Mean Difference (I-J) No meditation Meditates 3 days 5.200* Meditates 6 days 6.000* Meditates 3 days No meditation -5.200* Meditates 6 days .800 Meditates 6 days No meditation -6.000* Meditates 3 days -.800 *. The mean difference is significant at the 0.05 level.

Std. Error 1.666 1.666 1.666 1.666 1.666 1.666

Sig. .007 .001 .007 .881 .001 .881

95% Confidence Interval Lower Bound Upper Bound 1.24 9.16 2.04 9.96 -9.16 -1.24 -3.16 4.76 -9.96 -2.04 -4.76 3.16

The Tukey post hoc test was used since the ns for each group were the same (35 each).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 NOTE: Since the ANOVA test renders results involving multiple comparisons, it may be helpful to organize the findings as shown in the table below. SPSS does not generate this table directly, but you can construct it manually. You can copy the group names and means from the Descriptives table, and the p values from the Sig. column in the Multiple Comparisons table.

Groups (μ = resting pulse rate after 2 weeks) No meditation (μ = 97.40) : Meditation 3x / wk. (μ = 92.20) No meditation (μ = 97.40) : Meditation 6x / wk. (μ = 91.40) Meditation 3x / wk. (μ = 92.20) : Meditation 6x / wk. (μ = 91.40) *Statistically significant difference ( = .05).

p *.007 *.001 .881

Practicing meditation for 2 weeks was effective in statistically significantly reducing resting pulse rate, however there was no statistically significant difference in resting pulse rate when comparing those who meditated for 30 minutes three times a week to those who meditated for 30 minutes six times a week. Based on these findings, we reject H0, and we do not reject H1. (d) This study analyzed the effects that meditation had on resting pulse rates. The subjects were randomly assigned to one of three groups; members of the control group did not meditate, those in the second group meditated for 30 minutes on Monday, Wednesday and Friday, and members of the third group meditated for 30 minutes Monday through Saturday. After 2 weeks, those who meditated (3x / wk., μ = 92.20; 6x / wk. μ = 91.40) showed a statistically significant reduction (p = .007 and p = .001, respectively) in resting pulse rate compared to those who did not meditate (μ = 97.40) using a .05  level. We found no statistically significant difference in the resting pulse rates between those who meditated 3 days per week, compared to those who meditated 6 days per week (p = .881).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 6.1, Data Set B (a) H0: Practicing meditation has no effect on resting pulse rate.

H1: Practicing meditation reduces resting pulse rate. (b) Histograms with normal curve plots show a normal distribution of pulse for the three groups as shown in the three figures below, hence, the pretest criteria of normality is satisfied.

Normal distribution for pulse in Group 1 (No meditation)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 Normal distribution for pulse in Group 2 (meditated 30 minutes a day, 3 days per week)

Normal distribution for pulse in Group 3 (meditated 30 minutes a day, 6 days per week)

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8

Test of Homogeneity of Variances pluse Levene Statistic df1 df2 Sig. .241 2 96 .786

The homogeneity of variance score shows a significance (p) of .786; since this is greater than the  level of .05, this suggests that there is no statistically significant difference among the variances of the three groups, hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below are 33, 35, and 31; since the ns are greater than 30, this criterion passes also. (c) The ANOVA revealed the following: Descriptives pluse

No meditation Meditates 3 days Meditates 6 days Total

N 33 35 31 99

Mean 95.15 93.54 92.68 93.81

Std. Deviation 5.901 6.797 6.700 6.494

Std. Error 1.027 1.149 1.203 .653

95% Confidence Interval for Mean Lower Bound Upper Bound 93.06 97.24 91.21 95.88 90.22 95.14 92.51 95.10

Minimum 80 79 79 79

Maximum 105 107 104 107

ANOVA pluse Between Groups Within Groups Total

Sum of Squares 101.651 4031.702 4133.354

df 2 96

Mean Square 50.826 41.997

F 1.210

Sig. .303

98 Multiple Comparisons

pluse Sidak (I) group No meditation Meditates 3 days Meditates 6 days

(J) group Meditates 3 days Meditates 6 days No meditation Meditates 6 days No meditation Meditates 3 days

Mean Difference (I-J) 1.609 2.474 -1.609 .865 -2.474 -.865

Std. Error 1.572 1.621 1.572 1.598 1.621 1.598

Sig. .670 .342 .670 .931 .342 .931

95% Confidence Interval Lower Bound Upper Bound -2.21 5.43 -1.46 6.41 -5.43 2.21 -3.02 4.75 -6.41 1.46 -4.75 3.02

The Sidak post hoc test was used since the ns for each group were not the same (ns = 33, 35, 31).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9

Groups (μ = resting pulse rate after 2 weeks) No meditation (μ = 95.15) : Meditation 3x / wk. (μ = 93.54) No meditation (μ = 95.15) : Meditation 6x / wk. (μ = 92.68) Meditation 3x / wk. (μ = 93.54) : Meditation 6x / wk. (μ = 92.68)

p .670 .342 .931

Per the table above, practicing meditation for 2 weeks produced no statistically significant reduction in resting pulse rate using a .05  level. Based on these findings, we would not reject H0, and we would reject H1. (d) This study analyzed the effects that meditation had on resting pulse rates. The subjects were randomly assigned to one of three groups; members of the control group did not meditate, those in the second group meditated for 30 minutes on Monday, Wednesday and Friday, and members of the third group meditated for 30 minutes Monday through Saturday. After 2 weeks, resting pulse rates were recorded for each participant. Those who did not meditate had a mean resting pulse rate of 95.15, which was slightly higher than those who meditated (3 days per week: μ = 93.54, 6 days per week: μ = 92.68); however, we detected no statistically significant differences among any of the three groups using a .05  level, suggesting that the meditation schedules tested were not effective in reducing resting pulse rates.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 6.2, Data Set A (a) H0: Mentorship has no effect on freshman’s term grades.

H1: Mentorship enhances freshman’s term grades. (b) Histograms with normal curve plots show a normal distribution of term scores for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No mentor

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11 Group 2—With in-person mentor

Group 3—With e-mentor

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12

Test of Homogeneity of Variances grade Levene Statistic df1 df2 Sig. 2.234 2 72 .114

The homogeneity of variance score shows a significance (p) of .114; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 25 for each group; although the ANOVA becomes more robust with an n of at least 30 per group, we’ll proceed with the results given. (c) The ANOVA test revealed the following: Descriptives grade

No mentor In-person mentor E-mentor Total

N 25 25 25 75

Mean 68.84 69.12 75.28 71.08

Std. Deviation 7.565 7.322 10.616 9.025

Std. Error 1.513 1.464 2.123 1.042

95% Confidence Interval for Mean Lower Upper Bound Bound 65.72 71.96 66.10 72.14 70.90 79.66 69.00 73.16

Minimum Maximum 53 79 57 85 50 90 50 90

ANOVA grade Between Groups Within Groups Total

Sum of Squares 662.480 5365.040 6027.520

df 2 72

Mean Square 331.240 74.514

F 4.445

Sig. .015

74 Multiple Comparisons

grade Tukey HSD (I) group

(J) group

Mean Difference (I-J) No mentor In-person mentor -.280 E-mentor -6.440* In-person mentor No mentor .280 E-mentor -6.160* E-mentor No mentor 6.440* In-person mentor 6.160* *. The mean difference is significant at the 0.05 level.

Std. Error 2.442 2.442 2.442 2.442 2.442 2.442

Sig. .993 .027 .993 .036 .027 .036

95% Confidence Interval Lower Bound Upper Bound -6.12 5.56 -12.28 -.60 -5.56 6.12 -12.00 -.32 .60 12.28 .32 12.00

The Tukey post hoc test was used since the ns for each group were the same (25 each).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13

Groups (μ = Freshman score) μ(No mentor) = 68.84 : μ(In-person mentor) = 69.12 μ(No mentor) = 68.84 : μ(E-mentor) = 75.28 μ(In-person mentor) = 69.12 : μ(E-mentor) = 75.28 *Statistically significant difference ( = .05).

p .993 .027* .036*

There was no statistically significant difference in GPA between those who had no mentor, and those who had in-person mentoring. Students in the E-mentoring had GPAs statistically significantly higher than the other two groups. These findings lead us to reject H0 and not reject H1. (d) This study assessed the impact that providing a sophomore to provide mentorship to a freshman has on freshman grades. Freshmen were randomly assigned to one of three groups: Group 1 received no mentor, Group 2 received in-person mentorship, and Group 3 received e-mentorship (used digital communication). There was no statistically significant difference between the GPAs for students who had no mentoring (μ = 68.84) compared to those assigned to an in-person mentor (μ = 69.12) (p = .993), however, students assigned to the e-mentoring group (μ = 75.28) statistically significantly outperformed the No-mentor group (p = .027) and the In-person mentor group (p = .036) using an  level of .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 6.2, Data Set B (a) H0: Mentorship has no effect on freshman’s term grades.

H1: Mentorship enhances freshman’s term grades. (b) Histograms with normal curve plots show a normal distribution of term scores for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No mentor

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 Group 2—With in-person mentor

Group 3—With e-mentor

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16

Test of Homogeneity of Variances grade Levene Statistic df1 df2 Sig. .090 2 72 .914

The homogeneity of variance score shows a significance (p) of .914; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 25 for each group; although the ANOVA becomes more robust with an n of at least 30 per group, we’ll proceed with the results given. (c) The ANOVA test revealed the following: Descriptives grade 95% Confidence Interval for Mean Std.

Std.

Lower

Upper

Deviation

Error

Bound

Bound

N

Mean

Minimum

Maximum

No mentor

25

63.56

7.042

1.408

60.65

66.47

48

77

In-person mentor

25

69.40

7.539

1.508

66.29

72.51

54

83

E-mentor

25

69.88

7.468

1.494

66.80

72.96

55

83

Total

75

67.61

7.808

.902

65.82

69.41

48

83

ANOVA grade Between Groups Within Groups Total

Sum of Squares 618.987 3892.800 4511.787

df 2 72

Mean Square 309.493 54.067

F 5.724

Sig. .005

74 Multiple Comparisons

grade Tukey HSD (I) group

(J) group

Mean Difference (I-J) No mentor In-person mentor -5.840* E-mentor -6.320* In-person mentor No mentor 5.840* E-mentor -.480 E-mentor No mentor 6.320* In-person mentor .480 *. The mean difference is significant at the 0.05 level.

Std. Error 2.080 2.080 2.080 2.080 2.080 2.080

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Sig. .017 .009 .017 .971 .009 .971

95% Confidence Interval Lower Bound Upper Bound -10.82 -.86 -11.30 -1.34 .86 10.82 -5.46 4.50 1.34 11.30 -4.50 5.46

17

The Tukey post hoc test was used since the ns for each group were the same (25 each).

Groups (μ = Freshman score) μ(No mentor) = 63.56 : μ(In-person mentor) = 69.40 μ(No mentor) = 63.56 : μ(E-mentor) = 69.88 μ(In-person mentor) = 69.40 : μ(E-mentor) = 69.88 *Statistically significant difference ( = .05).

p .017* .009* .971

The mean GPAs for each of the two mentoring groups statistically significantly outperformed those in the control group, who received no mentoring. Also, even though the e-mentoring group had a slightly higher term grade than the in-person mentoring group, this was not a statistically significant difference. These findings lead us to reject H0 and not reject H1. (d) This study assessed the impact that providing a sophomore to provide mentorship to a freshman has on freshman grades. Freshmen were randomly assigned to one of three groups: Group 1 received no mentor, Group 2 received in-person mentorship, and Group 3 received e-mentorship (used digital communication). The GPA for those who had in-person mentoring (μ = 69.40) statistically significantly outperformed those who had no mentoring (μ = 63.56; p = .017,  = .05); similarly, those who had e-mentoring (μ = 69.88) statistically significantly outperformed the no-mentoring control group (p = .009). Although those in the e-mentor group earned a slightly higher GPA than those in the in-person mentoring group, the difference is not statistically significant (p = .971), hence, either form of mentoring seems to help enhance freshman GPAs.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Exercise 6.3, Data Set A (a) H0: Tending to a plant has no effect on depressive mood.

H1: Tending to a plant reduces depressive mood. (b) Despite the few low score outliers shown in the histogram for Group 2, the Histograms with normal curve plots exhibit a normal distribution of the depress variable for all groups as shown in the three figures below, hence, the pretest criteria of normality is satisfied.

Normal distribution for depress in Group 1 (No plant)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

19 Normal distribution for depress in Group 2 (Bamboo)

Normal distribution for depress in Group 3 (Cactus)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20

Test of Homogeneity of Variances depress Levene Statistic df1 df2 Sig. 2.037 2 177 .133

The homogeneity of variance score for mood shows a significance (p) of .133; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the three groups, hence, this pretest criterion passes.

The n for each group is 60 (see Descriptives table below), which satisfies the 30 per group minimum criterion. (c) The ANOVA test revealed the following: Descriptives depress N No plant Bamboo Cactus Total

Mean 19.60 18.05 19.63 19.09

60 60 60 180

Std. Deviation 2.701 2.500 2.490 2.657

Std. Error .349 .323 .322 .198

95% Confidence Interval for Mean Lower Bound Upper Bound 18.90 20.30 17.40 18.70 18.99 20.28 18.70 19.49

Minimum 15 8 14 8

ANOVA depress Between Groups Within Groups

Sum of Squares 98.211 1165.183

Total

1263.394

df 2 177

Mean Square 49.106 6.583

F 7.459

Sig. .001

179

Multiple Comparisons depress Tukey HSD (I) group (J) group

Mean Difference (I-J) Std. Error No plant Bamboo 1.550* .468 Cactus -.033 .468 Bamboo No plant -1.550* .468 Cactus -1.583* .468 Cactus No plant .033 .468 * Bamboo 1.583 .468 *. The mean difference is significant at the 0.05 level.

95% Confidence Interval Sig. .003 .997 .003 .003 .997 .003

Lower Bound .44 -1.14 -2.66 -2.69 -1.07 .48

Upper Bound 2.66 1.07 -.44 -.48 1.14 2.69

Groups (μ = depression) p No plant (μ = 19.60) : Bamboo (μ = 18.05) *.003 No plant (μ = 19.60) : Cactus (μ = 19.63) .997 Bamboo (μ = 18.05) : Cactus (μ = 19.63) *.003 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Maximum 25 24 25 25

21

There is no statistically significant difference in the average scores between those who received no plant (μ = 19.60) and those who received a cactus (μ = 19.63) (p = .997,  = .05). The mean depression score for those who received a bamboo plant (μ = 18.05) was statistically significant lower than those who received no plant (p = .003) and those who received a cactus (p = .003).

Since those in the Bamboo group had a statistically significantly lower depression score than those who received no plant, we would reject H0. By that same reasoning, we would not reject H1. (d) We hypothesized that empowering nursing home residents with an opportunity to provide nurturance would help reduce depression. To test this hypothesis, 180 residents were randomly assigned to one of three groups: Those in Group 1 constituted the control group, and were given no plant. Those in Group 2 were given a small bamboo plant to tend to along with a card providing care instructions. Participants in Group 3 were given a cactus plant along with a card providing care instructions. After 90 days, we administered the Acme Depression Scale (1 = Low depression, 100 = High depression) to members of all three groups. We found that those who were given the bamboo plant scored an average of 18.05; using a .05  level, we found that their depression level was statistically significantly lower than those who were given no plant (μ = 19.60, p = .003), and those who were given a cactus (μ = 19.63, p = .003). We found that those who received a cactus had a slightly higher average depression level (μ = 19.63) than those who were given no plant (μ = 19.60), however, there was no statistically significant difference in depression scores when comparing those who were given no plant to those who were given a cactus (p = .997). These findings suggest that tending to a small plant has the potential to reduce depression in nursing home residents, but the cactus, which essentially requires no tending, did not provide the desired effect, whereas the bamboo, which required monitoring and watering, did.

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22 Exercise 6.3, Data Set B (a) H0: Tending to a plant has no effect on depressive mood.

H1: Tending to a plant reduces depressive mood. (b) The Histograms with normal curve plot exhibits a normal distribution of the depress variable for all groups as shown in the three figures below, hence, the pretest criteria of normality is satisfied.

Normal distribution for depress in Group 1 (No plant)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 Normal distribution for depress in Group 2 (Bamboo)

Normal distribution for depress in Group 3 (Cactus)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24

Test of Homogeneity of Variances depress Levene Statistic df1 df2 Sig. 1.108 2 171 .333

The homogeneity of variance score for mood shows a significance (p) of .333; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of among the three groups, hence, this pretest criterion passes.

The ns for the groups are 58, 51, and 65 (see Descriptives table below), which satisfies the 30 per group minimum criterion. (c) The ANOVA test revealed the following: Descriptives depress N No plant Bamboo Cactus Total

58 51 65 174

Mean 15.69 16.37 17.03 16.39

Std. Deviation 4.210 3.521 4.224 4.043

Std. Error .553 .493 .524 .306

95% Confidence Interval for Mean Lower Bound Upper Bound 14.58 16.80 15.38 17.36 15.98 18.08 15.79 17.00

Minimum

ANOVA depress Between Groups Within Groups Total

Sum of Squares 55.151 2772.274

df 2 171

2827.425

Mean Square 27.576 16.212

F 1.701

Sig. .186

173 Multiple Comparisons

depress Sidak (I) group No plant Bamboo Cactus

(J) group Bamboo Cactus No plant Cactus No plant Bamboo

Mean Difference (I-J) -.683 -1.341 .683 -.658 1.341 .658

Std. Error .773 .727 .773 .753 .727 .753

Sig. .760 .188 .760 .766 .188 .766

95% Confidence Interval Lower Bound Upper Bound -2.55 1.18 -3.09 .41 -1.18 2.55 -2.47 1.16 -.41 3.09 -1.16 2.47

Groups (μ = depression) No plant (μ = 15.69) : Bamboo (μ = 16.37) No plant (μ = 15.69) : Cactus (μ = 17.03) Bamboo (μ = 16.37) : Cactus (μ = 17.03)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .760 .188 .766

8 10 8 8

Maximum 26 25 26 26

25 Inspection of the Sig. (p) figure in the ANOVA table (p = .186, which is greater than the .05  level) tells us that there is no statistically significant difference(s) detected in the depression scores among any of the groups.

Upon reviewing the comparisons presented in the Multiple Comparisons table, we see that this finding is confirmed; we see that the p level for each pair of depression scores is greater than the specified .05  level, hence there are no statistically significant differences between any of the groups as shown in the table above. (d) We hypothesized that empowering nursing home residents with an opportunity to provide nurturance would help reduce depression. To test this hypothesis, 174 residents were randomly assigned to one of three groups: Those in Group 1 constituted the control group and were given no plant. Those in Group 2 were given a small bamboo plant to tend to along with a card providing care instructions. Participants in Group 3 were given a cactus plant along with a card providing care instructions. After 90 days, we administered the Acme Depression Scale (1 = Low depression, 100 = High depression) to members of both groups. We found that those who were given the cactus scored an average of 17.03, those who were given a bamboo plant had an average score of 16.37, and those who were given no plant scored an average of 15.69.; using a .05  level, we found no statistically significant differences among any of these groups (p ranged from .188 to .766). We found that these plants were not helpful in reducing depression among these nursing home residents.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 Exercise 6.4, Data Set A (a) H0: Eating chocolate does not enhance mood.

H1: Eating chocolate enhances mood. (b) Histograms with normal curve plots show a normal distribution of mood for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No chocolate

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27 Group 2—One chocolate with breakfast, lunch and dinner

Group 3—Two chocolates with breakfast, lunch and dinner

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28

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. .922 2 72 .403

The homogeneity of variance score shows a significance (p) of .403; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is 25 for each group; the ANOVA test becomes more robust when the ns are at least 30, but we’ll proceed with the figures as is. (c) The ANOVA test revealed the following: Descriptives mood

No chocolate Chocolate (1 per meal) Chocolate (2 per meal) Total

N Mean 25 73.00 25 76.68 25 74.72 75 74.80

Std. Deviation 5.148 4.488 3.348 4.588

Std. Error 1.030 .898 .670 .530

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 70.88 75.12 60 82 74.83 78.53 67 83 73.34 76.10 69 82 73.74 75.86 60 83

ANOVA mood Between Groups Within Groups

Sum of Squares 169.520 1388.480

Total

df

1558.000

2 72

Mean Square 84.760 19.284

F 4.395

Sig. .016

74 Multiple Comparisons

mood Tukey HSD (I) group No chocolate

(J) group

Chocolate (1 per meal) Chocolate (2 per meal) Chocolate (1 per meal) No chocolate Chocolate (2 per meal) Chocolate (2 per meal) No chocolate Chocolate (1 per meal) *. The mean difference is significant at the 0.05 level.

Mean Difference (I-J) -3.680* -1.720 3.680* 1.960 1.720 -1.960

Std. Error 1.242 1.242 1.242 1.242 1.242 1.242

Sig. .011 .354 .011 .262 .354 .262

95% Confidence Interval Lower Bound Upper Bound -6.65 -.71 -4.69 1.25 .71 6.65 -1.01 4.93 -1.25 4.69 -4.93 1.01

Groups (μ = Mood) μ(No chocolate) = 73.00 : μ(Chocolate 1 per meal) = 76.68 μ(No chocolate) = 73.00 : μ(Chocolate 2 per meal) = 74.72 μ(Chocolate 1 per meal) = 76.68 : μ(Chocolate 2 per meal) = 74.72 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .011* .354 .262

29 The mean mood for Group 1 (No chocolate) is 73.00, whereas the mean mood for Group 2 (1 per meal) is 76.68. This 3.68-point difference is statistically significant since the significance (p) is .011 (which is less than the .05  level), so I would reject H0 and not reject H1. No statistically significant difference (p = .354) in mood was detected between Group 1 (No chocolate;  = 73.00) and Group 3 (2 chocolates with each meal;  = 74.72). (d) This study analyzed the effects that chocolate with each meal has on mood. The participants were randomly assigned to one of three groups: a group that ate their regular meals (with no chocolate), a group that ate one piece of chocolate after breakfast, lunch, and dinner, and a group that ate two pieces of chocolate with their three daily meals. Results revealed a mean mood score of 73.00 on the Acme Mood Scale for those who did not have chocolate and 76.68 for those who had one piece of chocolate with their meals. Using a .05  level, the p value of .011 suggests that eating one piece of chocolate with meals facilitates a significant increase in mood; hence, we reject H0 and do not reject H1. The group that ate two pieces of chocolate with each meal had a mean score of 74.72, however, compared to the control group, this more modest difference is not statistically significant (p = .354). It seems that mood is enhanced by a moderate level of chocolate in the diet administered at breakfast, lunch and dinner among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

30 Exercise 6.4, Data Set B (a) H0: Eating chocolate does not enhance mood.

H1: Eating chocolate enhances mood. (b) Histograms with normal curve plots show a normal distribution of mood for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No chocolate

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31 Group 2—One chocolate with breakfast, lunch and dinner

Group 3—Two chocolates with breakfast, lunch and dinner

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32

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. 2.917 2 75 .060

The homogeneity of variance score shows a significance (p) of .060; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is under 30 for each group; the ANOVA test becomes more robust when the ns are at least 30, but we’ll proceed with the figures as is. (c)

The ANOVA test revealed the following: Descriptives

mood

No chocolate Chocolate (1 per meal) Chocolate (2 per meal) Total

N Mean 28 78.82 23 79.17 27 82.22 78 80.10

Std. Deviation 8.667 7.075 5.308 7.252

Std. Error 1.638 1.475 1.022 .821

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 75.46 82.18 63 98 76.11 82.23 67 96 80.12 84.32 67 93 78.47 81.74 63 98

ANOVA mood Between Groups Within Groups

Sum of Squares 187.101 3862.078

Total

4049.179

df 2 75

Mean Square 93.551 51.494

F 1.817

Sig. .170

77 Multiple Comparisons

mood Sidak (I) group

(J) group

No chocolate Chocolate (1 per meal) Chocolate (2 per meal)

Chocolate (1 per meal) Chocolate (2 per meal) No chocolate Chocolate (2 per meal) No chocolate Chocolate (1 per meal)

Mean Difference (I-J) -.352 -3.401 .352 -3.048 3.401 3.048

Std. Error 2.019 1.936 2.019 2.036 1.936 2.036

Sig. .997 .229 .997 .361 .229 .361

95% Confidence Interval Lower Bound Upper Bound -5.28 4.58 -8.13 1.33 -4.58 5.28 -8.02 1.92 -1.33 8.13 -1.92 8.02

Groups (μ = mood) μ(No chocolate) = 78.82 : μ(Chocolate 1 per meal) = 79.17 μ(No chocolate) = 78.82 : μ(Chocolate 2 per meal) = 82.22 μ(Chocolate 1 per meal) = 79.17 : μ(Chocolate 2 per meal) = 82.22 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .997 .229 .361

33 The Sidak post hoc test was run since the groups had different ns. The Sig(nificance), or p level, rendered on the ANOVA table is .170, which is greater than the .05  level, indicating that there are no statistically significant differences among these (three) groups. This is confirmed by inspecting the Multiple Comparisons table; the Sig. (p levels) range from .229 to .997—all of which are greater than .05. While the means varied among the groups, they are not different enough from each other to say that any group outperformed any of the other groups. Hence, I would not reject H0 and I would reject H1. (d) This study analyzed the effects that chocolate with each meal has on mood. The participants were randomly assigned to one of three groups: a group that ate their regular meals (with no chocolate), a group that ate one piece of chocolate after breakfast, lunch, and dinner, and a group that ate two pieces of chocolate with their three daily meals. Results revealed a mean mood score of 78.82 on the Acme Mood Scale for those who did not have chocolate, 79.17 for those who ate one piece of chocolate with their three meals per day, and 82.22 among those who ate two pieces with each of their three meals. The mood scores of these three groups were processed using ANOVA, which revealed a p value of .170; since this is greater than the .05  level, this indicates that despite the moderate variability in mood detected among these groups, these differences are not considered to be statistically significant using an  level of .05. It seems that chocolate, at these levels, does not serve to enhance mood among these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 Exercise 6.5, Data Set A (a) H0: Providing flu shot informational media has no impact on flu shot receptivity.

H1: Providing flu shot informational pamphlet has a positive impact on flu shot receptivity. (b) The histograms (below) for all groups show normal distributions of flu shots, hence the pretest criterion of normality is satisfied.

Group 1—No flu shot informational media

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35 Group 2—Flu shot informational pamphlet

Group 3—Flu shot informational video

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36

Test of Homogeneity of Variances shots Levene Statistic df1 df2 Sig. .855 2 117 .428

The homogeneity of variance score shows a significance (p) of .428; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is over 30 for each group, which satisfies that criterion. (c) The ANOVA test revealed the following: Descriptives shots

Nothing Flu shot pamphlet Flu shot video Total

N Mean Std. Deviation 40 16.52 4.151 40 16.55 3.651 40 19.60 4.634 120 17.56 4.377

Std. Error .656 .577 .733 .400

95% Confidence Interval for Mean Lower Bound Upper Bound 15.20 17.85 15.38 17.72 18.12 21.08 16.77 18.35

Minimum Maximum 7 25 9 23 10 29 7 29

ANOVA shots Between Groups Within Groups

Sum of Squares 250.117 2029.475

Total

2279.592

df 2 117

Mean Square 125.058 17.346

F 7.210

Sig. .001

119 Multiple Comparisons

shots Tukey HSD (I) group

(J) group

Mean Difference (I-J) Nothing Flu shot pamphlet -.025 Flu shot video -3.075* Flu shot pamphlet Nothing .025 Flu shot video -3.050* Flu shot video Nothing 3.075* Flu shot pamphlet 3.050* *. The mean difference is significant at the 0.05 level.

Std. Error .931 .931 .931 .931 .931 .931

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Sig. 1.000 .004 1.000 .004 .004 .004

95% Confidence Interval Lower Bound Upper Bound -2.24 2.19 -5.29 -.86 -2.19 2.24 -5.26 -.84 .86 5.29 .84 5.26

37

Groups (μ = Flu Shots) μ(Nothing) = 16.52 : μ(Flu shot pamphlet) = 16.55 μ(Nothing) = 16.52 : μ(Flu shot video) = 19.60 μ(Flu shot pamphlet) = 16.55 : μ(Flu shot video) = 19.60 *Statistically significant difference ( = .05).

p 1.000 .004* .004*

The Tukey post hoc test was run since the groups all had the same ns (n = 40). The Sig(nificance), or p level, rendered on the ANOVA table is .001, which is less than the .05  level, indicating that there are statistically significant differences among these (three) groups. This is confirmed by inspecting the Multiple Comparisons table; upon reviewing the mean number of flu shots given per day for each group, the flu shot video (μ = 19.60) statistically significantly outperformed no media (μ = 16.52) and the flu shot informational pamphlet (μ = 16.55) with p = .004 ( = .05) for both comparisons. Hence, I would reject H0 and not reject H1. (d) In an effort to discover if the media was effective in promoting flu shot receptivity among patients, individuals at a walk-in health clinic were randomly assigned to one of three groups: Group1 constituted the control group, and received no media or messaging promoting the utility of the flu shot (which is available to all who request it at this clinic), members of Group 2 were issued a flu shot informational pamphlet, and members of Group 3 were shown a brief flu shot informational video, containing the same educational points as the pamphlet. Group 1 (No information) and Group 2 (Pamphlet) rendered an average of 16.52 and 16.55 flu shots per day respectively, whereas Group 3 (Video) statistically significantly outperformed both other groups with an average of 19.60 flu shots per day (p = .004 for both comparisons;  = .05). These findings suggest that giving a pamphlet is essentially equivalent to giving nothing (Group 1 : Group 2 rendered p = 1.00), whereas this cohort seemed most receptive to a brief informational video promoting the flu shot. Our future studies will focus on assessing the effectiveness of such videos by varying parameters such as duration, content, graphics, and complexity of message.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 Exercise 6.5, Data Set B (a) H0: Providing flu shot informational media has no impact on flu shot receptivity.

H1: Providing flu shot informational pamphlet has a positive impact on flu shot receptivity. (b) The histograms (below) for the groups show normal distributions of flu shots, hence the pretest criterion of normality is satisfied.

Group 1—No flu shot informational media

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39 Group 2—Flu shot informational pamphlet

Group 3—Flu shot informational video

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40

Test of Homogeneity of Variances shots Levene Statistic df1 df2 Sig. 1.177 2 177 .310

The homogeneity of variance score shows a significance (p) of .310; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is over 30 for each group, which satisfies that criterion. (c) The ANOVA test revealed the following: Descriptives shots

Nothing Flu shot pamphlet Flu shot video Total

N Mean Std. Deviation 60 29.70 10.179 60 33.97 8.326 60 35.23 8.996 180 32.97 9.450

Std. Error 1.314 1.075 1.161 .704

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 27.07 32.33 9 48 31.82 36.12 16 53 32.91 37.56 14 55 31.58 34.36 9 55

ANOVA shots Between Groups Within Groups Total

Sum of Squares 1008.533 14977.267 15985.800

df 2 177

Mean Square 504.267 84.617

F 5.959

Sig. .003

179 Multiple Comparisons

shots Tukey HSD (I) group

(J) group

Mean Difference (I-J) Nothing Flu shot pamphlet -4.267* Flu shot video -5.533* Flu shot pamphlet Nothing 4.267* Flu shot video -1.267 Flu shot video Nothing 5.533* Flu shot pamphlet 1.267 *. The mean difference is significant at the 0.05 level.

Std. Error 1.679 1.679 1.679 1.679 1.679 1.679

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Sig. .032 .003 .032 .731 .003 .731

95% Confidence Interval Lower Bound Upper Bound -8.24 -.30 -9.50 -1.56 .30 8.24 -5.24 2.70 1.56 9.50 -2.70 5.24

41

Groups (μ = Flu Shots) μ(Nothing) = 29.70 : μ(Flu shot pamphlet) = 33.97 μ(Nothing) = 29.70 : μ(Flu shot video) = 35.23 μ(Flu shot pamphlet) = 33.97 : μ(Flu shot video) = 35.23 *Statistically significant difference ( = .05).

p .032* .003* .731

The Tukey post hoc test was run since the groups all had the same ns (n = 60). The Sig(nificance), or p level, rendered on the ANOVA table is .003, which is less than the .05  level, indicating that there are statistically significant differences among these (three) groups. This is confirmed by inspecting the Multiple Comparisons table; upon reviewing the mean number of flu shots given per day for each group, we find that the pamphlet group (μ = 33.97) and the video group (μ = 35.23) statistically significantly outperformed the group that got no media (μ = 29.70) with p = .032 and p = .003 respectively ( = .05). Hence, I would reject H0 and not reject H1. (d) In an effort to discover if educational media was effective in promoting flu shot receptivity among patients, individuals at a walk-in health clinic were randomly assigned to one of three groups: Group1 constituted the control group, and received no media or messaging promoting the utility of the flu shot (which is available to all who request it at this clinic), members of Group 2 were issued a flu shot informational pamphlet, and members of Group 3 were shown a brief flu shot informational video, containing the same educational points as the pamphlet. Group 1 (No information) (μ = 29.70 flu shots per day) was outperformed by Group 2 (Pamphlet) (μ = 29.70, p = .032) and Group 3 (Video) (μ = 35.23, p = .003). Although the video faired best, we detected no statistically significant difference (1.26 tests daily) between the pamphlet and the video when it came to average daily testing. This suggests that paper or video messaging perform essentially equivalently, and both are more effective than providing no such media. Our future research will focus on variations on this media to assemble optimal and cost effective messaging most suitable to our patient population.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

42 Exercise 6.6, Data Set A (a) H0: A laugh track on a comedy video does not enhance viewer enjoyment.

H1: A laugh track on a comedy video enhances viewer enjoyment. (b) Histograms with normal curve plots show a normal distribution of enjoyment for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No laugh track

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

43 Group 2—Laugh track with 50-person audience

Group 3—Laugh track with 100-person audience

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

44

Test of Homogeneity of Variances enjoy Levene Statistic df1 df2 Sig. 2.120 2 95 .126

The homogeneity of variance score shows a significance (p) of .126; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below, is over 30 for each group, which satisfies that criterion. (c) The ANOVA test revealed the following: Descriptives enjoy N Mean Std. Deviation 32 3.47 1.646 33 4.21 1.364 33 4.48 1.034 98 4.06 1.420

No laugh track Laugh track 50 Laugh track 100 Total

Std. Error .291 .237 .180 .143

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 2.88 4.06 1 8 3.73 4.70 2 7 4.12 4.85 2 6 3.78 4.35 1 8

ANOVA enjoy Between Groups Within Groups

Sum of Squares 17.906 177.726

Total

195.633

df 2 95

Mean Square 8.953 1.871

F 4.786

Sig. .010

Sig. .090 .010 .090 .805 .010 .805

95% Confidence Interval Lower Bound Upper Bound -1.57 .08 -1.84 -.19 -.08 1.57 -1.09 .55 .19 1.84 -.55 1.09

97 Multiple Comparisons

enjoy Sidak (I) group

(J) group

Mean Difference (I-J) No laugh track Laugh track 50 -.743 Laugh track 100 -1.016* Laugh track 50 No laugh track .743 Laugh track 100 -.273 Laugh track 100 No laugh track 1.016* Laugh track 50 .273 *. The mean difference is significant at the 0.05 level.

Std. Error .339 .339 .339 .337 .339 .337

Groups (μ = enjoyment) μ(No laugh track) = 3.47 : μ(Laugh track 50) = 4.21 μ(No laugh track) = 3.47 : μ(Laugh track 100) = 4.48 μ(Laugh track 50) = 4.21 : μ(Laugh track 100) = 4.48 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .090 .010* .805

45 The Sidak post hoc test was run since the groups had different ns. The Sig(nificance), or p level, rendered on the ANOVA table is .010, which is less than the .05  level, indicating that there are statistically significant differences among these (three) groups.

This is confirmed by inspecting the Multiple Comparisons table; the Sig. (p levels); the only pair that produced a statistically significant difference (p = .010) is the comparison between Group 1 (No laugh track) and Group 3 (Laugh track with a 100-person audience). Hence, I would reject H0 and not reject H1. (d) This study analyzed the effects that a laugh track has on viewer enjoyment of a comedy video. The participants were randomly assigned to one of three groups: a group that watched a comedy video with no laugh track, a group that watched the same video with the laughter of a 50-member audience, and a group that watched the same video with the laughter of a 100-member audience. Results revealed an enjoyment level of 3.47 (on a 5-point scale) for those who watched without the laugh track, 4.21 for those who watch with the 50-person laugh track, and 4.48 for those who watch with the 100-person laugh track. Although participants reported higher levels of enjoyment when exposed to the 50-person laugh track, the 100-person laugh track was found most enjoyable of the three groups. Comparing the control group to the group that watched with the 100person audience laugh track produced a statistically significant difference in enjoyment (p = .010,  = .05). This suggests that the laugh track significantly enhances enjoyment, but only if there the (recorded) audience is of a sufficient size.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

46 Exercise 6.6, Data Set B (a) H0: A laugh track on a comedy video does not enhance viewer enjoyment.

H1: A laugh track on a comedy video enhances viewer enjoyment. (b) Histograms with normal curve plots show a normal distribution of enjoyment for all groups as shown in the three figures below; hence, the pretest criterion of normality is satisfied.

Group 1—No laugh track

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

47 Group 2—Laugh track with 50-person audience

Group 3—Laugh track with 100-person audience

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

48

Test of Homogeneity of Variances enjoy Levene Statistic df1 df2 Sig. .366 2 85 .694

The homogeneity of variance score shows a significance (p) of .694; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

Only one of the groups has an n of at least 30; the findings would be considered more robust if the n for each group was at least 30. (c) The ANOVA test revealed the following: Descriptives enjoy N Mean Std. Deviation 35 2.49 .853 26 2.62 1.098 27 2.52 .975 88 2.53 .958

No laugh track Laugh track 50 Laugh track 100 Total

Std. Error .144 .215 .188 .102

95% Confidence Interval for Mean Lower Bound Upper Bound Minimum Maximum 2.19 2.78 1 4 2.17 3.06 1 6 2.13 2.90 1 4 2.33 2.74 1 6

ANOVA enjoy Between Groups Within Groups

Sum of Squares .260 79.637

Total

79.898

df 2 85

Mean Square .130 .937

F .139

Sig. .871

87 Multiple Comparisons

enjoy Sidak (I) group

(J) group

No laugh track Laugh track 50 Laugh track 100

Laugh track 50 Laugh track 100 No laugh track Laugh track 100 No laugh track Laugh track 50

Mean Difference (I-J) -.130 -.033 .130 .097 .033 -.097

Std. Error .251 .248 .251 .266 .248 .266

Sig. .939 .999 .939 .977 .999 .977

95% Confidence Interval Lower Bound Upper Bound -.74 .48 -.64 .57 -.48 .74 -.55 .74 -.57 .64 -.74 .55

Groups (μ = Enjoyment) μ(No laugh track) = 2.49 : μ(Laugh track 50) = 2.62 μ(No laugh track) = 2.49 : μ(Laugh track 100) = 2.52 μ(Laugh track 50) = 2.62 : μ(Laugh track 100) = 2.52 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .939 .999 .977

49 The Sidak post hoc test was run since the groups had different ns. The Sig(nificance), or p level, rendered on the ANOVA table is .871, which is greater than the .05  level, indicating that there are no statistically significant differences among these (three) groups. This is confirmed by inspecting the Multiple Comparisons table; the Sig. (p levels), which are all greater than .05. Based on these findings, I would not reject H0 and reject H1. (d) This study analyzed the effects that a laugh track has on viewer enjoyment of a comedy video. The participants were randomly assigned to one of three groups: a group that watched a comedy video with no laugh track, a group that watched the same video with the laughter of a 50-member audience, and a group that watched the same video with the laughter of a 100-member audience. Results revealed an enjoyment level of 2.49 (on a 5-point scale) for those who watched without the laugh track, 2.62 for those who watch with the 50-person laugh track, and 2.52 for those who watch with the 100-person laugh track. Comparing these three groups to each other revealed no statistically significant differences (p > .93 for all three groups;  = .05). These findings suggest that the laugh track does not significantly enhance enjoyment among these participants, hence, we do not reject our null hypothesis (H0), and reject H1, which states that including a laugh track will enhance audience enjoyment.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

50 Exercise 6.7, Dataset A (a) H0: Light therapy has no effect on depression.

H1: Light therapy is effective in reducing depression. (b) Histograms with normal curve plots show a normal distribution of mood for all groups as shown in the three figures below, hence, the pretest criteria of normality is satisfied.

Group 1 (No light therapy)

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51 Group 2 (Light therapy: even days)

Group 3 (Light therapy: every day)

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52

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. 1.409 2 237 .246

The homogeneity of variance score for mood shows a significance (p) of .246; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the three groups, hence, this pretest criterion passes.

The n for each group is 80 in each group, which satisfies the 30 per group minimum criterion (see Descriptives table below). (c) The ANOVA test revealed the following: Descriptives mood N No light therapy Light therapy: even days Light therapy: every day Total

80 80 80 240

Mean 59.13 61.88 62.69 61.23

Std. Deviation 8.299 7.077 6.929 7.585

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .928 57.28 60.97 .791 60.30 63.45 .775 61.15 64.23 .490 60.26 62.19

Minimum 42 46 48 42

Maximum 77 79 78 79

ANOVA mood Between Groups Within Groups Total

Sum of Squares 557.708 13190.688 13748.396

df 2 237

Mean Square 278.854 55.657

F 5.010

Sig. .007

239 Multiple Comparisons

mood Tukey HSD (I) group

No light therapy

(J) group

Light therapy: even days Light therapy: every day Light therapy: even days No light therapy Light therapy: every day Light therapy: every day No light therapy Light therapy: even days *. The mean difference is significant at the 0.05 level.

Mean Difference (I-J) -2.750 -3.563* 2.750 -.813 3.563* .813

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

95% Confidence Interval Std. Error 1.180 1.180 1.180 1.180 1.180 1.180

Sig. .053 .008 .053 .770 .008 .770

Lower Bound -5.53 -6.34 -.03 -3.59 .78 -1.97

Upper Bound .03 -.78 5.53 1.97 6.34 3.59

53

Groups (μ = mood) μ(No light th.) = 59.1 : μ(Light th. even days) = 61.9 μ(No light th.) = 59.1 : μ(Light th. every day) = 62.7 μ(Light th. even days) = 61.9 : μ(Light th. every day) = 62.7 Means rounded to one decimal digit. *Statistically significant difference ( = .05).

p .053 .008* .770

After 1 month of treatment, participants who received light therapy for 1 hour a day scored an average of 62.7 on a mood test, compared to 59.1 among those who had no light therapy; this 3.6 difference in their scores is statistically significant (p = .008,  = .05). Those who received 1 hour of light therapy every other day showed a better mood score (61.9) than those who received no light therapy, however, the improvement is not considered to be statistically significant (p = .053) using the .05  level. Incidentally, comparing the mean mood score of those who received light therapy (61.9) for everyother-day, and for daily use (62.7) revealed no statistically significant difference between those two groups (p = .770,  = .05). (d) In order to determine if light therapy is a viable supplement to treating depression, 240 subjects diagnosed with depression were randomly assigned to one of three groups: The control group received no light therapy; the second group received 1 hour of light therapy every other day for a month; the third group received light therapy for 1 hour every day for a month. After 30 days, all participants completed the Acme Mood Scale, a 10 question survey that renders a score from 1 to 100 (1 = Extremely bad mood, 100 = Extremely good mood). The group average scores on the mood test were similar among the two light therapy groups—61.9 for the every-other day group, and 62.7 for the daily group. Although these differences were not statistically significantly different from each other (p = .770,  = .05), only the group that received light therapy on a daily basis (μ = 62.7) showed a statistically significant improvement in mood, when compared to those who received no light therapy (μ = 59.1) (p = .008,  = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

54 Exercise 6.7, Data Set B (a) H0: Light therapy has no effect on depression.

H1: Light therapy has is effective in reducing depression. (b) Histograms with normal curve plots show a normal distribution of mood for all groups per the three figures below, hence, the pretest criterion of normality is satisfied.

Group 1 (No light therapy)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

55 Group 2 (Light therapy: even days)

Group 3 (Light therapy: every day)

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56

Test of Homogeneity of Variances mood Levene Statistic df1 df2 Sig. 1.352 2 138 .262

The homogeneity of variance score for mood shows a significance (p) of .262; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the three groups, hence, this pretest criterion passes.

The ns for these groups are 48, 56, and 37, which satisfies the 30 per group minimum criterion (see Descriptives table below). (c) The ANOVA test revealed the following: Descriptives mood N No light therapy Light therapy: even days Light therapy: every day Total

48 56 37 141

Mean 45.44 44.86 45.54 45.23

Std. Deviation 3.631 3.806 4.652 3.972

95% Confidence Interval for Mean Std. Error Lower Bound Upper Bound .524 44.38 46.49 .509 43.84 45.88 .765 43.99 47.09 .335 44.57 45.90

Min. 38 37 37 37

Max. 53 53 53 53

ANOVA mood Between Groups Within Groups

Sum of Squares 13.418 2195.859

Total

2209.277

df

Mean Square 6.709 15.912

2 138

F .422

Sig. .657

140 Multiple Comparisons

mood Sidak (I) group

(J) group

No light therapy Light therapy: even days Light therapy: every day

Light therapy: even days Light therapy: every day No light therapy Light therapy: every day No light therapy Light therapy: even days

Mean Difference (IJ) .580 -.103 -.580 -.683 .103 .683

95% Confidence Interval Std. Error .785 .873 .785 .845 .873 .845

Sig. .843 .999 .843 .805 .999 .805

Groups (μ = mood) μ(No light th.) = 45.44 : μ(Light th. even days) = 44.86 μ(No light th.) = 45.44 : μ(Light th. every day) = 45.54 μ(Light th. even days) = 44.86 : μ(Light th. every day) = 45.54 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Lower Bound -1.32 -2.21 -2.48 -2.73 -2.01 -1.36

p .843 .999 .805

Upper Bound 2.48 2.01 1.32 1.36 2.21 2.73

57 After 1 month of treatment, participants who received light therapy for 1 hour a day scored an average of 45.54 on a mood test; those who had light therapy every other day scored an average of 44.86, and those who had no light therapy had an average score of 45.44. The ANOVA table reports a Sig. (p) value of .657 which is greater than the .05  level, indicating that there are no statistically significant differences among the groups. This is confirmed by the Sig. column on the Multiple Comparisons table, wherein the p values range from .805 to .999, which is well above the .05  level. Hence, we can conclude that for this sample, the light therapy protocol produced no statistically significant improvement in mood. (d) In order to determine if light therapy is a viable supplement to treating depression, 141 subjects diagnosed with depression were randomly assigned to one of three groups: The control group received no light therapy; the second group received 1 hour of light therapy every other day for a month; the third group received light therapy for 1 hour every day for a month. After 30 days, all participants completed the Acme Mood Scale, a 10 question survey that renders a score from 1 to 100 (1 = Extremely bad mood, 100 = Extremely good mood). The group average scores on the mood test were similar; 45.44 for those who received no light therapy, 44.86 for those who had light therapy every other day, and 45.54 for those who had light therapy daily. The p values among these three groups ranged from .805 to .999; using an  level of .05, we conclude that this schedule of light therapy did not produce a statistically significant improvement in mood for these participants.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

58 Exercise 6.8, Data Set A (a) H0: Walking in the morning will have no effect on energy.

H1: Walking in the morning enhances energy. (b) Although the histogram for Group 1 (below) shows some low outliers, the majority of the data forms a normal curve for energy. The histograms for the other groups appears normally distributed. I’d say the pretest criterion of normality is sufficiently satisfied.

Group 1—No walking

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59 Group 2—Walked 30 minutes each morning

Group 3—Walked 60 minutes each morning

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60

Test of Homogeneity of Variances energy Levene Statistic df1 df2 Sig. 2.019 2 348 .134

The homogeneity of variance score shows a significance (p) of .134; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below are greater than 30; the n quotas are satisfied. (c) The ANOVA test revealed the following: Descriptives energy

No walking Walking: 30 min.

Walking: 60 min.

Total

N 132 124 95 351

Mean 81.23 82.60 82.77 82.13

Std. Deviation Std. Error 4.328 .377 4.320 .388 4.716 .484 4.476 .239

95% Confidence Interval for Mean Lower Bound Upper Bound 80.49 81.98 81.84 83.37 81.81 83.73 81.66 82.60

Minimum Maximum 61 88 73 93 73 93 61 93

ANOVA energy Between Groups Within Groups Total

Sum of Squares 172.444 6840.262 7012.707

df 2 348

Mean Square 86.222 19.656

F 4.387

Sig. .013

350 Multiple Comparisons

energy Sidak (I) group

(J) group

Mean Difference (I-J) No walking Walking: 30 min.

-1.370* Walking: 60 min.

-1.534* Walking: 30 min.

No walking 1.370* Walking: 60 min.

-.164 Walking: 60 min.

No walking 1.534* Walking: 30 min. .164 *. The mean difference is significant at the 0.05 level.

Std. Error .554 .597 .554 .604 .597 .604

Sig. .041 .031 .041 .990 .031 .990

95% Confidence Interval Lower Bound Upper Bound -2.70 -.04 -2.96 -.10 .04 2.70 -1.61 1.29 .10 2.96 -1.29 1.61

The Sidak post hoc test was used since the ns for each group differed from each other.

Groups (μ = energy) μ(No walking) = 81.23 : μ(Walking 30 minutes) = 82.60 μ(No walking) = 81.23 : μ(Walking 60 minutes) = 82.77 μ(Walking 30 minutes) = 82.60 : μ(Walking 60 minutes) = 82.77 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .041* .031* .990

61 End-of-the-day energy was statistically significantly higher for the groups that walked compared to the group that did not walk. These findings lead us to reject H0 and not reject H1. (d) This study measured the end-of-day energy of individuals assigned to one of three groups; Group 1 served as the control group and did no walking; the other groups took a morning walk—Group 2 walked for 30 minutes, and Group 3 walked for 1 hour. At the conclusion of this study, participants answered the Acme End-of-the-Day Energy Scale.

This instrument produces a score between 1 and 100 (1 = Extremely low energy, 100 = Extremely high energy). Our analysis showed that those who did not walk scored 81.23; those who walked had statistically significantly higher levels of energy using an  level of .05—Group 2 scored 82.60 (p = .041), and those in Group 3 scored 82.77 (p = .031).

Although Group 3 scored slightly higher than Group 2, this is not considered to be a statistically significant difference (p = .990). Based on these findings, we reject H0 which asserts that that walking made no difference in one’s energy, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

62 Exercise 6.8, Data Set B (a) H0: Walking in the morning will have no effect on energy.

H1: Walking in the morning enhances energy. (b) The histogram for the three groups (below) appear to be normally distributed for energy; the pretest criterion of normality is satisfied.

Group 1—No walking

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63 Group 2—Walked 30 minutes each morning

Group 3—Walked 60 minutes each morning

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64

Test of Homogeneity of Variances energy Levene Statistic df1 df2 Sig. .787 2 267 .456

The homogeneity of variance score shows a significance (p) of .456; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances of the groups; hence, this pretest criterion passes.

The n for each group, as shown in the Descriptives table below are greater than 30; the n quotas are satisfied. (c) The ANOVA test revealed the following: Descriptives energy

No walking Walking: 30 min.

Walking: 60 min.

Total

N Mean Std. Deviation 90 54.22 10.994 90 55.43 9.971 90 58.33 10.349 270 56.00 10.550

Std. Error 1.159 1.051 1.091 .642

95% Confidence Interval for Mean Lower Bound Upper Bound 51.92 56.52 53.34 57.52 56.17 60.50 54.73 57.26

Minimum Maximum 32 77 35 77 35 79 32 79

ANOVA energy Between Groups Within Groups Total

Sum of Squares 803.341 29137.656 29940.996

df 2 267

Mean Square 401.670 109.130

F 3.681

Sig. .026

269 Multiple Comparisons

energy Tukey HSD (I) group

(J) group

Mean Difference (I-J) No walking Walking: 30 min.

-1.211 Walking: 60 min.

-4.111* Walking: 30 min.

No walking 1.211 Walking: 60 min.

-2.900 Walking: 60 min.

No walking 4.111* Walking: 30 min.

2.900 *. The mean difference is significant at the 0.05 level.

Std. Error 1.557 1.557 1.557 1.557 1.557 1.557

Sig. .717 .024 .717 .152 .024 .152

95% Confidence Interval Lower Bound Upper Bound -4.88 2.46 -7.78 -.44 -2.46 4.88 -6.57 .77 .44 7.78 -.77 6.57

The Tukey post hoc test was used since the ns for each group were 90.

Groups (μ = Energy) μ(No walking) = 54.22 : μ(Walking 30 minutes) = 55.43 μ(No walking) = 54.22 : μ(Walking 60 minutes) = 58.33 μ(Walking 30 minutes) = 55.43 : μ(Walking 60 minutes) = 58.33 *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

p .717 .024* .152

65 Those in the walking groups (Groups 2 and 3) had higher levels of energy than those who did not walk (Group 1); although those who walked for 60 minutes had higher energy than those who walked for only 30 minutes, the energy difference between these two groups is not statistically significant. The only significant difference was detected between Group 1 and Group 3. These findings lead us to reject H0 and not reject H1. (d) This study measured the end-of-day energy of individuals assigned to one of three groups; Group 1 served as the control group and did no walking; the other groups took a morning walk—Group 2 walked for 30 minutes, and Group 3 walked for 1 hour. At the conclusion of this study, participants answered the Acme End-of-the-Day Energy Scale.

This instrument produces a score between 1 and 100 (1 = Extremely low energy, 100 = Extremely high energy). Our analysis showed that those who walked had more energy than those who did not walk—in fact, the more walking, the more energy participants reported, however, only those in Group 3, who walked for an hour each morning ( = 58.33) had energy scores that were statistically significantly higher than those who did not walk ( = 54.22); this comparison produced a p value of .024 ( = .05). Based on these findings, we reject H0, which stated that walking made no difference in one’s energy and we would fail to reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

66 Exercise 6.9, Data Set A (a) H0: Lighting source has no effect on reading rate.

H1: Lighting source has an effect on reading rate. (b) Histograms with normal curve plots show a normal distribution of seconds for all groups as shown in the four figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (Room lighting)

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67 Normal distribution for seconds in Group 2 (Acme reading lamp)

Normal distribution for seconds in Group 3 (Generic reading lamp)

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68 Normal distribution for seconds in Group 4 (Flashlight)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 1.499 3 103 .219

The homogeneity of variance score for seconds shows a significance (p) of .219; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the four groups, hence, this pretest criterion passes.

The Generic lamp group was the only group that had the minimal n of 30. The Room lighting, Acme lighting, and Flashlight groups had ns of 25, 28 and 24 respectively (see Descriptives table below). The findings of the ANOVA test would be more robust if the ns were slightly higher for these three groups.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

69 (c) The ANOVA test revealed the following: Descriptives seconds

Room lighting Acme lamp Generic lamp Flashlight Total

N 25 28 30 24 107

Mean 435.88 405.93 409.67 441.25 421.90

Std. Deviation 38.511 31.184 42.174 40.623 40.851

Std. Error 7.702 5.893 7.700 8.292 3.949

95% Confidence Interval for Mean Lower Bound Upper Bound 419.98 451.78 393.84 418.02 393.92 425.41 424.10 458.40 414.07 429.73

Minimum 374 357 328 368 328

Maximum 509 455 470 512 512

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 25504.205 151385.664 176889.869

df 3 103

Mean Square 8501.402 1469.764

F 5.784

Sig. .001

106 Multiple Comparisons

seconds Sidak (I) group

(J) group

Mean Difference (I-J) Room lighting Acme lamp 29.951* Generic lamp 26.213 Flashlight -5.370 Acme lamp Room lighting -29.951* Generic lamp -3.738 Flashlight -35.321* Generic lamp Room lighting -26.213 Acme lamp 3.738 Flashlight -31.583* Flashlight Room lighting 5.370 Acme lamp 35.321* Generic lamp 31.583* *. The mean difference is significant at the 0.05 level.

Std. Error 10.549 10.382 10.956 10.549 10.074 10.665 10.382 10.074 10.499 10.956 10.665 10.499

Sig. .032 .076 .997 .032 .999 .008 .076 .999 .020 .997 .008 .020

95% Confidence Interval Lower Bound Upper Bound 1.65 58.25 -1.64 54.06 -34.76 24.02 -58.25 -1.65 -30.76 23.29 -63.93 -6.71 -54.06 1.64 -23.29 30.76 -59.75 -3.42 -24.02 34.76 6.71 63.93 3.42 59.75

Groups (μ = reading time in seconds) p Room lighting (μ = 436) : Acme Lamp (μ = 406) .032* Room lighting (μ = 436) : Generic lamp (μ = 410) .076 Room lighting (μ = 436) : Flashlight (μ = 441) .997 Acme lamp (μ = 406) : Generic lamp (μ = 410) .999 Acme lamp (μ = 406) : Flashlight (μ = 441) .008* Generic lamp (μ = 410) : Flashlight (μ = 441) .020* Means rounded to nearest second. *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

70 Per the table above, since the mean reading time in the Acme reading lamp group is statistically significantly lower than scores of those who read using Room lighting and by Flashlight, we reject H0. For the same reason, we would not reject H1. (d) This study analyzed the effects that the Acme reading lamp had on reading speed. The 107 participants were randomly assigned to one of four groups; one group read a 1,000word essay using regular room lighting, the second group read the same essay using the new Acme reading lamp, the third group read using a generic reading lamp, and the fourth group read using a flashlight. Results revealed that on the average, those who read using the Acme reading lamp read significantly faster (μ = 406) than those who read using a flashlight (μ = 441, p = .008), or regular room lighting (μ = 436, p = .032) using an  level of .05. Incidentally, those who used a generic reading lamp (μ = 410) finished reading the essay significantly faster than those who read by flashlight (μ = 441, p = .020). We also discovered that those who read using a Acme reading lamp (μ = 406) completed the essay faster than those who used the generic reading lamp (μ = 410), however this difference was not found to be statistically significant (p = .999).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

71 Exercise 6.9, Data Set B (a) H0: Lighting source has no effect on reading rate.

H1: Lighting source has an effect on reading rate. (b) Histograms with normal curve plots show a normal distribution of seconds for all groups as shown in the four figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (Room lighting)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

72 Normal distribution for seconds in Group 2 (Acme reading lamp)

Normal distribution for seconds in Group 3 (Generic reading lamp)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

73 Normal distribution for seconds in Group 4 (Flashlight)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 1.163 3 96 .328

The homogeneity of variance score for seconds shows a significance (p) of .328; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the four groups, hence, this pretest criterion passes.

The groups each had an n of 25 (see Descriptives table below). The findings of the ANOVA test would be more robust if the ns were at least 30 per group. (c) The ANOVA test revealed the following: Descriptives seconds N Room lighting Acme lamp Generic lamp Flashlight Total

25 25 25 25 100

Mean 416.44 415.60 413.68 448.68 423.60

Std. Deviation 33.904 38.045 39.161 47.434 41.947

Std. Error 6.781 7.609 7.832 9.487 4.195

95% Confidence Interval for Mean Lower Bound Upper Bound 402.44 430.44 399.90 431.30 397.52 429.84 429.10 468.26 415.28 431.92

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Minimum 331 344 338 361 331

Maximum 489 481 470 525 525

74

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 21066.960 153131.040 174198.000

df 3 96

Mean Square 7022.320 1595.115

F 4.402

Sig. .006

99 Multiple Comparisons

seconds Tukey HSD (I) group

(J) group

Mean Difference (I-J) Room lighting Acme lamp .840 Generic lamp 2.760 Flashlight -32.240* Acme lamp Room lighting -.840 Generic lamp 1.920 Flashlight -33.080* Generic lamp Room lighting -2.760 Acme lamp -1.920 Flashlight -35.000* Flashlight Room lighting 32.240* Acme lamp 33.080* Generic lamp 35.000* *. The mean difference is significant at the 0.05 level.

Std. Error 11.296 11.296 11.296 11.296 11.296 11.296 11.296 11.296 11.296 11.296 11.296 11.296

Sig. 1.000 .995 .027 1.000 .998 .022 .995 .998 .013 .027 .022 .013

95% Confidence Interval Lower Bound Upper Bound -28.70 30.38 -26.78 32.30 -61.78 -2.70 -30.38 28.70 -27.62 31.46 -62.62 -3.54 -32.30 26.78 -31.46 27.62 -64.54 -5.46 2.70 61.78 3.54 62.62 5.46 64.54

Groups (μ = reading time in seconds) p Room lighting (μ = 416) : Acme Lamp (μ = 416) 1.000 Room lighting (μ = 416) : Generic lamp (μ = 414) .995 Room lighting (μ = 416) : Flashlight (μ = 449) .027* Acme lamp (μ = 416) : Generic lamp (μ = 414) .998 Acme lamp (μ = 416) : Flashlight (μ = 449) .022* Generic lamp (μ = 414) : Flashlight (μ = 449) .013* Means rounded to nearest second. *Statistically significant difference ( = .05).

Per the table above, since the mean reading time in the Acme lamp group (μ = 416) is statistically significantly lower than those who read using a Flashlight (μ = 449, p = .022), based on the .05  level, we reject H0 and not reject H1. Additionally, Room lighting (μ = 416) statistically significantly outperformed the reading rate of the Flashlight (μ = 449, p = .027), and finally, the reading rate for the generic lamp (μ = 416) outperformed the Flashlight (p = .013).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

75 (d) This study analyzed the effects that the Acme reading lamp had on reading speed. The 100 participants were randomly assigned to one of four groups; one group read a 1,000word essay using regular room lighting, the second group read the same essay using the new Acme reading lamp, the third group read using a generic reading lamp, and the fourth group read using a flashlight. There was no statistically significant difference in reading times among those who used the Acme reading lamp (μ = 416), Room lighting (μ = 416) or the Generic lamp (μ = 414) using an  level of .05. All three of those groups read statistically significantly faster than the fourth group, who read using a flashlight (μ = 449); p values ranged from .013 to .027.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

76 Exercise 6.10, Data Set A (a) H0: Classical music has no effect on problem-solving skills.

H1: Classical music enhances problem-solving skills. (b) Histograms with normal curve plots show a normal distribution of seconds for all of the groups as shown in the four figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (No music)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

77 Normal distribution for seconds in Group 2 (Music at 30 dB)

Normal distribution for seconds in Group 3 (Music at 60 dB)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

78 Normal distribution for seconds in Group 4 (Music at 90 dB)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 1.180 3 156 .319

The homogeneity of variance score for seconds shows a significance (p) of .319; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the four groups, hence, this pretest criterion passes.

The n for each group is 40 (see Descriptives table below), which satisfies the 30 per group minimum criterion. (c) The ANOVA test revealed the following: Descriptives seconds

No music Music at 30 dB Music at 60 dB Music at 90 dB Total

N 40 40 40 40 160

Mean 619.55 593.95 595.90 625.67 608.77

Std. Deviation 35.380 47.862 46.115 44.422 45.525

Std. Error 5.594 7.568 7.291 7.024 3.599

95% Confidence Interval for Mean Lower Bound Upper Bound 608.23 630.86 578.64 609.26 581.15 610.65 611.46 639.88 601.66 615.87

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Minimum 541 497 505 525 497

Maximum 690 707 696 727 727

79

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 31480.092 298058.137 329538.229

df 3 156

Mean Square 10493.364 1910.629

F 5.492

Sig. .001

159 Multiple Comparisons

seconds Tukey HSD (I) group

(J) group

Mean Difference (I-J) No music Music at 30 dB 25.598* Music at 60 dB 23.648 Music at 90 dB -6.121 Music at 30 dB No music -25.598* Music at 60 dB -1.950 Music at 90 dB -31.719* Music at 60 dB No music -23.648 Music at 30 dB 1.950 Music at 90 dB -29.769* Music at 90 dB No music 6.121 Music at 30 dB 31.719* Music at 60 dB 29.769* *. The mean difference is significant at the 0.05 level.

Std. Error 9.774 9.774 9.774 9.774 9.774 9.774 9.774 9.774 9.774 9.774 9.774 9.774

Sig. .047 .078 .924 .047 .997 .008 .078 .997 .014 .924 .008 .014

Groups (μ = seconds to complete puzzle) No music (μ = 620) : Music at 30 dB (μ = 594) No music (μ = 620) : Music at 60 dB (μ = 596) No music (μ = 620) : Music at 90 dB (μ = 626) Music at 30 dB (μ = 594) : Music at 60 dB (μ = 596) Music at 30 dB (μ = 594) : Music at 90 dB (μ = 626) Music at 60 dB (μ = 596) : Music at 90 dB (μ = 626) Means rounded to nearest second. *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

95% Confidence Interval Lower Bound Upper Bound .22 50.98 -1.73 49.03 -31.50 19.26 -50.98 -.22 -27.33 23.43 -57.10 -6.34 -49.03 1.73 -23.43 27.33 -55.15 -4.39 -19.26 31.50 6.34 57.10 4.39 55.15

p .047* .078 .924 .997 .008* .014*

80 Participants who assembled the puzzle with classical music at 30 dB (μ = 594) completed the puzzle statistically significantly prompter than those who had no music (μ = 620) (p = .047,  = .05), hence I would reject H0 and not reject H1. (d) This experiment was designed to determine if classical music facilitates problem solving. We recruited 160 people, and randomly assigned 40 participants to one of four groups: Members of each group were given a 100-piece jigsaw puzzle to solve; those in Group 1 worked in silence, those in Groups 2, 3, and 4 solved the puzzle with classical music playing at different volumes in each group—soft (30 dB), medium (60 dB), and loud (90 dB) respectively. We found that those who listened to the soft classical music (at 30 dB) completed the puzzle significantly faster (μ = 594) than those who worked in silence (μ = 620) (p = .047;  = .05), however, it seems that as the music was played louder, the beneficial effect was lost: Those who listened at a medium volume completed the puzzle in 596 seconds, and those who were exposed to the loud volume took 626 seconds. It seems that while the soft classical music helped facilitate the problem solving, louder volumes may have been distracting.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

81 Exercise 6.10, Data Set B (a) H0: Classical music has no effect on problem-solving skills.

H1: Classical music enhances problem-solving skills. (b) Histograms with normal curve plots show a normal distribution of seconds for all of the groups as shown in the four figures below, hence, the pretest criterion of normality is satisfied.

Normal distribution for seconds in Group 1 (No music)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

82 Normal distribution for seconds in Group 2 (Music at 30 dB)

Normal distribution for seconds in Group 3 (Music at 60 dB)

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

83 Normal distribution for seconds in Group 4 (Music at 90 dB)

Test of Homogeneity of Variances seconds Levene Statistic df1 df2 Sig. 1.279 3 149 .284

The homogeneity of variance score for seconds shows a significance (p) of .284; since this is greater than the  level of .05, this suggests that there is no statistically significant difference between the variances among the four groups, hence, this pretest criterion passes.

The n for each group is over 30 (see Descriptives table below), which satisfies the 30 per group minimum criterion. (c) The ANOVA test revealed the following: Descriptives seconds

No music Music at 30 dB Music at 60 dB Music at 90 dB Total

N 43 39 37 34 153

Mean 608.93 606.33 608.49 617.09 609.97

Std. Deviation 11.194 12.461 10.189 12.505 12.147

Std. Error 1.707 1.995 1.675 2.145 .982

95% Confidence Interval for Mean Lower Bound Upper Bound 605.49 612.38 602.29 610.37 605.09 611.88 612.72 621.45 608.03 611.91

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Minimum 588 585 588 599 585

Maximum 635 637 630 644 644

84

ANOVA seconds Between Groups Within Groups Total

Sum of Squares 2366.460 20061.436 22427.895

df 3 149

Mean Square 788.820 134.641

F 5.859

Sig. .001

152 Multiple Comparisons

seconds Sidak (I) group

(J) group

Mean Difference (I-J) No music Music at 30 dB 2.597 Music at 60 dB .444 Music at 90 dB -8.158* Music at 30 dB No music -2.597 Music at 60 dB -2.153 Music at 90 dB -10.755* Music at 60 dB No music -.444 Music at 30 dB 2.153 Music at 90 dB -8.602* Music at 90 dB No music 8.158* Music at 30 dB 10.755* Music at 60 dB 8.602* *. The mean difference is significant at the 0.05 level.

Std. Error 2.566 2.602 2.663 2.566 2.663 2.723 2.602 2.663 2.757 2.663 2.723 2.757

Sig. .895 1.000 .015 .895 .962 .001 1.000 .962 .013 .015 .001 .013

95% Confidence Interval Lower Bound Upper Bound -4.24 9.44 -6.49 7.38 -15.26 -1.06 -9.44 4.24 -9.25 4.95 -18.01 -3.50 -7.38 6.49 -4.95 9.25 -15.95 -1.25 1.06 15.26 3.50 18.01 1.25 15.95

Groups (μ = seconds to complete puzzle) p No music (μ = 609) : Music at 30 dB (μ = 606) .895 No music (μ = 609) : Music at 60 dB (μ = 608) 1.000 No music (μ = 609) : Music at 90 dB (μ = 617) .015* Music at 30 dB (μ = 606) : Music at 60 dB (μ = 608) .962 Music at 30 dB (μ = 606) : Music at 90 dB (μ = 617) .001* Music at 60 dB (μ = 608) : Music at 90 dB (μ = 617) .013* Means rounded to nearest second. *Statistically significant difference ( = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

85 There was no statistically significant difference in the participants’ time to complete the puzzle among those who worked in silence (μ = 609), those who listened to classical music at a soft volume (μ = 606), and those who listened at a medium volume (μ = 608) using an  of .05; however, those who solved the puzzle with the classical music playing loud (90 dB) took significantly longer (μ = 671) compared to those who worked with no music (p = .015), music at a soft volume (p = .001), or moderate volume (p = .013). It seems that classical music does not aid in such problem solving, in fact, if played too loud, it can serve as a distraction. (d) This experiment was designed to determine if classical music facilitates problem solving. We recruited 153 subjects, and randomly assigned them to one of four groups: those in Group 1 worked on a 100-piece jigsaw puzzle in silence; those in Groups 2, 3, and 4 solved the same puzzle with classical music playing at different volumes in each group—soft (30 dB), medium (60 dB), and loud (90 dB), respectively. We found no statistically significant difference in puzzle solving time among those who worked in silence (μ = 609), or with classical music played at a soft volume (μ = 606) or moderate volume (μ = 609) (p > .05). However, participants who worked on the puzzle while listening to loud classical music (90 dB) took significantly longer (μ = 617) to solve the puzzle compared to those who worked in silence (μ = 509) (p = .015,  = .05), suggesting that classical music has no effect on this sort of problem solving, unless it is played loud, in which case, the music appears to act as a distracter.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 7 Paired t Test and Wilcoxon Test Solutions to All Exercises

Exercise

Page

Exercise

Page

7.1A....................2

7.6A ................. 22

7.1B....................4

7.6B ................. 24

7.2A....................6

7.7A ................. 26

7.2B....................8

7.7B ................. 28

7.3A..................10

7.8A ................. 30

7.3B..................12

7.8B ................. 32

7.4A..................14

7.9A ................. 34

7.4B..................16

7.9B ................. 36

7.5A..................18

7.10A ............... 38

7.5B..................20

7.10B ............... 40

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 7.1, Data Set A (a) H0: Acme Monster Spray has no effect on children’s monster anxiety.

H1: Acme Monster Spray reduces children’s monster anxiety. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 6.75 4.08

pretest - posttest

Mean 2.667

N 12 12

Std. Deviation 1.485 1.443

Std. Error Mean .429 .417

Paired Samples Test Paired Differences 95% Confidence Interval of Std. the Difference Std. Error Deviation Mean Lower Upper 1.923 .555 1.445 3.888

t 4.804

df 11

Sig. (2-tailed) .001

Prior to using the Monster Spray, the children’s mean anxiety level was 6.75; after using the spray, that level dropped to 4.08. This 2.67-point reduction in reported anxiety is statistically significant since the p value of .001 is less than the specified  level of .05.

Based on these findings, we would reject H0, and not reject H1. (d) In order to help children rest easier at night, 12 children were asked to rate their bedtime anxiety due to fear of nighttime monsters on a 1 to 10 scale (1 = not afraid at all, 10 = very afraid), then Acme Monster Spray, an inert sweet-smelling mist was administered by their parents, after which children were asked to rate their anxiety level.

Upon spraying, children reported a 2.67-point average drop in anxiety (6.75 before spraying, down to 4.08 after spraying). Paired t test analysis revealed this change to be statistically significant (p = .001) using a .05  level, suggesting that the (placebo) effect of this spray may help children rest more comfortably.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 Exercise 7.1, Data Set B (a) H0: Acme Monster Spray has no effect on children’s monster anxiety.

H1: Acme Monster Spray reduces children’s monster anxiety. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 5.70 5.40

pretest - posttest

N 10 10

Mean .300

Std. Deviation Std. Error Mean 1.947 .616 2.066 .653

Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper .483 .153 -.046 .646

t 1.964

df 9

Sig. (2-tailed) .081

Prior to using the Monster Spray, the children’s mean anxiety level was 5.70; after using the spray, that level dropped to 5.40. This .30-point reduction in reported anxiety is not statistically significant since the p value of .081 is greater than the specified  level of .05. Based on these findings, we would not reject H0, and reject H1. (d) In order to help children rest easier at night, 10 children were asked to rate their bedtime anxiety due to fear of nighttime monsters on a 1 to 10 scale (1 = not afraid at all, 10 = very afraid), then Acme Monster Spray, an inert sweet-smelling mist was administered by their parents, after which children were asked to rate their anxiety level.

Upon spraying, children reported a .30-point average drop in anxiety (5.70 before spraying, down to 5.40 after spraying). Paired t test analysis revealed a p level of .081; using a .05  level, this suggests that this difference in scores is not statistically significant, hence, parents will need to find a different way to console their children at nighttime.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 7.2, Data Set A (a) H0: The heart health lecture will not change elevator/stair usage.

H1: The heart health lecture will change elevator/stair usage. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 2.56 2.38

N 16 16

Std. Deviation Std. Error Mean 1.209 .302 1.310 .328

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Mean Std. Deviation Std. Error Mean Lower Upper .188 2.007 .502 -.882 1.257

t .374

df 15

Sig. (2-tailed) .714

Prior to the heart health seminar, attendees reported that they took the stairs (as opposed to the elevator) an average of 2.56 times per week; a week after the seminar, that number (unexpectedly) dropped to 2.38, however, using an  level of .05, the observed p value of .714 suggests that this difference is not statistically significant. (d) In an effort to increase healthy behaviors, a heart health seminar was offered to voluntary participants. Prior to the presentation, each attendee was asked to write down the number of times that he or she used the stairs instead of the elevator at work over the course of the last week; a week after the seminar, the same data were gathered from those who attended. Prior to the seminar, attendees reported using the stairs an average of 2.56 times per week; a week after the seminar, that figure unexpectedly dropped to 2.38 times per week. Despite this unexpected decline in stair usage, the p value of .714 suggests that the mean weekly change in stair usage is not statistically significant (using a traditional .05  level). Based on these findings, we are considering retooling this seminar.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 Exercise 7.2, Data Set B (a) H0: The heart health lecture will not change elevator/stair usage.

H1: The heart health lecture will change elevator/stair usage. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest - posttest

pretest posttest

Mean 4.15 7.00

N 13 13

Std. Deviation Std. Error Mean 2.703 .750 2.160 .599

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Mean Std. Deviation Std. Error Mean Lower Upper -2.846 4.100 1.137 -5.324 -.369

t -2.503

df 12

Sig. (2-tailed) .028

Prior to the heart health seminar, attendees reported that they took the stairs (as opposed to the elevator) an average of 4.15 times per week; a week after the seminar, that number increased to 7.00; using an  level of .05, the observed p value of .028 suggests that this difference is statistically significant. Based on these findings, I would reject H0 and not reject H1. (d) In an effort to increase healthy behaviors, a heart health seminar was offered to voluntary participants. Prior to the presentation, each attendee was asked to write down the number of times that he or she used the stairs instead of the elevator at work over the course of the last week; a week after the seminar, the same data were gathered from those who attended. Prior to the seminar, attendees reported using the stairs an average of 4.15 times per week; a week after the seminar, that figure increased to 7.00 times per week (% = 68.67); this increase is statistically significant (p = .028) using the traditional .05  level. These findings suggest that the seminar was useful. It would be interesting to see if these figures are sustainable over time.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 7.3, Data Set A (a) H0: Students do not significantly improve their spelling skills over the course of a month.

H1: Students improve their spelling skills over the course of a month. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 62.05 69.55

pretest - posttest

N

Mean -7.500

20 20

Std. Deviation 9.041 9.478

Std. Error Mean 2.022 2.119

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Std. Error Deviation Mean Lower Upper 13.097 2.929 -13.629 -1.371

t -2.561

df Sig. (2-tailed) 19 .019

At the start of the month, students were administered a 100-word spelling test to find out how many words on the prescribed spelling list for that month students could already spell correctly. Students spelled an average of 62.05 words correctly on this pretest. At the end of the month, students were readministered this 100-word test, and spelled an average of 69.55 words correctly. The 7.5 increase in score constitutes a statistically significant improvement since the p level is .019, which is less than the specified  level of .05. Based on these findings, we would reject H0, and not reject H1. (d) In order to assess if students substantially advance their spelling proficiency on a monthly basis, students were given a 100-word spelling test at the beginning of the month; after studying 25 words per week from the list, students took the same 100-word test 30 days later. At the end of the month, students spelled an average of 69.55 of the words correctly, compared to 62.05 at the beginning of the month. Using an  level of .05, this 7.5-point improvement in score was found to be statistically significant (p = .019).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 Exercise 7.3, Data Set B (a) H0: Students do not significantly improve their spelling skills over the course of a month.

H1: Students improve their spelling skills over the course of a month. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 86.14 87.59

pretest - posttest

N 22 22

Std. Deviation 4.201 4.469

Std. Error Mean .896 .953

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Std. Error Mean Deviation Mean Lower Upper -1.455 6.185 1.319 -4.197 1.288

t -1.103

df 21

Sig. (2-tailed) .283

At the start of the month, students were administered a 100-word spelling test to find out how many words on the prescribed spelling list for that month students could already spell correctly. Students spelled an average of 86.14 words correctly on this pretest. At the end of the month, students were readministered this 100-word test, and spelled an average of 87.59 words correctly. The 1.45-point increase in score is not a statistically significant improvement since the p level is .283, which is greater than the specified  level of .05. Based on these findings, we would not reject H0, and reject H1. (d) In order to find out if students substantially advance their spelling proficiency on a monthly basis, students were given a 100-word spelling test at the beginning of the month; after studying 25 words per week from the list, students took the same 100-word test 30 days later. At the end of the month, students spelled an average of 87.59 of the words correctly, compared to 86.14 at the beginning of the month. Using an  level of .05, this 1.45-point improvement in score is not statistically significant (p = 283).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 7.4, Data Set A (a) H0: Short-term therapy does not reduce depression.

H1: Short-term therapy reduces depression. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff despite the slightly skewed distribution, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest - posttest

Mean 1.389

pretest posttest

Mean 53.83 52.44

N 18 18

Std. Deviation Std. Error Mean 8.893 2.096 10.782 2.541

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Deviation Std. Error Mean Lower Upper 4.217 .994 -.708 3.486

t 1.397

df 17

Sig. (2-tailed) .180

Depression levels were measured before and after administering short-term therapy using the Acme Depression Inventory; the mean pretest score was 53.83, whereas the mean posttest score dropped to 52.44. However, the p value is .180, which is greater than the .05  level; hence, this reduction in depression is not considered to be significant. Based on this, I would not reject H0 and reject H1. (d) In order to determine the effectiveness of a short-term therapeutic implementation, we administered the Acme Depression Inventory (ADI), which renders a score from 0 to 75 (0 = low depression, 75 = high depression) before and after treatment for a group of 18 participants. The mean level of the depression dropped from 53.83 to 52.44, however this 1.39-point change is not considered to be statistically significant (p = .180;  = .05).

Based on these findings, we will be reassessing our therapeutic methods in terms of treatment approach and duration of care.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 Exercise 7.4, Data Set B (a) H0: Short-term therapy does not reduce depression.

H1: Short-term therapy reduces depression. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

17 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 69.80 67.20

Mean 2.600

N 15 15

Std. Deviation Std. Error Mean 2.007 .518 3.968 1.024

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Deviation Std. Error Mean Lower Upper 3.247 .838 .802 4.398

t 3.101

df 14

Sig. (2-tailed) .008

Depression levels were measured before and after administering short-term therapy using the Acme Depression Inventory; the mean pretest score was 69.80, whereas the mean posttest score dropped to 67.20. The p value is .008, which is less than the .05  level; hence, this reduction in depression is considered to be significant. Based on this, I would reject H0 and not reject H1. (d) In order to determine the effectiveness of a short-term therapeutic implementation, we administered the Acme Depression Inventory (ADI), which renders a score from 0 to 75 (0 = low depression, 75 = high depression) before and after treatment for a group of 15 participants. The mean level of the depression dropped from 69.80 to 67.20; this 2.6point change (% = -3.72) is considered to be statistically significant (p = .008;  = .05).

These findings suggest that this short-term therapy model facilitates an effective reduction in depressive symptoms among these individuals.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Exercise 7.5, Data Set A (a) H0: A 15-minute individual session with a bowling coach has no effect on bowling scores.

H1: A 15-minute individual session with a bowling coach enhances bowling scores. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

19 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 151.60 157.73

pretest - posttest

N 15 15

Std. Deviation 15.459 13.936

Std. Error Mean 3.991 3.598

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Std. Error Mean Deviation Mean Lower Upper -6.133 6.512 1.681 -9.740 -2.527

t -3.648

df 14

Sig. (2-tailed) .003

Fifteen students bowled an initial game and scored a average of 151.60, then a coach provided 15 minutes of instructions based on observations made during the student’s first game. Student’s average score in the second game was 157.73. This 6.13-point increase produced a p level of .003; since this is less than the  level of .05, this is considered to be a statistically significant difference. Based on these findings, we would reject H0, and not reject H1. (d) To assess the effectiveness of short-term coaching, 15 students bowled one game with a coach observing unobtrusively. Next, the coach provided 15 minutes of individual coaching, after which, each student bowled a second game. On the average, scores were 6.13 points higher in the second game (157.73, up from 151.60 in their first game).

This finding is considered to be statistically significant (p = .003,  = .05). Based on these findings, we will continue to use this coaching method for bowling, and we will be evaluating the utility of providing this style of coaching for other sports.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20 Exercise 7.5, Data Set B (a) H0: A 15-minute individual session with a bowling coach has no effect on bowling scores.

H1: A 15-minute individual session with a bowling coach enhances bowling scores. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

21 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 72.50 74.25

pretest - posttest

N 8 8

Mean -1.750

Std. Deviation 3.742 3.919

Std. Error Mean 1.323 1.386

Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper 4.773 1.688 -5.741 2.241

t -1.037

df 7

Sig. (2-tailed) .334

Eight students bowled an initial game and scored a average of 72.50, then a coach provided 15 minutes of instructions based on observations made during the student’s first game. Student’s average score in the second game was 74.25. This 1.75-point increase produced a p level of .334; since this is greater than the  level of .05, this is not considered to be a statistically significant difference. Based on these findings, we would not reject H0, and reject H1. (d) To assess the effectiveness of short-term coaching, eight students bowled one game with a coach observing unobtrusively. Next, the coach provided 15 minutes of individual coaching, after which, the student bowled a second game. On the average, students’ scores were 1.75 points higher in their second game (74.25, up from 72.50 in their first game). This finding is not considered to be statistically significant (p = .334,  = .05). Based on these findings, we are considering evaluating if this form of coaching may provide more promising results for different individual sports (e.g., golf, archery, weight training).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

22 Exercise 7.6, Data Set A (a) H0: Using a laptop computer does not enhance grades.

H1: Using a laptop computer enhances grades. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 67.50 76.15

Mean -8.650

N 20 20

Std. Deviation 24.528

Std. Deviation Std. Error Mean 18.936 4.234 16.024 3.583 Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Error Mean Lower Upper 5.485 -20.129 2.829

t -1.577

df Sig. (2-tailed) 19 .131

Grades (0%-100%) were gathered on 20 students for the semesters before and after having been issued a laptop computer. Mean grade scores increased from 67.50 to 76.15; however, since the p value of .131 is greater than the .05  level, this modest increase is not considered to be significantly different. Based on this, I would not reject H0 and reject H1. (d) We issued laptop computers to 20 students to determine if having such a device would impact academic performance. We compared their mean overall grades (0%-100%) from the semester before to the semester after the laptops were issued; overall, mean grade scores increased from 67.50 to 76.15, however using an  level of .05, this 8.65point increase was determined not to be statistically significant (p = .131).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24 Exercise 7.6, Data Set B (a) H0: Using a laptop computer does not enhance grades.

H1: Using a laptop computer enhances grades. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

25 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 75.50 82.70

Mean -7.200

N

Std. Deviation 13.117

20 20

Std. Deviation Std. Error Mean 11.062 2.474 7.512 1.680

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Error Mean Lower Upper 2.933 -13.339 -1.061

t -2.455

df 19

Sig. (2-tailed) .024

Grades (0%-100%) were gathered on 20 students for the semesters before and after having been issued a laptop computer. Mean grade scores increased from 75.5 to 82.7, with a p value of .024; since this is less than the .05  level, this increase is considered to be significant. Based on this, I would reject H0 and not reject H1. (d) We issued laptop computers to 20 students to determine if having such a device would impact academic performance. We compared their mean overall grades (0%-100%) from the semester before to the semester after the laptops were issued; overall, mean grade scores increased 7.2 points, from 75.5 to 82.7. Using an  level of .05, this 7.2point increase (% = 9.5) was determined to be a statistically significant improvement (p = .024).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 Exercise 7.7, Data Set A (a) H0: Acme allergy medicine has no effect on sneezing.

H1: Acme allergy medicine reduces sneezing. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

27 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 15.39 12.61

pretest - posttest

N 18 18

Mean 2.778

Std. Deviation Std. Error Mean 3.274 .772 3.165 .746 Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper 3.318 .782 1.128 4.428

t 3.552

df 17

Sig. (2-tailed) .002

Eighteen people who were experiencing allergy symptoms were recruited and asked to count their total number of sneezes for a day. The next day, they took the Acme allergy medicine as directed, and counted their total number of sneezes for that (second) day.

This resulted in an average of 2.77 fewer sneezes (an average of 15.39 on the first day, and 12.61 on the second day). Using a .05  level, this difference is considered to be statistically significant. As such, we would reject H0, and not reject H1. (d) To determine if Acme allergy medicine helps reduce sneezing among those experiencing allergy symptoms, 18 participants were recruited and instructed to count their total number of sneezes for 1 day. The next morning, each took the Acme allergy medicine as directed, and counted their total sneezes for that day. On average, participants sneezed a total of 15.39 times the day before taking the medication, and 12.61 times after taking the medication; an average of 2.77 fewer sneezes. This difference is considered to be statistically significant (p = .002,  = .05), suggesting that the medicine provided some allergy symptom relief.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

28 Exercise 7.7, Data Set B (a) H0: Acme allergy medicine has no effect on sneezing.

H1: Acme allergy medicine reduces sneezing. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

29 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 4.10 3.95

pretest - posttest

N 21 21

Mean .143

Std. Deviation Std. Error Mean 1.640 .358 1.830 .399 Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper 2.798 .611 -1.131 1.416

t .234

df 20

Sig. (2-tailed) .817

Twenty-one people who were experiencing allergy symptoms were recruited and asked to count their total number of sneezes for a day. The next day, they took the Acme allergy medicine as directed, and counted their total number of sneezes for that (second) day. This resulted in an average of .15 fewer sneezes (an average of 4.10 on the first day, and 3.95 on the second day). This rendered a p of .817; since the p value is greater than the designated .05  level, this difference is not considered to be statistically significant. As such, we would not reject H0, and reject H1. (d) To determine if Acme allergy medicine helps reduce sneezing among those experiencing allergy symptoms, 21 participants were recruited and instructed to count their total number of sneezes for 1 day. The next morning, they took the Acme allergy medicine as directed, and counted their total sneezes for that day. On average, participants sneezed a total of 4.10 times the day before taking the medication, and 3.95 times after taking the medication, amounting to an average of .15 fewer sneezes.

This reduction is not considered to be statistically significant (p = .817,  = .05), suggesting that this medicine was not particularly helpful for these individuals.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

30 Exercise 7.8, Data Set A (a) H0: Tutsle root tea does not lower fever.

H1: Tutsle root tea lowers fever. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

31 (1c)

The paired t test revealed the following: Paired Samples Statistics

Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 100.893 100.782

Mean .1110

N 100 100

Std. Deviation Std. Error Mean .7727 .0773 .6911 .0691

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Deviation Std. Error Mean Lower Upper 1.1094 .1109 -.1091 .3311

t 1.001

df 99

Sig. (2-tailed) .319

Body temperatures were gathered on 100 patients who had fever before and after giving each a cup of Tutsle root tea. The mean pre-tea temperature was 100.893; after the tea, the mean temperature dropped .111 to 100.782, however, since the p value of .319 is greater than the .05  level, we would say that the Tutsle root tea did not make a statistically significant impact in terms of reducing temperature in these patients. Based on this, I would not reject H0 and reject H1. (d) To determine if Tutsle root tea had any viable medicinal value when it comes to reducing fever, we recruited 100 patients who had fever. We recorded their body temperature before and 1 hour after having a cup of this tea. Mean temperature went from 100.893 down to 100.782, however this .111 decrease is not considered to be statistically significant (p = .319;  = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

32 Exercise 7.8, Data Set B (a) H0: Tutsle root tea does not lower fever.

H1: Tutsle root tea lowers fever. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

33 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

Mean 100.817 100.593

pretest posttest

pretest - posttest

Mean .2240

N 150 150

Std. Deviation Std. Error Mean .8229 .0672 .7443 .0608

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Deviation Std. Error Mean Lower Upper 1.0644 .0869 .0523 .3957

t 2.577

df 149

Sig. (2-tailed) .011

Body temperatures were gathered on 100 patients who had fever before and after giving each a cup of Tutsle root tea. The mean pre-tea temperature was 100.817; after the tea, the mean temperature dropped .224 to 100.593. Since the p value of .011 is less than the .05  level, we would say that the Tutsle root tea made a statistically significant impact in terms of reducing temperature in these patients. Based on this, I would reject H0 and not reject H1. (d) To determine if Tutsle root tea had any viable medicinal value when it comes to reducing fever, we recruited 100 patients who had fever. We recorded their body temperature before and 1 hour after having a cup of this tea. Mean temperature was reduced .224, from 100.817 down to 100.593. This finding is considered to be statistically significant (p = .011  = .05).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 Exercise 7.9, Data Set A (a) H0: Chocolate has no effect on attitude.

H1: Chocolate enhances attitude. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

35 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 81.91 80.85

pretest - posttest

N 75 75

Mean 1.053

Std. Deviation Std. Error Mean 5.707 .659 5.897 .681 Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper 9.078 1.048 -1.035 3.142

t 1.005

df 74

Sig. (2-tailed) .318

Seventy-five people were recruited to determine if chocolate helps enhance attitude. We began by administering the Acme Attitude Survey (AAS) (0 = very bad attitude, 100 = very good attitude) resulting in an average score of 81.91. After eating a piece of chocolate fudge cake, participants answered the AAS again; on average, the results dropped by .96 points to 80.85. This change in the AAS score produced a p level of .318, which using a .05  level is not statistically significant. This suggests that the chocolate cake did not make a statistically significant impact on attitude, hence, we would not reject H0, and reject H1. (d) To better comprehend the effects that chocolate might have on attitude, 75 participants were recruited; we began by administering the Acme Attitude Survey (AAS) which renders a score ranging from 0 to 100 (0 = very bad attitude, 100 = very good attitude).

Next, each participant was served a generous slice of chocolate fudge cake. After the cake, participants were asked to complete a second AAS. The pretest revealed a mean attitude score of 81.91; contrary to our expectations, the post-chocolate AAS score dropped an average of .96 points, to 80.85, however, this rendered a p value of .318.

Using a .05  level, this drop in the AAS is not considered to be statistically significant.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

36 Exercise 7.9, Data Set B (a) H0: Chocolate has no effect on attitude.

H1: Chocolate enhances attitude. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

37 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

Mean 81.17 83.27

pretest - posttest

N 75 75

Mean -2.093

Std. Deviation Std. Error Mean 5.869 .678 6.267 .724 Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Difference Std. Error Deviation Mean Lower Upper 8.056 .930 -3.947 -.240

t -2.250

df 74

Sig. (2-tailed) .027

Seventy-five people were recruited to determine if chocolate helps enhance attitude. We began by administering the Acme Attitude Survey (AAS) (0 = very bad attitude, 100 = very good attitude) resulting in an average score of 81.17. After eating a piece of chocolate fudge cake, participants answered the AAS again; on average, the results rose by 2.10 points to 83.27. This change in the AAS score produced a p level of .027, which, using a .05  level, is considered to be statistically significant. This suggests that the chocolate cake made a statistically significant impact on attitude; hence, we would reject H0, and not reject H1. (d) To better comprehend the effects that chocolate might have on attitude, 75 participants were recruited. We began by administering the Acme Attitude Survey (AAS) which renders a score ranging from 0 to 100 (0 = very bad attitude, 100 = very good attitude).

After collecting the AAS forms, each participant was served a generous slice of chocolate fudge cake. After the cake, participants were asked to complete a second AAS. The pretest revealed a mean attitude score of 81.17, and after dining on the chocolate cake, the mean AAS score went up an average of 2.10 points, to 83.27.

These figures rendered a p value of .027. Using a .05  level, this increase in the AAS score suggests that chocolate may help enhance attitude.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 Exercise 7.10, Data Set A (a) H0: The speech will not enhance voter’s likelihood to vote for the candidate.

H1: The speech will enhance voter’s likelihood to vote for the candidate. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

39 (1c)

The paired t test revealed the following: Paired Samples Statistics

Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 3.68 4.47

N 53 53

Std. Deviation Std. Error Mean 1.578 .217 1.908 .262

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Mean Std. Deviation Std. Error Mean Lower Upper -.792 2.522 .346 -1.488 -.097

t -2.288

df 52

Sig. (2-tailed) .026

Prior to listening to a candidate’s speech, attendees were asked to rate their voting intentions using a 7-point scale (1 = absolutely won’t vote for the candidate, 7 = absolutely will vote for the candidate). After the speech, the survey is readministered to determine the impact (if any) of the speech. The pretest score was 3.68, and the posttest score was 4.47, with a p value of .026. Using the traditional .05  level, this suggests that the speech facilitated a statistically significant (positive) impact. Based on this, I would reject H0 and not reject H1. (d) To gauge the impact of a political speech, attendees were asked to rate their voting intentions prior to the speech (1 = absolutely won’t vote for the candidate, 7 = absolutely will vote for the candidate); at the conclusion of the speech, attendees were asked to respond (again) to the same question. The scores increased by 21.47%, from 3.68 to 4.47. The p value of .026 is less than the  level of .05 suggesting that this speech made a statistically significant impact. Per these findings, we will continue to use this message in the campaign efforts.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40 Exercise 7.10, Data Set B (a) H0: The speech will not enhance voter’s likelihood to vote for the candidate.

H1: The speech will enhance voter’s likelihood to vote for the candidate. (b) After computing the difference between the pretest score and posttest score (diff = posttest - pretest), a histogram with normal curve was plotted for this difference (diff).

The graph below presents a symmetrical (bell-shaped) normal curve for diff, thus satisfying this criterion.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

41 (c) The paired t test revealed the following: Paired Samples Statistics Pair 1

Pair 1

pretest posttest

pretest - posttest

Mean 3.96 3.94

N 53 53

Std. Deviation Std. Error Mean 1.467 .202 1.549 .213

Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Mean Std. Deviation Std. Error Mean Lower Upper .019 2.325 .319 -.622 .660

t .059

df Sig. (2-tailed) 52 .953

Prior to listening to a candidate’s speech, attendees were asked to rate their voting intentions using a 7-point scale (1 = absolutely won’t vote for the candidate, 7 = absolutely will vote for the candidate). After the speech, the survey is readministered to determine the impact (if any) of the speech. The pretest score was 3.96, and the posttest score was 3.94, with a p value of .953. Using the traditional .05  level, this suggests that although the speech had a negative impact, it was not statistically significant. Based on this, I would not reject H0 and reject H1. (d) To gauge the impact of a political speech, attendees were asked to rate their voting intentions prior to the speech (1 = absolutely won’t vote for the candidate, 7 = absolutely will vote for the candidate); at the conclusion of the speech, attendees were asked to respond (again) to the same question. The scores (unexpectedly) dropped by .02 points (% = -.51) from 3.96 to 3.94. The p value of .953 is greater than the  level of .05, suggesting that while this speech appeared to have lowered voter’s opinions of the candidate, this reduction is not considered to be statistically significant. Per these findings, it is clear that the speech needs to be retooled to impart a more (positively) effective message.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 8 Correlation and Regression— Pearson and Spearman Solutions to All Exercises

Exercise

Page

Exercise

Page

8.1A....................2

8.6A ................. 32

8.1B....................5

8.6B ................. 35

8.2A....................8

8.7A ................. 38

8.2B..................11

8.7B ................. 41

8.3A..................14

8.8A ................. 44

8.3B..................17

8.8B ................. 46

8.4A..................20

8.9A ................. 49

8.4B..................23

8.9B ................. 50

8.5A..................26

8.10A ............... 51

8.5B..................29

8.10B ............... 52

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 8.1, Data Set A (a) H0: There is no significant correlation between hours of walking and weight loss H1: There is a significant correlation between hours of walking and weight loss. (b) Histograms with normal curve plots show a normal distribution for walkhrs and wtloss as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 The scatterplot below shows that the straight regression line reasonably fits the field of points, hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, hence the criterion of homoscedasticity is satisfied.

NOTE: Scatterplot with regression line for walkhrs and wtloss is linear and homoscedastic (pronounced: hoe-moe-skuh-daz-tick). (c) The correlations table below shows a positive correlation (r = .624) between walkhrs and wtloss; p = .006, which is less than the specified .05  level, indicating that this is a statistically significant correlation.

Correlations walkhrs walkhrs

wtloss

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

18 .624** .006

wtloss .624** .006

N 18 **. Correlation is significant at the 0.01 level (2-tailed).

18 1 18

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 (d) In a study examining the effects of brisk walking on weight loss, 18 adults were recruited and instructed to walk as many days of the week they could for as long as they could. The researcher gathered each participant’s daily walking time, as well as their weight at the beginning and end of the week and found a positive, statistically significant correlation between the amount of walking time and the amount of weight lost (r = .624, p = .006;  = .05). In other words, the more the participants walked, the more weight they lost. These findings suggest that moderate daily exercise may be effective in facilitating weight loss. As such, we reject H0, and do not reject H1.

NOTE: You might also inspect the descriptive statistics for walkhrs and wtloss, and consider including the supplement in your findings: “Participants averaged 4.1 hours of walking per week and had an average weight loss of 1.5 pounds.”

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 Exercise 8.1, Data Set B (1) H0: There is no significant correlation between hours of walking and weight loss H1: There is a significant correlation between hours of walking and weight loss. (b) Histograms with normal curve plots show a normal distribution for walkhrs and wtloss as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 The scatterplot below shows that the straight regression line reasonably fits the field of points, hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a positive correlation (r = .250) between walkhrs and wtloss; however, since p = .317, which is greater than the specified .05  level, this indicates that this is not a statistically significant correlation.

Correlations walkhrs walkhrs

wtloss

wtloss .250 .317

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

18 .250 .317

18 1

18

18

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 (d) In a study examining the effects of brisk walking on weight loss, 18 adults were recruited and instructed to walk as many days of the week they could for as long as they could. The researcher gathered each participant’s daily walking time, as well as their weight at the beginning and end of the week and found a positive, correlation between the amount of walking time and the amount of weight lost (r = .250). Although the participants experienced some weight loss in this study, the correlation between walking and weight loss was not statistically significant (p = .317;  = .05). As such, we do not reject H0, and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 Exercise 8.2, Data Set A (a) H0: There is no significant correlation between nonwork computer usage and socialization satisfaction.

H1: There is a significant correlation between nonwork computer usage and socialization satisfaction. (b) Histograms with normal curve plots show a normal distribution for comphrs and assi as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a positive correlation (r = .317) between comphrs and assi; p = .173, which is greater than the specified .05  level. This indicates that this is not a statistically significant correlation.

Correlations comphrs

assi

Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N

comphrs 1

assi .317 .173

20 .317 .173

20 1

20

20

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 (d) We recruited 20 participants to investigate if there was a correlation between the number of hours individuals spend using computers in their nonwork hours compared to their level of social satisfaction. Participants provided an estimate of their weekly nonwork computer hours and administered the Acme Social Satisfaction Index, which quantifies socialization satisfaction (0 = very low social satisfaction, 80 = very high social satisfaction). Though a positive correlation between these two variables was detected (r = .317), this is not considered to be a statistically significant correlation (p = .173;  = .05). Per these findings, we do not reject H0 and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 Exercise 8.2, Data Set B (a) H0: There is no significant correlation between nonwork computer usage and socialization satisfaction.

H1: There is a significant correlation between nonwork computer usage and socialization satisfaction. (b) Histograms with normal curve plots show a normal distribution for comphrs and assi as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.497) between comphrs and assi; p = .016, which is less than the specified .05  level. This indicates that this is a statistically significant correlation.

Correlations comphrs

assi

Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed)

comphrs 1

assi -.497* .016

23 -.497* .016

23 1

N 23 *. Correlation is significant at the 0.05 level (2-tailed).

23

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 (d) We recruited 23 participants to investigate if there was a correlation between the number of hours individuals spend using computers in their nonwork hours compared to their level of social satisfaction. Participants provided an estimate of their weekly nonwork computer hours and administered the Acme Social Satisfaction Index, which quantifies socialization satisfaction (0 = very low social satisfaction, 80 = very high social satisfaction). We detected a negative correlation between these two variables (r = -.497). This is considered to be a statistically significant correlation (p = .016;  = .05); hence, it appears that individuals who spend fewer nonwork hours using a computer tend to have higher levels of socialization satisfaction. Per these findings, we rejected H0 and we did not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 8.3, Data Set A (a) H0: There is no significant correlation between income and happiness.

H1: There is a significant correlation between income and happiness. (b) Histograms with normal curve plots show a normal distribution for income and alhs as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 The scatterplot below shows that the straight regression line reasonably fits the field of points, hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.026) between income and alhs; however, p = .917, which is greater than the specified .05  level, indicating that this is not a statistically significant correlation, as illustrated in the above scatterplot.

Note the flatness of the regression line, along with the distance of the points from the regression line.

Correlations income income

alhs

alhs -.026 .917

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

18 -.026 .917

18 1

18

18

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 (d) In a study exploring the relationship between money and happiness, 18 adults were recruited and given a self-administered survey, which asked their annual income. The survey also included the Acme Life Happiness Scale (ALHS), a 10-question survey that renders a score from 0 to 100, with 0 being very unhappy, and 100 being very happy.

Our findings revealed a slight negative correlation (r = -.026), meaning that earning more money was slightly associated with less happiness, however, this (negative) correlation was not found to be statistically significant (p = .917;  = .05). As such, we did not reject H0, and we rejected H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

17 Exercise 8.3, Data Set B (a) H0: There is no significant correlation between income and happiness.

H1: There is a significant correlation between income and happiness. (b) Histograms with normal curve plots show a normal distribution for income and alhs as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 The scatterplot below shows that the straight regression line reasonably fits the field of points, hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a positive correlation (r = .468) between income and alhs. Since p = .032, is less than the specified .05 α level, this indicates that this is a statistically significant correlation.

Correlations income income

alhs

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

21 .468* .032

alhs .468* .032

N 21 *. Correlation is significant at the 0.05 level (2-tailed).

21 1 21

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

19 (d) In a study exploring the relationship between money and happiness, 21 adults were recruited and given a self-administered survey that asked their annual income; the survey also included the Acme Life Happiness Scale (ALHS), a 10-question survey that renders a score from 0 to 100 (0 = very unhappy, 100 = very happy). Our findings revealed a positive correlation (r = .468), meaning that earning more money was associated with higher levels of happiness; this (positive) correlation was found to be statistically significant (p = .032; α = .05). As such, we reject H0 but do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20

Exercise 8.4, Data Set A (a) H0: There is no significant correlation between the duration of listening to a news broadcast and mood.

H1: There is a significant correlation between the duration of listening to a news broadcast and mood. (b) Histograms with normal curve plots show a normal distribution for minnews and amr as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

21 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.657) between minnews and amr; p = .011, which is less than the specified .05  level, indicates that this is a statistically significant correlation.

Correlations minnews minnews

amr

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

14 -.657* .011

N 14 *. Correlation is significant at the 0.05 level (2-tailed).

amr -.657* .011 14 1 14

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

22 (d) We recruited 14 participants to investigate if there was a correlation between the duration of listening to a news broadcast and mood. Participants were played a recording of a morning news broadcast and instructed to press STOP whenever they chose; we recorded this as minnews (minutes of news). Next, each participant completed the Acme Mood Report (AMR), a self-administered instrument that renders a score between 0 and 100 (0 = very bad mood, 100 = very good mood). We detected a negative correlation between these two variables (r = -.657); this is considered to be a statistically significant correlation (p = .011;  = .05), hence it appears that those who spend more time listening to broadcast news can expect to have lower mood quality.

Per these findings, we rejected H0 and we did not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 Exercise 8.4, Data Set B (a) H0: There is no significant correlation between the duration of listening to a news broadcast and mood.

H1: There is a significant correlation between the duration of listening to a news broadcast and mood. (b) Histograms with normal curve plots show a normal distribution for minnews and amr as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a positive correlation (r = .562) between minnews and amr; p = .091, which is greater than the specified .05  level, indicates that this is not a statistically significant correlation.

Correlations minnews minnews

amr

amr .562 .091

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

10 .562 .091

10 1

10

10

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

25 (d) We recruited 10 participants to investigate if there was a correlation between the duration of listening to a news broadcast and mood. Participants were played a recording of a morning news broadcast and instructed to press STOP whenever they chose; we recorded this as minnews (minutes of news). Next, each participant completed the Acme Mood Report (AMR), a self-administered instrument that renders a score between 0 and 100 (0 = very bad mood, 100 = very good mood). Although we detected a positive correlation between these two variables (r = .562), suggesting that listening to news is positively correlated with mood, this correlation is not statistically significant (p = .091;  = .05). Per these findings, we did not reject H0 and rejected H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 Exercise 8.5, Data Set A (a) H0: There is no significant correlation between years of education and job satisfaction.

H1: There is a significant correlation between years of education and job satisfaction. (b) Histograms with normal curve plots show a normal distribution for yearsed and ajsi as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

27 The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a positive correlation (r = .679) between income and ajsi; p = .004, which is less than the specified .05  level, indicating that this is a statistically significant correlation, as illustrated in the scatterplot above; note the positive slope of the regression line and that most of the points are clustered fairly close to the regression line.

Correlations yearsed yearsed

ajsi

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

16 .679** .004

ajsi .679** .004

N 16 **. Correlation is significant at the 0.01 level (2-tailed).

16 1 16

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

28 (d) In order to assess the possible correlation between years of education and job satisfaction, 16 adults were recruited and given a self-administered survey which asked how many years of education they had; the survey also included the Acme Job Satisfaction Inventory (AJSI), a six question survey that renders a score from 0 to 60, with 0 being very dissatisfied with one’s job, and 60 being very satisfied. The participants’ education level ranged from 11th grade through master’s degree. Our findings revealed a relatively strong positive correlation (r = .679), suggesting that those with more education tended to get more satisfaction from their jobs; this correlation was found to be statistically significant (p = .004;  = .05). As such, we reject H0, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

29 Exercise 8.5, Data Set B (a) H0: There is no significant correlation between years of education and job satisfaction.

H1: There is a significant correlation between years of education and job satisfaction. (b) Histograms with normal curve plots show a normal distribution for yearsed and ajsi as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

30 The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a relatively weak positive correlation (r = .196) between income and ajsi, however, p = .484, which is greater than the specified .05  level, indicating that this is not a statistically significant correlation, as illustrated in the scatterplot above; note the slight positive slope of the regression line and that most of the points are clustered fairly far from the regression line.

Correlations yearsed yearsed

ajsi

ajsi .196 .484

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

15 .196 .484

15 1

15

15

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

31 (d) In order to assess the possible correlation between years of education and job satisfaction, 15 adults were recruited and given a self-administered survey which asked how many years of education they had; the survey also included the Acme Job Satisfaction Inventory (AJSI), a six question survey that renders a score from 0 to 60, with 0 being very dissatisfied with one’s job, and 60 being very satisfied. The participant’s education level ranged from 11th grade through master’s degree. Our findings revealed a relatively weak positive correlation (r = .196), suggesting that those with more education tended to get somewhat more satisfaction from their jobs, however this correlation was not found to be statistically significant (p = .484;  = .05). As such, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

32 Exercise 8.6, Data Set A (a) H0: There is no significant correlation between age and number of meals eaten out of the house.

H1: There is a significant correlation between age and number of meals eaten out of the house. (b) Histograms with normal curve plots show a normal distribution for age and mealsout as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

33 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.181) between age and mealsout; p = .433, which is greater than the specified .05  level, indicates that this is not a statistically significant correlation.

Correlations age age

mealsout

mealsout -.181 .433

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

21 -.181 .433

21 1

21

21

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 (d) We recruited 21 participants to investigate if there was a correlation between age and the number of meals eaten outside the home in a given month. Although we detected a negative correlation between these two variables (r = -.181) (e.g., older individuals tended to have fewer meals out than those who are younger), this is not considered to be a statistically significant correlation (p = .433;  = .05). Per these findings, we did not reject H0 and we did reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

35 Exercise 8.6, Data Set B (a) H0: There is no significant correlation between age and number of meals eaten out of the house.

H1: There is a significant correlation between age and number of meals eaten out of the house. (b) Histograms with normal curve plots show a normal distribution for age and mealsout as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

36 The scatterplot below shows that the straight regression line reasonably fits the field of points, and hence the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends, and hence the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.538) between age and mealsout. The p = .032, which is less than the specified .05  level, indicates that this is a statistically significant correlation.

Correlations age age

mealsout

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

16 -.538* .032

mealsout -.538* .032

N 16 *. Correlation is significant at the 0.05 level (2-tailed).

16 1 16

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

37 (d) We recruited 16 participants to investigate if there was a correlation between age and the number of meals eaten outside the home in a given month. We detected a negative correlation between these two variables (r = -.538); older individuals tended to have fewer meals out than those who are younger. This correlation is considered to be statistically significant (p = .032;  = .05). Per these findings, we rejected H0 and did not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 Exercise 8.7, Data Set A (a) H0: There is no significant correlation between height and self-confidence.

H1: There is a significant correlation between height and self-confidence. (b) Histograms with normal curve plots show a normal distribution for height and asci as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

39 The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a relatively weak negative correlation (r = -.024) between height and asci; p = .882, which is greater than the specified .05  level, indicating that this is not a statistically significant correlation. As illustrated in the above scatterplot, the regression line is relatively flat and most of the points are clustered fairly far from the regression line.

Correlations height height

asci

asci -.024 .882

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

41 -.024 .882

41 1

41

41

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40 (d) To evaluate the possible correlation between height and self-confidence, 41 adults were recruited and given a self-administered survey which asked them to indicate their height; the survey also included the Acme Self-Confidence Index (ASCI), a 10-question survey that renders a score from 0 to 50 (0 = very low self-confidence, 50 = very high self-confidence). Our findings suggest that although there was a negative correlation between the variables (r = -.024), suggesting that taller people were slightly less selfconfident than shorter people. Further analysis revealed that this correlation is not statistically significant (p = .882;  = .05). As such, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

41 Exercise 8.7, Data Set B (a) H0: There is no significant correlation between height and self-confidence.

H1: There is a significant correlation between height and self-confidence. (b) Histograms with normal curve plots show a normal distribution for height and asci as shown in the two figures below, hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

42 The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a relatively weak positive correlation (r = .098) between height and asci, however, p = .492, which is greater than the specified .05  level, indicating that this is not a statistically significant correlation. As illustrated in the above scatterplot, the regression line is relatively flat and most of the points are clustered fairly far from the regression line.

Correlations height height

asci

asci .098 .492

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

51 .098 .492

51 1

51

51

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

43 (d) To evaluate the possible correlation between height and self-confidence, 51 adults were recruited and given a self-administered survey which asked to indicate their height; the survey also included the Acme Self-Confidence Index (ASCI), a 10-question survey that renders a score from 0 to 50 (0 = very low self-confidence, 50 = very high selfconfidence). Our findings suggest that although there was a slight positive correlation between the variables (r = .098), implying that taller people tend to have more selfconfidence than shorter people. However, it was determined that this correlation is not statistically significant (p = .492;  = .05). As such, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

44 Exercise 8.8, Data Set A (a) H0: There is no significant correlation between video game score and academic grade.

H1: There is a significant correlation between video game score and academic grade. (b) Histograms with normal curve plots show a normal distribution for score and grade as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

45

(c) The correlations table below shows a negative correlation (r = -.450) between score and academic grade. The p = .010, which is less than the specified .05  level, indicates that this is a statistically significant correlation.

Correlations score score

grade

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

32 -.450** .010

grade -.450** .010

N 32 **. Correlation is significant at the 0.01 level (2-tailed).

32 1 32

(d) We recruited 32 participants to investigate if there was a correlation between video game score and their overall grade. We detected a negative correlation between these two variables (r = -.450); those with higher video game scores were negatively correlated with academic grade. The principle behind this is that in order to achieve such (high) scores, more video game practice time is required, thereby compromising time that could be used for academics. This (negative) correlation is considered to be statistically significant (p = .010;  = .05). Per these findings, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

46 Exercise 8.8, Data Set B (a) H0: There is no significant correlation between video game score and academic grade.

H1: There is a significant correlation between video game score and academic grade. (b) Histograms with normal curve plots show a normal distribution for score and grade as shown in the two figures below; hence, the pretest criterion of normality is satisfied.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

47 The scatterplot below shows that the straight regression line reasonably fits the field of points; hence, the criterion of linearity is satisfied. The scatterplot also shows that the points are primarily clustered toward the center of the regression line with substantially fewer points toward the ends; hence, the criterion of homoscedasticity is satisfied.

(c) The correlations table below shows a negative correlation (r = -.322) between score and grade. The p = .088, which is greater than the specified .05  level, indicates that this is not a statistically significant correlation.

Correlations score score

grade

grade -.322 .088

Pearson Correlation Sig. (2-tailed)

1

N Pearson Correlation Sig. (2-tailed)

29 -.322 .088

29 1

29

29

N

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

48 (d) We recruited 29 participants to investigate if there was a correlation between video game score and their academic grade. We detected a negative correlation between these two variables (r = -.316); those with higher video game scores were negatively correlated with grade. The principle behind this is that in order to achieve such (high) scores, more video game practice time is required, thereby compromising time that could be used for academics. Despite this (expected) negative correlation, it is not considered to be statistically significant (p = .088;  = .05). Per these findings, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

49 Exercise 8.9, Data Set A (a) H0: There is no significant correlation in consumer car color preferences between the Pico and Sepulveda dealerships.

H1: There is a significant correlation in consumer car color preferences between the Pico and Sepulveda dealerships. (b) We gathered car sales data from the Pico and Sepulveda sites, noting how many of each color (black, blue, red, silver, white, yellow) were sold at each site. (c) The Spearman’s rho produced a positive correlation (.886) between pico and sepulveda; p = .019, which is less than the specified .05  level, indicating that this is a statistically significant correlation.

Correlations Spearman’s rho

pico

Correlation Coefficient Sig. (2-tailed) N sepulveda Correlation Coefficient Sig. (2-tailed) N *. Correlation is significant at the 0.05 level (2-tailed).

pico 1.000 .

6 .886* .019 6

sepulveda .886* .019 6 1.000 .

6

(d) To evaluate the similarity of consumer car color preferences between the Pico dealership and the Sepulveda dealership, we reviewed the sales database and ranked the color from most sold to least sold for the specified time frame for each site.

Spearman analysis revealed a statistically significant positive correlation (.886) suggesting that consumer car color preferences were similar between these two sites (p = .019,  = .05). As such, we reject H0, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

50 Exercise 8.9, Data Set B (a) H0: There is no significant correlation in consumer car color preferences between the Pico and Sepulveda dealerships.

H1: There is a significant correlation in consumer car color preferences between the Pico and Sepulveda dealerships. (b) We gathered car sales data from the Pico and Sepulveda sites, noting how many of each color (black, blue, red, silver, white, yellow) were sold at each site. (c) The Spearman’s rho produced a positive correlation (.143) between pico and sepulveda; p = .787, which is greater than the specified .05  level, indicating that this is not a statistically significant correlation.

Correlations Spearman’s rho

pico

sepulveda

Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N

pico 1.000 .

6 .143 .787 6

sepulveda .143 .787 6 1.000 .

6

(d) To evaluate the similarity of consumer car color preferences between the Pico dealership and the Sepulveda dealership, we reviewed the sales database and ranked the color from most sold to least sold for the specified time frame for each site.

Spearman analysis revealed a statistically insignificant positive correlation (.143) suggesting that consumer car color preferences were not similar between these two sites (p = .787,  = .05). As such, we do not reject H0, and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

51 Exercise 8.10, Data Set A (a) H0: There is no significant correlation in movie type preferences between Ariel and Dusty.

H1: There is a significant correlation in movie type preferences between Ariel and Dusty. (b) In order to assess movie viewing compatibility, we asked Ariel and Dusty to each indicate their preferences by placing 13 movie types (Action/Adventure, Animation, Comedy, Cult Movie, Documentary, Fantasy, Film Noir, Horror, Romantic, Sci-Fi, Spy, Western, Zombies) in order from most to least favorite. (c) The Spearman’s rho produced a negative correlation (-.335), with a p value of .263; since the p is greater than the specified .05  level, this suggests that there is no statistically significant correlation between Ariel’s and Dusty’s movie preferences.

Correlations Spearman’s rho

ariel

dusty

Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N

ariel 1.000 .

13 -.335 .263 13

dusty -.335 .263 13 1.000 .

13

(d) To evaluate the similarity of movie preference types between Ariel and Dusty, we provided each of them with a list of 13 movie types (Action/Adventure, Animation, Comedy, Cult Movie, Documentary, Fantasy, Film Noir, Horror, Romantic, Sci-Fi, Spy, Western, Zombies), and asked them to rank them from most- to least preferable.

Spearman analysis revealed a statistically insignificant negative correlation (rho = -.335, p = .263,  = .05), meaning that their movie preferences are dissimilar. As such, we do not reject H0, and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

52 Exercise 8.10, Data Set B (a) H0: There is no significant correlation in movie type preferences between Ariel and Dusty.

H1: There is a significant correlation in movie type preferences between Ariel and Dusty. (b) In order to assess movie viewing compatibility, we asked Ariel and Dusty to each indicate their preferences by placing 13 movie types (Action/Adventure, Animation, Comedy, Cult Movie, Documentary, Fantasy, Film Noir, Horror, Romantic, Sci-Fi, Spy, Western, Zombies) in order from most to least favorite. (c) The Spearman’s rho produced a positive correlation (.747), with a p value of .003; since the p is less than the specified .05  level, this suggests that there is a statistically significant correlation between Ariel’s and Dusty’s movie preferences.

Correlations Spearman’s rho

ariel

Correlation Coefficient Sig. (2-tailed) N dusty Correlation Coefficient Sig. (2-tailed) N **. Correlation is significant at the 0.01 level (2-tailed).

ariel 1.000 .

13 .747** .003 13

dusty .747** .003 13 1.000 .

13

(d) To evaluate the similarity of movie preference types between Ariel and Dusty, we provided each of them with a list of 13 movie types (Action/Adventure, Animation, Comedy, Cult Movie, Documentary, Fantasy, Film Noir, Horror, Romantic, Sci-Fi, Spy, Western, Zombies), and asked them to rank them from most- to least preferable.

Spearman analysis revealed a statistically significant positive correlation (rho = .747, p = .003,  = .05), meaning that their movie preferences are similar. As such, we reject H0, and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 9 Chi-Square Solutions to All Exercises

Exercise

Page

Exercise

Page

9.1A....................2

9.6A ................. 22

9.1B....................4

9.6B ................. 24

9.2A....................6

9.7A ................. 26

9.2B....................8

9.7B ................. 28

9.3A..................10

9.8A ................. 30

9.3B..................12

9.8B ................. 32

9.4A..................14

9.9A ................. 34

9.4B..................16

9.9B ................. 36

9.5A..................18

9.10A ............... 38

9.5B..................20

9.10B ............... 40

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 9.1, Data Set A (a) H0: There is no significant difference in bill-paying method in terms of age.

H1: There is a significant difference in bill-paying method in terms of age. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. age * billpay Crosstabulation Count Check age

Total

18 - 25 26 - 35 36 - 55 56 - 99

7 6 12 28 53

billpay E-pay 25 19 28 8 80

Other

Total 9 5 6 11 31

41 30 46 47 164

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

3 (c) The Chi-Square Tests table below shows a Sig. (p) value of .000, which is less than the specified .05  level, indicating that there is a statistically significant difference among the age groups when it comes to bill-paying preference.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 30.983a 32.731 7.707 164

df 6 6 1

Asymp. Sig. (2-sided) .000 .000 .006

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.67.

(d) To determine if age is associated with bill-paying method, we surveyed 164 adults. Epay was the predominate method of payment for those between 18 - 55; specifically, 61% of 18 - 25 year olds use e-pay, as did 63% of those between 26 - 35, and 61% of 36 - 55 year olds, whereas 60% of those over 56 years old opted for paying by check.

Our findings revealed a statistically significant difference in bill-paying method with respect to age (p < .001,  = .05). As such, we reject H0, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

4 Exercise 9.1, Data Set B (a) H0: There is no significant difference in bill-paying method in terms of age.

H1: There is a significant difference in bill-paying method in terms of age. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. age * billpay Crosstabulation Count Check age

Total

18 - 25 26 - 35 36 - 55 56 - 99

6 8 10 19 43

billpay E-pay 53 39 62 50 204

Other

Total 18 9 11 15 53

77 56 83 84 300

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 (c) The Chi-Square Tests table below shows a Sig. (p) value of .105, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the age groups when it comes to bill-paying preference.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 10.508a 10.359 4.866 300

df 6 6 1

Asymp. Sig. (2-sided) .105 .110 .027

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.03.

(d) To determine if age is associated with bill-paying method, we surveyed 300 adults. Epay was the predominate method of payment. Specifically, among 18 - 25 year olds, 69% opt for e-pay; among 26 - 35 year olds, 70% use e-pay; for 36 - 55 year olds, 75% use e-pay; and among those 56 and over, 60% use e-pay. Our findings revealed no statistically significant difference in bill-paying method with respect to age (p = .105,  = .05). As such, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 Exercise 9.2, Data Set A (a) H0: Gender has no bearing on headphone wearing on the bus.

H1: Gender has a bearing on headphone wearing on the bus. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. gender * headphones Crosstabulation Count

gender Total

Female Male

headphones Headphones No headphones 7 10 15 5 22 15

Total 17 20 37

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 (c) The Chi-Square Tests table below shows a Sig. (p) value of .037, which is less than the specified .05  level, indicating that there is a statistically significant difference among the genders when it comes to headphone wearing.

Chi-Square Tests Asymp. Sig. (2df sided) 1 .037

Pearson Chi-Square

Value 4.361a

Continuity Correctionb

3.071

1

.080

Likelihood Ratio

4.432

1

.035

Exact Sig. (2-sided)

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

.050 4.243

1

Exact Sig. (1-sided)

.039

.039

37

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.89. b. Computed only for a 2x2 table

(d) To determine if gender is associated with headphone usage on public buses, we unobtrusively gathered data on bus riders noting gender (female/male) and headphone wearing status (wearing headphones/not wearing headphones). Seven of the 17 females (41%) were observed wearing headphones, compared to 15 of the 20 (75%) of the males. Our X2 (chi-square) analysis revealed that there was a statistically significant difference in headphone wearing with respect to gender (p = .037,  = .05); male bus riders tend to wear headphones (statistically) significantly more than females. As such, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 Exercise 9.2, Data Set B (a) H0: Gender has no bearing on headphone wearing on the bus.

H1: Gender has a bearing on headphone wearing on the bus. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. gender * headphones Crosstabulation Count

gender Total

Female Male

headphones Headphones No headphones 18 8 11 6 29 14

Total 26 17 43

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 (c) The Chi-Square Tests table below shows a Sig. (p) value of .757, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the genders when it comes to headphone wearing.

Chi-Square Tests Asymp. Sig. (2df sided) 1 .757

Pearson Chi-Square

Value .096a

Continuity Correctionb

.000

1

1.000

Likelihood Ratio

.095

1

.757

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

Exact Sig. (2-sided)

1.000 .094

1

Exact Sig. (1-sided)

.506

.760

43

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.53. b. Computed only for a 2x2 table

(d) To determine if gender is associated with headphone usage on public buses, we unobtrusively gathered data on bus riders noting gender (female/male) and headphone wearing status (wearing headphones/not wearing headphones). Eighteen of the 26 females (69%) were observed wearing headphones, compared to 11 of the 17 (65%) of the males. Our X2 (chi-square) analysis revealed that there was no statistically significant difference in headphone wearing with respect to gender (p = .757,  = .05).

As such, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

10 Exercise 9.3, Data Set A (a) H0: The flu shot does not help prevent the flu.

H1: The flu shot helps prevent the flu. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. flushot * flusick Crosstabulation Count

flushot Total

Had flu shot Did not have flu shot

flusick Did not get sick Got sick with flu with flu 5 7 11 7 16 14

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 12 18 30

11 (c) The Chi-Square Tests table below shows a Sig. (p) value of .296, which is greater than the specified .05  level, indicating that there is no statistically significant difference in flu sickness comparing those who got a flu shot to those who did not.

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .296

Pearson Chi-Square

Value 1.094a

Continuity Correctionb

.452

1

.501

Likelihood Ratio

1.098

1

.295

Exact Sig. (2-sided)

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

.457 1.057

1

Exact Sig. (1-sided)

.251

.304

30

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.60. b. Computed only for a 2x2 table

(d) To determine if there were significantly fewer cases of flu among those who had a flu shot compared to those who did not, we analyzed the health status of 30 participants.

Sixty days after recruiting participants, our researcher contacted each one to find out if they had contracted the flu. We found that 12 had gotten flu shots, and 18 had not.

Among those who got the flu shot, 41% reported that they had gotten sick with the flu, compare to 61% among those who did not get a flu shot. Even though there were proportionally fewer cases of flu among those who had a flu shot, chi-square analysis indicates that this difference is not statistically significant (p = .296,  = .05). As such, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 Exercise 9.3, Data Set B (a) H0: The flu shot does not help prevent the flu.

H1: The flu shot helps prevent the flu. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. flushot * flusick Crosstabulation Count

flushot Total

Had flu shot Did not have flu shot

flusick Did not get sick Got sick with flu with flu 5 10 15 6 20 16

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 15 21 36

13 (c) The Chi-Square Tests table below shows a Sig. (p) value of .023, which is less than the specified .05  level, indicating that there is a statistically significant difference in flu sickness comparing those who got a flu shot to those who did not.

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .023

Pearson Chi-Square

Value 5.143a

Continuity Correctionb

3.716

1

.054

Likelihood Ratio

5.238

1

.022

Exact Sig. (2-sided)

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

.041 5.000

1

Exact Sig. (1-sided)

.026

.025

36

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.67. b. Computed only for a 2x2 table

(d) To determine if there were significantly fewer cases of flu among those who had a flu shot compared to those who did not, we analyzed the health status of 36 participants.

Sixty days after recruiting participants, our researcher contacted each one to find out if they had contracted the flu. We found that 15 had gotten flu shots, and 21 had not.

Among those who got the flu shot, 33% reported that they had gotten sick with the flu, compare to 63% among those who did not get a flu shot. Chi-square analysis indicates that this difference is statistically significant (p = .023,  = .05). As such, we reject H0, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14 Exercise 9.4, Data Set A (a) H0: Degree program (bachelor’s/master’s) has no bearing on type of learning selection (in classroom/remote learning).

H1: Degree program (bachelor’s/master’s) has a bearing on type of learning selection (in classroom/remote learning). (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. degree * location Crosstabulation Count

degree Total

Bachelor’s Master’s

location In classroom Remote learning 13 7 5 11 18 18

Total

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20 16 36

15 (c) The Chi-Square Tests table below shows a Sig. (p) value of .044, which is less than the specified .05  level, indicating that there is a statistically significant difference among the student’s degree program when it comes to preferred learning location.

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .044

Pearson Chi-Square

Value 4.050a

Continuity Correctionb

2.813

1

.094

Likelihood Ratio

4.134

1

.042

Exact Sig. (2-sided)

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

.092 3.938

1

Exact Sig. (1-sided)

.046

.047

36

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.00. b. Computed only for a 2x2 table

(d) To determine if the student’s current degree program is associated with preferred learning location we analyzed data on bachelor’s and master’s students. Thirteen of the 20 bachelor’s students (65%) preferred in-classroom learning over remote learning, whereas 11 of the 16 (69%) master’s students opted for remote learning. Our X2 (chisquare) analysis revealed this difference to be statistically significant (p = .044,  = .05).

As such, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 Exercise 9.4, Data Set B (a) H0: Degree program (bachelor’s/master’s) has no bearing on type of learning selection (in classroom/remote learning).

H1: Degree program (bachelor’s/master’s) has a bearing on type of learning selection (in classroom/remote learning). (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. degree * location Crosstabulation Count

degree Total

Bachelor’s Master’s

location In classroom Remote learning 12 9 5 8 17 17

Total

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

21 13 34

17 (c) The Chi-Square Tests table below shows a Sig. (p) value of .290, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the student’s degree program when it comes to preferred learning location.

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .290

Pearson Chi-Square

Value 1.121a

Continuity Correctionb

.498

1

.480

Likelihood Ratio

1.129

1

.288

Exact Sig. (2-sided)

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

.481 1.088

1

Exact Sig. (1-sided)

.241

.297

34

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.50. b. Computed only for a 2x2 table

(d) To determine if the student’s current degree program is associated with preferred learning location we analyzed data on bachelor’s and master’s students. Twelve of the 21 bachelor’s students (57%) preferred in-classroom learning over remote learning, compared to 5 of the 13 (38%) master’s students. Our X2 (chi-square) analysis revealed that this difference is not statistically significant (p = .290,  = .05). As such, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Exercise 9.5, Data Set A (a) H0: Responses are the same across media (face-to-face interview, mail-in survey, online survey) when it comes to asking about substance abuse.

H1: Responses vary significantly across media (face-to-face interview, mail-in survey, online survey) when it comes to asking about substance abuse. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. media * drugs Crosstabulation Count drugs Yes media

Total

Face-to-face interview Mail-in survey Online survey

No 5 5 6 16

Total 10 12 8 30

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 17 14 46

19 (c) The Chi-Square Tests table below shows a Sig. (p) value of .729, which is greater than the specified .05  level, indicating that there is no statistically significant difference in responses across the three media tested: face-to-face interview, mail-in survey, and online survey.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value .632a .626 .270 46

df 2 2 1

Asymp. Sig. (2-sided) .729 .731 .603

a. 1 cells (16.7%) have expected count less than 5. The minimum expected count is 4.87.

(d) To determine if media makes a difference in responses when it comes to inquiries regarding illegal substance use, we recruited 46 subjects and asked each to respond to one question: “Have you ever used illegal drugs?” however our method of inquiry varied. Subjects were randomly assigned to one of three groups; the 15 participants in Group 1 were asked the question via face-to-face interview, the 17 people assigned to Group 2 responded via standard pencil and paper mail-in survey, and the 14 in Group 3 were directed to an online survey website. The results revealed that 33% of those that were asked the question via face-to-face replied “Yes,” they had used illegal (drugs at least once), compared to 29% in the mail-in group, and 43% in the online group.

Though there is some response variability among these media, chi-square analysis revealed that these differences are not statistically significant (p = .729,  = .05). Hence, we do not reject H0, and we do reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

20 Exercise 9.5, Data Set B (a) H0: Responses are the same across media (face-to-face interview, mail-in survey, online survey) when it comes to asking about substance abuse.

H1: Responses vary across media (face-to-face interview, mail-in survey, online survey) when it comes to asking about substance abuse. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criteria are satisfied. media * drugs Crosstabulation Count drugs Yes media

Total

Face-to-face interview Mail-in survey Online survey

No 6 13 11 30

Total 12 5 6 23

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 18 17 53

21 (c) The Chi-Square Tests table below shows a Sig. (p) value of .045, which is less than the specified .05  level, indicating that there is a statistically significant difference in responses across the three media tested: face-to-face interview, mail-in survey, and online survey.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 6.210a 6.287 3.537 53

df 2 2 1

Asymp. Sig. (2-sided) .045 .043 .060

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.38.

(d) To determine if media makes a difference in responses when it comes to inquiries regarding illegal substance use, we recruited 53 subjects and asked each to respond to one question: “Have you ever used illegal drugs?” however our method of inquiry varied. Subjects were randomly assigned to one of three groups; the 18 participants in Group 1 were asked the question via face-to-face interview, the 18 people assigned to Group 2 responded via standard pencil and paper mail-in survey, and the 17 in Group 3 were directed to an online survey website. The results revealed that 33% of those who were asked the question face-to-face replied “Yes,” they had used illegal drugs (at least once), compared to 72% in the mail-in group, and 64% in the online group. Chi-square analysis revealed that these differences are statistically significant (p = .045,  = .05).

Hence, we would reject H0, and not reject H1. These findings suggest that when it comes to sensitive issues, participants who are interviewed face-to-face seem to “sanitize”/alter their responses to reveal less negative disclosure than those responding by less identifiable means (mail-in/online surveys).

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

22 Exercise 9.6, Data Set A (a) H0: Degree program (bachelor’s/master’s/doctorate) has no bearing on preferred class time (day/night).

H1: Degree program (bachelor’s/master’s/doctorate) has a bearing on preferred class time (day/night). (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. time * degree Crosstabulation Count

time Total

Day Night

Bachelor’s 26 9 35

degree Master’s 20 16 36

Doctorate 9 5 14

Total 55 30 85

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

23 (c) The Chi-Square Tests table below shows a Sig. (p) value of .256, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the student’s degree program when it comes to preferred class time selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 2.727a 2.759 1.150 85

df 2 2 1

Asymp. Sig. (2-sided) .256 .252 .284

a. 1 cells (16.7%) have expected count less than 5. The minimum expected count is 4.94.

(d) To determine if the student’s current degree program (bachelor’s/master’s/doctorate) is associated with preferred class time (day/night courses) we surveyed 85 students; 26 of the 35 bachelor’s students (74%) preferred day classes, along with 20 of the 36 (56%) of the master’s students and 9 of the 14 (64%) of the doctoral students. Our X2 (chisquare) analysis revealed that this difference is not statistically significant (p = .256,  = .05). As such, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

24 Exercise 9.6, Data Set B (a) H0: Degree program (bachelor’s/master’s/doctorate) has no bearing on preferred class time (day/night).

H1: Degree program (bachelor’s/master’s/doctorate) has a bearing on preferred class time (day/night). (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. time * degree Crosstabulation Count

time Total

Day Night

Bachelor’s 35 11 46

degree Master’s 19 29 48

Doctorate 8 5 13

Total 62 45 107

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

25 (c) The Chi-Square Tests table below shows a Sig. (p) value of .002, which is less than the specified .05  level, indicating that there is a statistically significant difference among the student’s degree program when it comes to preferred class time selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 12.923a 13.247 5.168 107

df 2 2 1

Asymp. Sig. (2-sided) .002 .001 .023

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.47.

(d) We surveyed 107 students: 46 bachelor’s, 48 master’s, and 13 doctoral students to determine if the student’s current degree program is associated with preferred class time (day/night courses). We found that 76% of bachelor’s students and 62% of doctoral students prefer day classes, while 60% of master’s students prefer night classes. Our X2 (chi-square) analysis revealed that these differences are statistically significant; degree appears to have some bearing with respect to class time preference (p = .002,  = .05).

As such, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

26 Exercise 9.7, Data Set A (a) H0: Age is not associated with voting practices.

H1: Age is associated with voting practices. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criteria is satisfied. age * vote Crosstabulation Count

age

Total

18-35 36-64 65 - older

Vote in person 6 11 9 26

vote Vote by mail 14 28 16 58

Not vote 6 19 8 33

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 26 58 33 117

27 (c) The Chi-Square Tests table below shows a Sig. (p) value of .802, which is greater than the specified .05  level, indicating that there is no statistically significant difference in voting practices across age groups.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 1.640a 1.630 .068 117

df 4 4 1

Asymp. Sig. (2-sided) .802 .803 .794

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.78.

(d) To determine if voting practices vary significantly across age groups, we surveyed a total of 117 participants in three age groups: 26 were 18 - 35, 58 were 36 - 64, and 33 were 65 or older, and asked each about how they voted in the last election: voted in person, voted by mail, or did not vote. Overall, half of those surveyed voted by mail; specifically, 24% of 36 - 64 year olds voted by mail, followed by 14% of those who are 65 or older, and 12% of the 18 - 35 year olds. Twenty-two percent of those surveyed indicated that they voted in-person, and 28% did not vote. Among those who opted not to vote, the majority (58%) were in the 36 - 64 age group. Despite the moderate variability in voting practices observed among these groups, chi-square analysis indicates that these differences are not statistically significant (p = .802,  = .05).

Hence, we do not reject H0, and we reject H1. Among these groups, mail-in voting appears to be the preferred option.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

28 Exercise 9.7, Data Set B (a) H0: Age is not associated with voting practices.

H1: Age is associated with voting practices. (b) Per the Crosstabluaion table below, each cell contains an n of at least 5; hence, the pretest criteria is satisfied. age * vote Crosstabulation Count

age

Total

18-35 36-64 65 - older

Vote in person 5 6 20 31

vote Vote by mail 8 15 16 39

Not vote 12 5 5 22

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 25 26 41 92

29 (c) The Chi-Square Tests table below shows a Sig. (p) value of .003, which is less than the specified .05  level, indicating that there is a statistically significant difference in voting practices based on age groups.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 15.871a 14.947 11.533 92

df 4 4 1

Asymp. Sig. (2-sided) .003 .005 .001

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.98.

(d) To determine if voting practices vary significantly across age groups, we surveyed a total of 92 participants in three age groups: 25 were 18 - 35, 26 were 36 - 64, and 41 were 65 or older, and asked each about how they voted in the last election: voted in person, voted by mail, or did not vote. Each group indicated a different majority: 48% of those in the 18 - 35 group did not vote, 58% of those in the 36 - 64 group voted by mail, and 49% of those 64 and older voted in-person. Chi-square analysis revealed that there is a statistically significant difference among age groups when it comes to voting practices (p = .003,  = .05). Hence, we rejected H0, and we did not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

30 Exercise 9.8, Data Set A (a) H0: Dog breed has no bearing on food selection.

H1: Dog breed has a bearing on food selection. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. dog * food Crosstabulation Count Food A dog

Total

Cocker Spaniel Beagle Keeshond

7 16 15 38

food Food B 19 8 9 36

Food C 4 6 6 16

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 30 30 30 90

31 (c) The Chi-Square Tests table below shows a Sig. (p) value of .033, which is less than the specified .05  level, indicating that there is a statistically significant difference among the dog breeds with respect to food selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 10.509a 10.567 1.098 90

df 4 4 1

Asymp. Sig. (2-sided) .033 .032 .295

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.33.

(d) We tested 90 dogs—30 Cocker Spaniels, 30 Beagles, and 30 Keeshonds individually, allowing each dog to select which of three different foods was the favorite. The majority (63%) of the Cocker Spaniels preferred Food B, whereas 53% of the Beagles and 50% of the Keeshonds opted for Food A. Our X2 (chi-square) analysis revealed that these differences are statistically significant; dog breed appears to have some bearing with respect to food preference (p = .033,  = .05). As such, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

32 Exercise 9.8, Data Set B (a) H0: Dog breed has no bearing on food selection.

H1: Dog breed has a bearing on food selection. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. dog * food Crosstabulation Count

dog

Total

Cocker Spaniel Beagle Keeshond

Food A 21 19 16 56

food Food B 5 7 8 20

Food C 4 4 6 14

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 30 30 30 90

33 (c) The Chi-Square Tests table below shows a Sig. (p) value of .745, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the dog breeds with respect to food selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 1.950a 1.959 1.442 90

df 4 4 1

Asymp. Sig. (2-sided) .745 .743 .230

a. 3 cells (33.3%) have expected count less than 5. The minimum expected count is 4.67.

(d) We tested 90 dogs—30 Cocker Spaniels, 30 Beagles, and 30 Keeshonds individually, allowing each dog to select which of three different foods was the favorite. The majority of dogs in each breed (70% of Cocker Spaniels, 63% of Beagles, and 53% of Keeshonds) showed a preference for Food A. Our X2 (chi-square) analysis revealed that there is no statistically significance among the breeds when it comes to food preference (p = .745,  = .05). Additionally, Foods B and C came in second and third place for all three breeds. As such, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

34 Exercise 9.9, Data Set A (a) H0: There is no significant difference in university admissions based on high school (public vs. private).

H1: There is a significant difference in university admissions based on high school (public vs. private). (b) Per the Crosstabluaion table below, each (highlighted) cell contains an n of at least 5; hence, the pretest criteria is satisfied. school * college Crosstabulation Count

school Total

Acme Academy Anytown High School

college Not attending Attending university university 22 27 109 116 131 143

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 49 225 274

35 (c) The Chi-Square Tests table below shows a Sig. (p) value of .652, which is greater than the specified .05  level, indicating that there is no statistically significant difference in university admissions based on school (public vs. private).

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .652

Pearson Chi-Square

Value .203a

Continuity Correctionb

.086

1

.770

Likelihood Ratio

.203

1

.652

Fisher’s Exact test

Exact Sig. (2-sided)

.753

Linear-by-Linear Association

.202

N of Valid Cases

274

1

Exact Sig. (1-sided)

.386

.653

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 23.43. b. Computed only for a 2x2 table

(d) We evaluated college admission rates from two schools: The Acme Academy, a private school with a graduating class of 49 students, and Anytown High school, a public school with a graduating class of 225 students. We found that 55% of those who graduated the Acme Academy were admitted to a university, compared to 52% of the students who graduated from Anytown High School. In terms of total students, Acme Academy launched a total of 27 students into higher education, compared to 116 students from Anytown High School. Despite the variability among these figures, chi-square analysis indicates that the difference is not statistically significant (p = .652,  = .05). Hence, we do not reject H0, and we reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

36 Exercise 9.9, Data Set B (a) H0: There is no significant difference in university admissions based on high school (public vs. private).

H1: There is a significant difference in university admissions based on high school (public vs. private). (b) Per the Crosstabluaion table below, each (highlighted) cell contains an n of at least 5, hence, the pretest criteria is satisfied. school * college Crosstabulation Count

school Total

Acme Academy Anytown High School

college Not attending Attending university university 5 28 72 78 77 106

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Total 33 150 183

37 (c) The Chi-Square Tests table below shows a Sig. (p) value of .001, which is less than the specified .05  level, indicating that there is a statistically significant difference in university admissions based on school (public vs. private).

Chi-Square Tests Asymp. Sig. df (2-sided) 1 .001

Pearson Chi-Square

Value 11.975a

Continuity Correctionb

10.666

1

.001

Likelihood Ratio

13.301

1

.000

11.910

1

.001

Fisher’s Exact test Linear-by-Linear Association N of Valid Cases

Exact Sig. (2-sided)

.000

Exact Sig. (1-sided)

.000

183

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 13.89. b. Computed only for a 2x2 table

(d) We evaluated college admission rates from two schools: The Acme Academy, a private school with a graduating class of 33 students, and Anytown High school, a public school with a graduating class of 150 students. We found that 85% of those who graduated the Acme Academy were admitted to a university, compared to 52% of the students who graduated from Anytown High School. In terms of total students, Acme Academy launched a total of 28 students into higher education, compared to 78 students from Anytown High School. Despite the higher total number of students admitted to a university from the public school, chi-square analysis indicates that proportionally, the Acme Academy significantly outperformed Anytown Public High School when it comes to college admissions (p = .001,  = .05). Hence, we reject H0, and we do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

38 Exercise 9.10, Data Set A (a) H0: Gender has no bearing on mayoral selection.

H1: Gender has a bearing on mayoral selection. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. gender * vote Crosstabulation Count Smith gender Total

Female Male

19 9 28

vote Jones 22 33 55

Undecided 11 6 17

Total

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

52 48 100

39 (c) The Chi-Square Tests table below shows a Sig. (p) value of .029, which is less than the specified .05  level, indicating that there is a statistically significant difference among the genders with respect to mayoral selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value 7.093a 7.199 .471 100

df 2 2 1

Asymp. Sig. (2-sided) .029 .027 .493

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.16.

(d) We surveyed 100 voters, 52 females and 48 males; both genders favored Jones in the next mayoral election, however whereas 42% of females opted for Jones, 69% of males favored Jones. Although Jones wins the plurality among both genders, our X2 (chisquare) analysis revealed a statistically significant difference among the genders when it comes to their voting propensities, in particular, the level of support for Jones (p = .029,  = .05). As such, we reject H0 and do not reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

40 Exercise 9.10, Data Set B (a) H0: Gender has no bearing on mayoral selection.

H1: Gender has a bearing on mayoral selection. (b) Per the Crosstabulation table below, each cell contains an n of at least 5; hence, the pretest criterion is satisfied. gender * vote Crosstabulation Count Smith gender Total

Female Male

15 17 32

vote Jones 24 31 55

Undecided

Total

7 6 13

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

46 54 100

41 (c) The Chi-Square Tests table below shows a Sig. (p) value of .796, which is greater than the specified .05  level, indicating that there is no statistically significant difference among the genders with respect to mayoral selection.

Chi-Square Tests

Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases

Value .456a .455 .053 100

df 2 2 1

Asymp. Sig. (2-sided) .796 .797 .818

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.98.

(d) We surveyed 100 voters—46 females and 54 males; both genders ranked the mayoral candidates in the same preference order—Jones first, Smith second, and finally, Undecided. Specifically, 57% of the men and 52% of the women surveyed opted for Jones. Our X2 (chi-square) analysis revealed no statistically significant differences among the genders when it comes to their voting propensities (p = .796,  = .05). As such, we do not reject H0 and reject H1.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

1

Chapter 10 Supplemental SPSS Operations Solutions to All Exercises

Exercise

Page

10.1 ................... 2 10.2 ................... 4 10.3 ................... 7 10.4 ................... 9 10.5 ................. 10 10.6 ................. 13 10.7 ................. 15 10.8 ................. 16 10.9 ................. 17 10.10 ............... 18

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

2 Exercise 10.1

Rec.# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

name Adrian Alex Avery Bailey Blaine Blake Bo Brett Brook Cameron Cary Casey Chris Corey Dale Daryl Dean Devin Drew Dustin Dusty Erin Evan Jaden Jan Jean Jess Jessie Kelly Kerry Kyle Lee Lindsay Morgan Ray Rene Riley Robin Ryan Sandy Sean Spencer Taylor Toby

(a) score 50 46 62 71 88 22 70 27 61 67 37 59 12 44 48 71 84 49 75 71 82 44 42 82 59 5 34 72 68 17 58 39 73 82 27 49 27 46 2 92 11 85 22 58

skill Novice Novice Novice Intermediate Expert Novice Intermediate Novice Novice Novice Novice Novice Novice Novice Novice Intermediate Intermediate Novice Intermediate Intermediate Intermediate Novice Novice Intermediate Novice Novice Novice Intermediate Novice Novice Novice Novice Intermediate Intermediate Novice Novice Novice Novice Novice Expert Novice Expert Novice Novice

Rec.# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

name Sandy Blaine Spencer Dean Dusty Jaden Morgan Drew Lindsay Jessie Bailey Daryl Dustin Bo Kelly Cameron Avery Brook Zane Casey Jan Kyle Toby Val Adrian Devin Rene Dale Alex Robin Corey Erin Evan Lee Cary Jess Brett Ray Riley Blake Taylor Kerry Chris Sean

(b) score 92 88 85 84 82 82 82 75 73 72 71 71 71 70 68 67 62 61 61 59 59 58 58 58 50 49 49 48 46 46 44 44 42 39 37 34 27 27 27 22 22 17 12 11

skill Expert Expert Expert Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice Novice

3 45 46

Val Zane

58 61

Novice Novice

45 46

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

Jean Ryan

5 2

Novice Novice

4 Exercise 10.2 NOTE: The random numbers will vary for each run.

The Syntax for this operation is: COMPUTE number=rnd(rv.uniform(852,5723)).

EXECUTE. 1532 2953 3834 2268 1611 4259 2539 3023 1107 1355 1540 1061 3880 1600 4336 5374 3668 2128 4383 1033 1342 4421 1950 1931 3824 5499 2006 2501 1109 4448 1436 1139 1768 1337 4144 4226 5074

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

5 2563 3270 4271 1855 4619 1178 3419 4076 5410 2390 3398 4582 1471 3577 5638 2436 3460 3325 2226 2543 5339 2840 1318 2478 3876 3975 4516 1850 1550 3024 2650 3216 1336 4387 1033 1703 2257 4110 4560 4764 4276 1085 2772 1966 4389 5150

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

6 1740 2214 4240 5248 1450 3325 1423 5356 3372 2174 3992 3988 5006 1169

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

7 Exercise 10.3 (a) Statistics score N

Valid Missing

11 0 Mean 75.73 Median 73.00 Mode 71a Std. Deviation 5.551 Variance 30.818 Range 14 Minimum 70 Maximum 84 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

8 (b) Statistics score N

Valid Missing

25 0 Mean 45.16 Median 46.00 Mode 27a Std. Deviation 12.957 Variance 167.890 Range 40 Minimum 22 Maximum 62 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

9 Exercise 10.4 (a) Descriptives Score N Control Treatment Total

Mean 79.44 80.60 80.03

43 45 88

Std. Deviation 3.588 3.374 3.508

Std. Error .547 .503 .374

95% Confidence Interval for Mean Lower Bound Upper Bound 78.34 80.55 79.59 81.61 79.29 80.78

Minimum 73 73 73

ANOVA Score Between Groups Within Groups

Sum of Squares 29.493 1041.405

Total

df 1 86

1070.898

Mean Square 29.493 12.109

F 2.436

Sig. .122

87

(b) Paired Samples Statistics Pair 1

Mean 498.69 516.96

pretest posttest

N 214 214

Std. Deviation Std. Error Mean 88.434 6.045 102.169 6.984

Paired Samples Correlations N Pair 1

Pair 1

pretest & posttest

pretest - posttest

214

Correlation -.087

Sig. .203

Paired Samples Test Paired Differences 95% Confidence Interval Std. of the Difference Std. Error Mean Deviation Mean Lower Upper -18.276 140.852 9.628 -37.255 .704

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

t -1.898

df 213

Sig. (2-tailed) .059

Maximum 86 87 87

10 Exercise 10.5 (a) Rec. # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

name Brook Ray Spencer Cary Morgan Erin Toby Zane Riley Lee Corey Ryan Drew Jess Jaden Dustin Bo Val Blake Dean Casey Jessie Chris Robin Evan Jan Daryl Dale Devin Sandy Avery Lindsay Rene Blaine Kyle Cameron Sean Kerry Brett Bailey Jean Kelly Taylor Alex

score 61 27 85 37 82 44 58 61 27 39 44 2 75 34 82 71 70 58 22 84 59 72 12 46 42 59 71 48 49 92 62 73 49 88 58 67 11 17 27 71 5 68 22 46

skill Novice Novice Expert Novice Intermediate Novice Novice Novice Novice Novice Novice Novice Intermediate Novice Intermediate Intermediate Intermediate Novice Novice Intermediate Novice Intermediate Novice Novice Novice Novice Intermediate Novice Novice Expert Novice Intermediate Novice Expert Novice Novice Novice Novice Novice Intermediate Novice Novice Novice Novice

result Fail Fail Pass Fail Pass Fail Fail Fail Fail Fail Fail Fail Pass Fail Pass Pass Pass Fail Fail Pass Fail Pass Fail Fail Fail Fail Pass Fail Fail Pass Fail Pass Fail Pass Fail Fail Fail Fail Fail Pass Fail Fail Fail Fail

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

11 45 46

Adrian Dusty

50 82

Novice Intermediate

Fail Pass

(b) Statistics score N

Valid Missing

32 0 Mean 40.97 Median 45.00 Mode 27a Std. Deviation 18.838 Variance 354.870 Range 66 Minimum 2 Maximum 68 a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

12 (c) Statistics score N

Valid

14

Missing

0

Mean

78.43

Median

78.50

Mode

71a

Std. Deviation

7.377

Variance

54.418

Range

22

Minimum

70

Maximum

92

a. Multiple modes exist. The smallest value is shown

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

13 Exercise 10.6 SORT CASES BY reading(A) writing(D) math(A).

FREQUENCIES VARIABLES=reading math /FORMAT=NOTABLE /STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN MODE /HISTOGRAM NORMAL /ORDER=ANALYSIS. Statistics N

Valid Missing

Mean Median Mode Std. Deviation Variance Range Minimum Maximum

reading 118 0 70.90 72.00 74 11.336 128.502 45 50 95

math 118 0 54.18 55.50 62 14.773 218.233 62 24 86

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

14

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

15 Exercise 10.7 comment Program: Report1.sas. comment Programmer: H Knapp. comment Revision: 1. comment Data file: Ch 10 - Exercise 06.sav. comment This program runs the report for the reading, writing, and math scores. comment It sorts the data: reading (ascending), writing (descending), math (ascending). comment Finally, it runs descriptive statistics with histograms for reading and math scores. comment Sort the data using a three-level sort: (1) reading [ascending], (2) writing [descending], (3) math [ascending].

SORT CASES BY reading(A) writing(D) math(A). comment Run descriptive statistics (mean, median, mode, maximum, minimum, range, standard deviation, and variance) for reading and math; also include histograms with normal curves for those variables.

FREQUENCIES VARIABLES=reading math /FORMAT=NOTABLE /STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN MODE /HISTOGRAM NORMAL /ORDER=ANALYSIS. comment End of Syntax file.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

16 Exercise 10.8 The Master file is the file that is prepared and ready to begin working with, but I wouldn’t perform any analyses on the Master file. Before starting any statistical work, it’s a good idea to make a backup of the Master file by naming it something like “MyData(Master).sav,” and then making a copy of that file that I’d use to do my analyses—that file should be called “MyData(Working).sav.” This way, if I were to make a mistake that alters or deletes any data, I could always get a fresh copy from the (untouched) Master file. The Master file should be stored safely on some backup media and/or a different computer. Any media or computer that contains any such data (Master or Work file) should be stored in an appropriately secure setting.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

17 Exercise 10.9 The purpose of the Work file is to preserve the source (Master) data set in its original form to protect against operator or system errors. Before beginning to work on a data set, it is good practice to make two copies of it: one to save in its original state, and another to work on. For example, if the original file is called Project18.sav, I would make two copies of the data: Project18[MASTER].sav and Project18[WORK].sav.

I would only work on the Project18[WORK].sav file and store Project18[MASTER].sav someplace safe. If somehow the Project18[WORK].sav file became altered or corrupted, I could easily create a new Project18[WORK].sav work file from the Project18[MASTER].sav file.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.

18 Exercise 10.10 As a scientific researcher, I am committed to storing the data in a way that will protect it from theft, physical harm, tampering, and unauthorized access so as not to breach the quality of the data or the confidentiality of those who are the focus of the analysis. The integrity of the data is absolutely essential in order to provide accurate analyses. Some data may contain sensitive information such as patient identification, medical information, grades, financial figures, etc. An important part of the research process is to safeguard the data.

Depending on the designated protocols for data handling and data storage, nondigital media (e.g., paper records, survey cards, journals) should be stored in a securely locked cabinet or safe. Digital information (on computers or external storage media) should be stored in the same secured fashion to guard against physical threats. Digital information may also use encryption software to help confound unauthorized efforts to access the data. Passwords should be used whenever possible. If off-site storage is permitted or required, the same precautions should be taken. Whenever possible, it is preferable to remove or encode identifying data (e.g., social security numbers, names, phone numbers) to help preserve confidentiality.

At the conclusion of the study, the research protocol/policy should specify how long such data are to be retained, during which time, it should be securely stored. The protocol should also specify what’s to become of the data after the expiration date (e.g., move materials to secured archives, shred paper documents, use appropriate software to execute secured deletion of digital information from computer media and other storage media).

At all times, the integrity, safety, and confidentiality of the data should be considered and respected.

Knapp, Introductory Statistics Using SPSS, Second Edition. © 2017, SAGE Publications.