A First Course In Statistics 11th Edition Solution Manual by Ace Test Banks

A First Course In Statistics 11th Edition By James McClave, Terry Sincich

INSTRUCTOR’S SOLUTIONS MANUAL NANCY S. BOUDREAU Bowling Green State University

A F IRST C OURSE IN S TATISTICS ELEVENTH EDITION

James T. McClave Info Tech, Inc. University of Florida

Terry Sincich University of South Florida

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Table of Contents Chapter 1: Statistics, Data, and Statistical Thinking

Chapter 2: Methods for Describing Sets of Data

Chapter 3: Probability

Chapter 4: Discrete Random Variables

Chapter 5: Inferences Based on a Single Sample Estimation with Confidence Intervals

134

Chapter 6: Inferences Based on a Single Sample Tests of Hypothesis

163

Chapter 7: Comparing Population Means

199

Chapter 8: Comparing Population Proportions

248

Chapter 9: Simple Linear Regression

288

Preface This solutions manual is designed to accompany the text, A First Course in Statistics, Eleventh Edition, by James T. McClave and Terry Sincich. It provides solutions to the even-numbered exercises for each chapter in the text. (For solutions to the odd-numbered exercises, please refer to the Student’s Solutions Manual.) This manual is provided to help instructors save time in preparing presentations of the solutions and to possibly provide another point of view regarding their meaning. Other methods of solution may also be appropriate; however, the author has presented one that she believes to be the most instructive to the beginning statistics student. Some of the exercises are subjective in nature. Subjective decisions regarding these exercises have been made and are explained by the author. Solutions based on these decisions are presented; the solution to this type of exercise is often most instructive. When an alternative interpretation of an exercise may occur, the author has often addressed it and given justification for the approach taken.

Nancy S. Boudreau Bowling Green State University Bowling Green, Ohio

Statistics, Data, and Statistical Thinking 1 Chapter

Statistics, Data, and Statistical Thinking

1.2

Descriptive statistics utilizes numerical and graphical methods to look for patterns, to summarize, and to present the information in a set of data. Inferential statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data.

1.4

The first major method of collecting data is from a published source. These data have already been collected by someone else and is available in a published source. The second method of collecting data is from a designed experiment. These data are collected by a researcher who exerts strict control over the experimental units in a study. These data are measured directly from the experimental units. The third method of collecting data is from a survey. These data are collected by a researcher asking a group of people one or more questions. Again, these data are collected directly from the experimental units or people. The final method of collecting data is observationally. These data are collected directly from experimental units by simply observing the experimental units in their natural environment and recording the values of the desired characteristics.

1.6

A population is a set of existing units such as people, objects, transactions, or events. A variable is a characteristic or property of an individual population unit such as height of a person, time of a reflex, amount of a transaction, etc.

1.8

A representative sample is a sample that exhibits characteristics similar to those possessed by the target population. A representative sample is essential if inferential statistics is to be applied. If a sample does not possess the same characteristics as the target population, then any inferences made using the sample will be unreliable.

1.10

Statistical thinking involves applying rational thought processes to critically assess data and inferences made from the data. It involves not taking all data and inferences presented at face value, but rather making sure the inferences and data are valid.

1.12

High school GPA is a number usually between 0.0 and 4.0. Therefore, it is quantitative.

High school class rank is a number: 1st, 2nd, 3rd, etc. Therefore, it is quantitative.

The scores on the SAT's are numbers between 200 and 800. Therefore, it is quantitative.

Gender is either male or female. Therefore, it is qualitative.

Parent's income is a number: $25,000, $45,000, etc. Therefore, it is quantitative.

Age is a number: 17, 18, etc. Therefore, it is quantitative.

Chapter 1

1.14

The variable “difference between before and after sprint times” is measured in seconds. Thus, it is quantitative. The variable “improvement” is measured as one of three categories. Thus, it is qualitative.

b. The data set is a sample. It contains observations from only 14 of all high school football players. 1.16

1.18

The population of interest is all the students in the class. The variable of interest is the GPA of a student in the class.

Since GPA is measured on a numerical scale, it is quantitative.

Since the population of interest is all the students in the class and you obtained the GPA of every member of the class, this set of data would be a census.

Assuming the class had more than 10 students in it, the set of 10 GPAs would represent a sample. The set of ten students in only a subset of the entire class.

This average would have 100% reliability as an "estimate" of the class average, since it is the average of interest.

The average GPA of 10 members of the class will not necessarily be the same as the average GPA of the entire class. The reliability of the estimate will depend on how large the class is and how representative the sample is of the entire population.

In order for the sample to be a random sample, every member of the class must have an equal

Flight capability can have only 2 possible outcomes: volant or flightless. Thus, it is qualitative.

Habitat type can have only 3 possible outcomes: aquatic, ground terrestrial, or aerial terrestrial. Thus, it is qualitative.

Nesting site can have only 4 possible outcomes: ground, cavity within ground, tree, or cavity above ground. Thus, it is qualitative.

Nest density can have only 2 possible outcomes: high or low. Thus, it is qualitative.

Diet can have only 4 possible outcomes: fish, vertebrates, vegetables, or invertebrates. Thus, it is qualitative.

Body mass is measured in grams, a meaningful number. Thus, it is quantitative.

Egg length is measured in millimeters, a meaningful number. Thus, it is quantitative.

Extinct status can have only 3 possible outcomes: extinct, absent from island, or present. Thus, it is qualitative.

Statistics, Data, and Statistical Thinking 3 1.20

1.22

The 500 surgical patients represent a sample. There are many more than 500 surgical patients.

Yes, the sample is representative. It says that the surgical patients were randomly selected.

The variable measures on each patient was the status of herbal or alternative medicines. These data are qualitative because each response was either “yes” or “no”.

a. The population of interest is the set of all computer security personnel at all United States businesses. b. The data collection method used was a survey. Surveys were sent to all computer security personnel at all U.S. corporations and government agencies. However, in 2006, only 616 organizations responded to the survey. There could be nonresponse bias. Often, only those subjects with strong opinions will respond to a survey. Thus, the responses may not reflect what the population as a whole thinks. c. The variable measured in the survey is whether or not there was unauthorized use of computer systems at the firms during the year. Since the responses will be either ‘Yes” or ‘No’, the variable is qualitative. d. If we assume that the responses were a random sample from the population, we could infer that about 52% of all computer security personnel will admit to unauthorized use of computer systems at their firms during the year.

1.24.

a. The population of interest for the National Association of Broadcasters is all satellite radio subscribers. b. The variable of interest is whether or not a satellite radio subscriber has a satellite radio receiver in his/her car or not. c. The data for this variable is qualitative. The answer will be ‘yes’ or ‘no’. d. The sample of interest is the 501 satellite radio subscribers that were contacted. e. Of the 501 satellite radio subscribers contacted, 396 responded that they had a satellite receiver in their cars. The proportion of subscribers with a satellite receiver in their cars is 396/501 = .79. We can infer that 79% of all satellite radio subscribers have satellite receivers in their cars.

1.26

a. The population of interest is the set of all adults living in Tennessee. The sample of interest is the set of 575 people selected from Tennessee. b. The data collection method used was a survey. A random-digit telephone dialing procedure was used to collect the sample. Since some people do not own phones, this would not be a random sample. Everyone in the state of Tennessee would not have an equal chance of being selected. Those without telephones would tend to be the undereducated. Thus, there could be potential biases in the data.

Chapter 1 c. The two variables identified in this problem are the number of years of education and the insomnia status of each subject. d. The researchers inferred that the fewer the years of education, the more likely the person was to have chronic insomnia.

1.28

1.30

The population of interest is all men and women.

The sample of interest is the approximately 300 men and women from Gainesville, Florida, who participated in the study.

The study involves inferential statistics. The researcher is not particularly interested in the responses of just those subjects who participated in the study. She is interested in generalizing her findings to all men and women.

One variable is measured for each of the 20 objects placed. For each variable, the 2 possible outcomes were "yes" (place of object was recalled) and "no" (place of object was not recalled). Since the outcomes "yes" and "no" are not measured on a numerical scale, the variables are qualitative.

a. The experimental units in this study are the 24 new software development projects. b. The population from which the sample was selected is the set of all new software development projects. c. The variable of interest in this project is the outcome of reusing previously developed software for the new software development projects. Since the outcomes could either be success or failures, the variable is qualitative. d. In the sample, 15 of the 24 projects were judged as successfully implemented or 62.5%. This is the success rate of the sample. This would be a good estimate of the population percentage of successfully implemented projects, but it is only an estimate. If we took another sample of size 24, the percentage of successful projects would not necessarily be 62.5%.

1.32

a. The data collection method used was a survey. b. The target population is the set of all American adults. c. The sample was not a random sample. Thus, it may not be representative of all American adults. Many people contacted on the telephone refuse to participate in surveys.

Methods for Describing Sets of Data 5 Chapter

Methods for Describing Sets of Data

2.2

In a bar graph, a bar or rectangle is drawn above each class of the qualitative variable corresponding to the class frequency or class relative frequency. In a pie chart, each slice of the pie corresponds to the relative frequency of a class of the qualitative variable.

2.4

First, we find the frequency of the grade A. The sum of the frequencies for all 5 grades must be 200. Therefore, subtract the sum of the frequencies of the other 4 grades from 200. The frequency for grade A is: 200 − (36 + 90 + 30 + 28) = 200 − 184 = 16 To find the relative frequency for each grade, divide the frequency by the total sample size, 200. The relative frequency for the grade B is 36/200 = .18. The rest of the relative frequencies are found in a similar manner and appear in the table: Grade on Statistics Exam A: 90−100 B: 80− 89 C: 65− 79 D: 50− 64 F: Below 50 Total

2.6

Frequency 16 36 90 30 28 200

Relative Frequency .08 .18 .45 .15 .14 1.00

The graph shown is a pie chart.

The qualitative variable described in the graph is opinion on library importance.

The most common opinion is more important, with 46.0% of the responders indicating that they think libraries have become more important.

Chapter 2 d.

Using MINITAB, the Pareto diagram is: Importance 50

Percent

Same Importance

Less

Of those who responded to the question, almost half (46%) believe that libraries have become more important to their community. Only 18% believe that libraries have become less important. a.

Data were collected on 3 questions. For questions 1 and 2, the responses were either ‘yes’ or ‘no’. Since these are not numbers, the data are qualitative. For question 3, the responses include ‘character counts’, ‘roots of empathy’, ‘teacher designed’, other’, and ‘none’. Since these responses are not numbers, the data are qualitative.

Using MINITAB, bar charts for the 3 questions are: Chart of Classroom Pets 60 50 40 Count

2.8

30 20 10 0

Yes Classroom Pets

Methods for Describing Sets of Data 7

Chart of Pet Visits 40

Count

Yes Pet Visits

Chart of Education 30 25

Count

20 15 10 5 0

Character counts

Roots of empathy

Teacher designed

Other

None

Education

2.10

Many different things can be written. Possible answers might be: Most of the classroom teachers surveyed (61/75 = .813) keep classroom pets. A little less than half of the surveyed classroom teachers (35/75 = .467) allow visits by pets.

A PIN pad is selected and the manufacturer is determined. Since manufacturer is not a number, the data collected are qualitative.

Chapter 2 b.

Using MINITAB, the frequency bar chart is: Chart of Manufacturer 120000 100000

Count

80000 60000 40000

ProvencoCadmus

SZZT Electronics

Toshiba TEC

Urmet

Pax Tech.

Glintt

Intelligent

Urmet

Pax Tech.

Omron

KwangWoo

Intelligent

Glintt

Fujuan Landi

CyberNet

Bitel

20000

Manufacturer

The Pareto chart for the data is: Chart of Manufacturer 120000 100000

Count

80000 60000 40000

Toshiba TEC

Bitel

CyberNet

ProvencoCadmus

Omron

KwangWoo

SZZT Electronics

Fujuan Landi

20000

Manufacturer

Most of the PIN pads were shipped by Fujian Landi. They shipped almost twice as many PIN pads as the second highest manufacturer, which was SZZT Electronics. The three manufacturers with the smallest number of Pin pads shipped were Glintt, Intelligent, and Urmet. 2.12

The two qualitative variables graphed in the bar charts are the occupational titles of clan individuals in the continued line and the occupational titles of clan individuals in the dropout line.

Methods for Describing Sets of Data 9 b.

Suppose we construct a relative frequency bar chart for this data. This will allow the archaeologists to compare the different categories easier. First, we must compute the relative frequencies for the categories. These are found by dividing the frequencies in each category by the total 837. For the burnished category, the relative frequency is 133 / 837 = .159. The rest of the relative frequencies are found in a similar fashion and are listed in the table. Pot Category

Number Found

Computation

Relative Frequency

Burnished

133

133 / 837

.159

Monochrome

460

460 / 837

.550

Slipped

55 / 837

.066

Curvilinear Decoration

14 / 837

.017

Geometric Decoration

165

165 / 837

.197

Naturalistic Decoration

4 / 837

.005

Cycladic White clay

4 / 837

.005

Cononical cup clay

2 / 837

.002

Total A relative frequency bar chart is:

837

1.001

Chart of Pot Category .60

.48 Relative Frequency

2.14

In the Continued Line, about 63% were in either the high or the middle grade. Only about 20% were in the nonofficial category. In the Dropout Line, only about 22% were in either the high or middle grade while about 64% were in the nonofficial category. The percents in the low grade and provincial official categories were about the same for the two lines.

.36

.24

.12

Burnished Monochrome

Slipped

C urv ilinear

Geometric

Naturalistic

Cy cladic

C onical

Pot Category

The most frequently found type of pot was the Monochrome. Of all the pots found, 55% were Monochrome. The next most frequently found type of pot was the Painted in Geometric Decoration. Of all the pots found, 19.7% were of this type. Very few pots of the types Painted in naturalistic decoration, Cycladic white clay, and Conical cup clay were found.

10 2.16

Chapter 2 Using MINITAB, a bar graph is: Chart of Fieldwork 5000

Count

4000

3000

2000

1000

1Interview

2Obs+Partic 3Observ Fieldwork

4Grounded

Most of the types of papers found were interviews. There were about twice as many interviews as all other types combined. 2.18

There were 1,470 responses that were missing. In addition, 14 responses were 8 = Don’t know and 7 responses were 9 = Missing. The missing values were not included, but those responding with an 8 were kept. Therefore, there were only 1333 useable responses. The frequency table is: Response 1 2 3 4 8 Totals

Frequency 450 627 219 23 14 1333

Relative Frequency 450/1333 = .338 627/1333 = .470 219/1333 = .164 23/1333 = .017 14/1333 = .011 1.000

Methods for Describing Sets of Data 11 b. Using MINITAB, the pie chart for the data is:

Pie Chart of Bible Categories C ategory 1 2 3 4 8

4 8 3 1

Using MINITAB a bar chart for the Extinct status versus flight capability is: C har t of Extinct, Flight 80 70 60 50 Count

2.20

The response with the highest frequency is 2, ‘the Bible is the inspired word of God but not everything is to be taken literally’. Almost 47% of the respondents selected this answer. About one-third of the respondents answered 1, ‘the Bible is the actual word of God and is to be taken literally’. Very few (1.7%) of the respondents chose response 4, ‘the Bible has some other origin’ and response 8 (1.1%), ‘Don’t know’.

40 30 20 10 0 Flight Extinct

No Yes Absent

No Yes Present

No Yes Extinct

It appears that extinct status is related to flight capability. For birds that do have flight capability, most of them are present. For those birds that do not have flight capability, most are extinct.