Elementary statistics 9th edition weiss test bank

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) Population data: 3, 4, 5, 6, 7.

1)

a. Find the mean, μ, of the variable. b. Use the population data below to construct a table giving the sample means of sample size n = 2. c. Draw a dotplot for the sampling distribution of the sample mean. d. Find the probability that the sample mean will equal the population mean. e. Find the probability that the sampling error made in estimating the population mean by the sampling mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

2) Population data: 5, 6, 9, 10.

2)

a. Find the mean, μ, of the variable. b. Use the population data below to construct a table giving the sample means of sample size n = 3. c. Draw a dotplot for the sampling distribution of the sample mean. d. Find the probability that the sample mean will equal the population mean. e. Find the probability that the sampling error made in estimating the population mean by the sampling mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Solve the problem.

3) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 290 310 250 255 220 Consider these players to be a population of interest. The mean weight, μ, for the population is 265 pounds. Construct a table that shows all of the possible samples of size two. For each of the possible samples, list the players in the sample, their weights, and the sample mean. The first line of the table is shown below.

Sample A, B

Weights 290, 310

x 300

Use your table to find the probability that, for a random sample of size two, the sample mean will equal the population mean.

1

3)

4) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 290 310 250 255 220

4)

Consider these players to be a population of interest. The mean weight, μ, for the population is 265 pounds. Construct a table that shows all of the possible samples of size three. For each of the possible samples, list the players in the sample, their weights, and the sample mean. The first line of the table is shown below.

Sample Weights x A, B, C 290, 310, 250 283.3 Use your table to find the probability that, for a random sample of size three, the sample mean will be within 15 lb of the population mean.

5) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 290 310 250 255 220

5)

Consider these players to be a population of interest. The mean weight, μ, for the population is 265 pounds. Construct a table that shows all of the possible samples of size four. For each of the possible samples, list the players in the sample, their weights, and the sample mean. The first line of the table is shown below.

Sample Weights x A, B, C, D 290, 310, 250, 255 276.25 Use your table to find the probability that, for a random sample of size four, the sample mean will be within 10 lb of the population mean.

6) The ages of six members of a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 32 52 43 64 41 50 Consider these board members to be a population of interest. The mean age, μ, for the population is 47. Construct a table that shows all of the possible samples of size two. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below.

Sample Ages x A, B 32, 52 42 Use your table to find the probability that, for a random sample of size two, the sample mean will equal the population mean.

2

6)

7) The ages of six members of a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 32 52 43 64 41 50

7)

Consider these board members to be a population of interest. The mean age, μ, for the population is 47. Construct a table that shows all of the possible samples of size four. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below.

Sample Ages x A, B, C, D 32, 52, 43, 64 47.75 Use your table to find the probability that, for a random sample of size four, the sample mean will be within 4 years of the population mean.

8) The ages of six members of a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 32 52 43 64 41 50

8)

Consider these board members to be a population of interest. The mean age, μ, for the population is 47. Construct a table that shows all of the possible samples of size five. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below.

Sample Ages x A, B, C, D, E 32, 52, 43, 64, 41 46.4 Use your table to find the probability that, for a random sample of size five, the sample mean will be within 2 years of the population mean.

Draw the specified dotplot.

9) The heights (in inches) of 5 players on a basketball team are given in the table.

Player Height (inches)

A 65

B 78

C 72

D 68

E 57

Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

3

9)

10) The heights (in inches) of 5 players on a basketball team are given in the table.

Player Height (inches)

A 65

B 78

C 72

D 68

10)

E 57

Draw a dotplot for the sampling distribution of the sample mean for samples of size 4.

11) The heights (in inches) of 5 players on a basketball team are given in the table.

Player Height (inches)

A 66

B 69

C 72

D 69

11)

E 72

Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

12) The heights (in inches) of 5 players on a basketball team are given in the table.

Player Height (inches)

A 66

B 69

C 72

D 69

12)

E 72

Draw a dotplot for the sampling distribution of the sample mean for samples of size 3.

13) The heights (in inches) of 5 players on a basketball team are given in the table.

Player Height (inches)

A 66

B 69

C 72

D 69

E 72

Draw a dotplot for the sampling distribution of the sample mean for samples of size 4.

4

13)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the requested probability.

14) The table reports the distribution of pocket money, in bills, of the 6 students in a statistics seminar.

14)

Student Hannah Ming Keshaun Tameeka Jose Vaishali Amount, in dollars 2 4 4 5 5 7 For a random sample of size two, find the probability, expressed as a percent rounded to the nearest tenth, that the sample mean will be within $1 of the population mean.

A) 80.0% B) 66.7% C) 73.3% D) 78.6% 15) The table reports the GPA for each of five students in a statistics class.

15)

Student Maria Alvin Elvis Ingrid Rashad GPA 3.52 3.65 3.66 3.92 3.95 For a random sample of size two, find the probability, expressed as a percent, that the sample mean will be within 0.1 of the population mean.

A) 30% B) 20% C) 70% D) 80% 16) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

16)

Find the probability, expressed as a percent, that the sample mean will be equal to the population mean.

A) 30% B) 5% C) 20% D) 10% 17) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

Find the probability, expressed as a percent, that the sample mean will be within 1 point of the population mean.

A) 22% B) 20% C) 10% D) 5%

5

17)

18) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

18)

Find the probability, expressed as a percent, that the sample mean will be within 2 points of the population mean.

A) 30% B) 20% C) 40% D) 50% 19) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

19)

Find the probability, expressed as a percent, that the sample mean will be within 3 points of the population mean.

A) 70% B) 40% C) 60% D) 50% 20) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

Find the probability, expressed as a percent, that the sample mean will be within 1 point of the population mean.

A) 20% B) 30% C) 10% D) 25%

6

20)

21) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

21)

Find the probability, expressed as a percent, that the sample mean will be within 2 points of the population mean.

A) 50% B) 40% C) 30% D) 60% 22) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

22)

Find the probability, expressed as a percent, that the sample mean will be within 3 points of the population mean.

A) 60% B) 72% C) 40% D) 50% 23) The test scores of 5 students are under consideration. The following is the dotplot for the sampling distribution of the sample mean for samples of size 2.

23)

Find the probability, expressed as a percent, that the sample mean will be within 5 points of the population mean.

A) 80% B) 95% C) 90% D) 100% Provide an appropriate response.

24) What is the sampling distribution of a statistic?

A) The distribution of all possible sizes of samples from a population that can be used to make observations of the statistic B) The distribution of all possible observations of the statistic for samples of a given size from a population C) The distribution of observations of a variable in a sample for a given value of the statistic D) The distribution of observations of the statistic for all possible sizes of samples from a population

7

24)

25) As a general rule, you cannot expect to exactly determine the sampling distribution of a statistic.

Why? A) Many populations are not normal.

B) Many populations are not uniform.

C) Many populations are too small.

D) Many populations are too large.

25)

26) Which of the following is not synonymous with the sampling distribution of the sample mean?

A) Distribution of all possible sample means from samples of a given size

26)

B) Distribution of x C) Distribution of a variable in a sample of a given size for a given x D) Distribution of the variable x 27) How many different samples of size 4 can be obtained from a population of size 5?

A) 10 B) 5 C) 4 D) 1

27)

28) What generally happens to the sampling distribution of the sample mean as the sample size is increased?

A) It becomes more tightly concentrated around the population mean.

B) It is unaffected.

C) It becomes less tightly concentrated around the population mean.

D) None of the above

28)

29) What generally happens to the sampling error as the sample size is increased?

A) It gets smaller.

B) It gets more predictable.

C) It gets larger.

D) It gets less predictable.

29)

Use the given table to determine the mean, μx , of the variable x for the given sample size.

30)

30) Sample 2, 3 2, 4 2, 5 2, 6 3, 4 3, 5 3, 6 4, 5 4, 6 5, 6 A) 4.5

x 2.5 3 3.5 4 3.5 4 4.5 4.5 5 5.5

Sample x 5, 6, 9 6.7 31) 5, 6, 10 7 5, 9, 10 8 6, 9, 10 8.3 A) 8

B) 3.5

C) 4

D) 5

31)

B) 10

C) 7.5

8

D) 7

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

32) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 275 310 290 250 215

32)

Consider these players to be a population of interest. The table below shows all of the possible samples of size two. For each sample, the players in the sample, their weights, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample A, B A, C A, D A, E B, C B, D B, E C, D C, E D, E

Weights x 275, 310 292.5 275, 290 282.5 275, 250 262.5 275, 215 245 310, 290 300 310, 250 280 310, 215 262.5 290, 250 270 290, 215 252.5 250, 215 232.5

33) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 290 310 250 255 220 Consider these players to be a population of interest. The table below shows all of the possible samples of size three. For each sample, the players in the sample, their weights, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample

Weights

x

A, B, C 290, 310,250 283.3 A, B, D 290, 310, 255 285 A, B, E 290, 310 220 273.3 A, C, D 290, 250, 255 265 A, C, E 290, 250, 220 253.3 A, D, E 290, 255, 220 255 B, C, D B, C, E

310, 250, 255 271.6 310, 250, 220 260

B, D, E

310, 255, 220 261.6

C, D, E

250, 255, 220 241.6

9

33)

34) The weights of five players on a football team are shown below.

Player A B C D E Weight (lb) 290 310 250 255 220

34)

Consider these players to be a population of interest. The table below shows all of the possible samples of size four. For each sample, the players in the sample, their weights, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample Weights A, B, C, D 290, 310, 250, 255 A, B, C, E 290, 310, 250, 220 A, B, D, E 290, 310, 255, 220 A, C, D, E 290, 250, 255, 220 B, C, D, E 310, 250, 255, 220

x 276.25 267.5 268.75 253.75 258.75

35) The ages of six members on a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 64 41 63 53 68 53 Consider these board members to be a population of interest. The table below shows all of the possible samples of size two. For each sample, the people in the sample, their ages, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample A, B A, C A, D A, E A, F B, C B, D B, E B, F C, D C, E C, F D, E D, F E, F

Ages 64, 41 64, 63 64, 53 64, 68 64, 53 41, 63 41, 53 41, 68 41, 53 63, 53 63, 68 63, 53 53, 68 53, 53 68, 53

x 52.5 63.5 58.5 66 58.5 52 47 54.5 47 58 65.5 58 60.5 53 60.5

10

35)

36) The ages of six members on a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 32 52 43 64 41 50

36)

Consider these board members to be a population of interest. The table below shows all of the possible samples of size four. For each sample, the people in the sample, their ages, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample A, B, C, D A, B, C, E A, B, C, F A, B, D, E A, B, D, F A, B, E, F A, C, D, E A, C, D, F A, C, E, F A, D, E, F B, C, D, E B, C, D, F B, C, E, F B, D, E, F C, D, E, F

Ages 32, 52, 43, 64 32, 52, 43, 41 32, 52, 43, 50 32, 52, 64, 41 32, 52, 64, 50 32, 52, 41, 50 32, 43, 64, 41 32, 43, 64, 50 32, 43, 41, 50 32, 64, 41, 50 52, 43, 64, 41 52, 43, 64, 50 52, 43, 41, 50 52, 64, 41, 50 43, 64, 41, 50

x 47.75 42 44.25 47.25 49.5 43.75 45 47.25 41.5 46.75 50 52.25 46.5 51.75 49.5

37) The ages of six members on a board of directors of a nonprofit organization are shown below.

Member A B C D E F Age 67 54 47 40 35 52 Consider these board members to be a population of interest. The table below shows all of the possible samples of size five. For each sample, the people in the sample, their ages, and the sample mean are listed. Use the table to find the mean of the variable x.

Sample A, B, C, D, E A, B, C, D, F A, B, C, E, F A, B, D, E, F A, C, D, E, F B, C, D, E, F

Ages x 67, 54, 47, 40, 35 48.6 67, 54, 47, 40, 52 52 67, 54, 47, 35, 52 51 67, 54, 40, 35, 52 49.6 67, 47, 40, 35, 52 48.2 54, 47, 40, 35, 52 45.6

11

37)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x.

38) The mean and the standard deviation of the sampled population are, respectively, 158.3 and 33.0. n = 81 A) μ

= 348.3; σ = 1.9 x C) μ = 158.3; σ = 3.7 x x

= 158.3 x D) μ = 33.0; σ = 3.7 x x B) μ

x

x

= 3.7; σ

39) The mean and the standard deviation of the sampled population are, respectively, 43.5 and 5.2. n = 289 A) μ

= 0.3 x C) μ = 5.2; σ = 0.3 x x x

38)

= 43.5; σ

39)

= 2.0 x D) μ = 0.3; σ = 43.5 x x B) μ

x

= 15.1; σ

40) The National Weather Service keeps records of snowfall in mountain ranges. Records indicate that in a certain range, the annual snowfall has a mean of 83 inches and a standard deviation of 14 inches. Suppose the snowfalls are sampled during randomly picked years. For samples of size 49, determine the mean and standard deviation of x.

A) μ = 83; σ = 2 x x C) μ = 14; σ = 83 x x

40)

= 83; σ = 14 x D) μ = 2; σ = 83 x x B) μ

x

41) One barge from Inland Waterways, Inc. can carry a load of 6284.8 lb. Records of past trips show that the weights of the cans that it carries have a mean of 94 lb and a standard deviation of 16 lb.

41)

For samples of size 64, find the mean and standard deviation of x.

A) μ = 2; σ = 94 B) μ = 94; σ = 16 x x x x C) μ = 16; σ = 94 D) μ = 94; σ = 2 x x x x 42) The National Weather Service keeps records of rainfall in valleys. Records indicate that in a certain valley, the annual rainfall has a mean of 97 inches and a standard deviation of 12 inches. Suppose

42)

the rainfalls are sampled during randomly picked years and x is the mean amount of rain in these years. For samples of size 36, determine the mean and standard deviation of x.

A) μ = 2; σ = 97 B) μ = 97; σ = 12 x x x x C) μ = 12; σ = 97 D) μ = 97; σ = 2 x x x x 43) One truck from Lakeland Trucking, Inc. can carry a load of 3880.8 lb. Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 14 lb. For samples of size 49, find the mean and standard deviation of x.

A) μ = 2; σ = 75 B) μ = 75; σ = 2 x x x x C) μ = 75; σ = 14 D) μ = 14; σ = 75 x x x x

12

43)

Provide an appropriate response.

44) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let x denote the mean height for a sample of people picked randomly from the population. True or false, the

44)

standard deviation of x for samples of size 30 is greater than the standard deviation of x for samples of size 20?

A) True B) False 45) The mean height for a population is 65 inches. Let x denote the mean height for a sample of people

45)

picked randomly from the population. True or false, the standard deviation of x for samples of size 30 is smaller than the standard deviation, σ, of the population?

A) True B) False 46) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B denote the events described below.

46)

Event A: The height of a randomly selected person is 5 inches or more from the population mean.

Event B: The mean height in a random sample of 16 people is 5 inches or more from the population mean.

True or false, the probability of event A is greater than the probability of event B? A) True B) False 47) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B denote the events described below.

47)

Event A: The height of a randomly selected person is within 3 inches of the population mean.

Event B: The mean height in a random sample of 16 people is within 3 inches of the population mean.

True or false, the probability of event A is greater than the probability of event B? A) True B) False 48) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B denote the events described below.

Event A: The mean height in a random sample of 16 people is within 1 inch of the population mean.

Event B: The mean height in a random sample of 50 people is within 1 inch of the population mean.

True or false, the probability of event A is greater than the probability of event B? A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

49) Suppose that μ represents the mean height for a population of people. Suppose that you use a sample mean, x, to estimate μ. Explain what is meant by sampling error in this situation. Why does x vary from one sample to the next? How can you reduce the likely sampling error?

13

49)

48)

50) The mean height for a population of people is 65 inches. Suppose that you pick a sample of

50)

50 people and determine the sample mean, x. You then repeat this procedure three more times. You learned in class that μ = μ. Can you conclude that the mean of the four x sample means will be equal to the population mean of 65 inches? Why or why not?

51) A population of people has a mean height of 65 inches. Andrew picks a person at random from the population and records his or her height. He repeats this procedure 49 times more. Bob picks a sample of 30 people at random from the population and records the mean height of the sample. He repeats this procedure 49 times more. Which set of numbers (those recorded by Andrew or those recorded by Bob) do you think will have more variability? Explain your reasoning.

51)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately normal and give its mean and standard deviation.

52) The weights of people in a certain population are normally distributed with a mean of 159 lb and a 52) standard deviation of 24 lb. Determine the sampling distribution of the mean for samples of size 5.

A) Approximately normal, mean = 159 lb, standard deviation = 10.73 lb B) Normal, mean = 159 lb, standard deviation = 10.73 lb C) Approximately normal, mean = 159 lb, standard deviation = 4.8 lb D) Normal, mean = 159 lb, standard deviation = 24 lb 53) The heights of people in a certain population are normally distributed with a mean of 67 inches and a standard deviation of 3.1 inches. Determine the sampling distribution of the mean for samples of size 35.

A) Approximately normal, mean = 67 inches, standard deviation = 0.09 inches B) Normal, mean = 67 inches, standard deviation = 3.1 inches C) Normal, mean = 67 inches, standard deviation = 0.09 inches D) Normal, mean = 67 inches, standard deviation = 0.52 inches

53)

54) The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5100. The distribution of incomes is skewed to the right. Determine the sampling distribution of the mean for samples of size 74.

A) Approximately normal, mean = $28,520, standard deviation = $5100 B) Normal, mean = $28,520, standard deviation = $593 C) Approximately normal, mean = $28,520, standard deviation = $593 D) Normal, mean = $28,520, standard deviation = $69

54)

55) Let x represent the number that shows up when a balanced die is rolled. Then x is a random

55)

variable with a mean of 3.5 and a standard deviation of 1.71. Let x denote the mean of the numbers obtained when the die is rolled 32 times. Determine the sampling distribution of x.

A) Approximately normal, mean = 3.5, standard deviation = 1.71 B) Normal, mean = 3.5, standard deviation = 0.3 C) Approximately normal, mean = 3.5, standard deviation = 0.3 D) Normal, mean = 3.5, standard deviation = 0.05

14

56) For the population of one town, the number of siblings, x, is a random variable whose relative frequency histogram has a reverse J-shape. The mean number of siblings is 1.3 and the standard

56)

deviation is 1.5. Let x denote the mean number of siblings for a random sample of size 31.

Determine the sampling distribution of the mean for samples of size 31.

A) Normal, mean = 1.3, standard deviation = 1.5 B) Approximately normal, mean = 1.3, standard deviation = 0.27 C) Normal, mean = 1.3, standard deviation = 0.27 D) Approximately normal, mean = 1.3, standard deviation = 1.5 Find the indicated probability or percentage for the sampling error.

57) The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50?

A) 0.6876 B) 0.3124 C) 0.3438 D) Cannot be determined, because the distribution of the population is not normal.

57)

58) The distribution of weekly salaries at a large company is reverse J-shaped with a mean of $1000 and a standard deviation of $370. What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 80 employees will be at most $75?

A) 0.9298 B) 0.0702 C) 0.4649 D) Cannot be determined, because the distribution of the population is not normal.

58)

59) Scores on an aptitude test are distributed with a mean of 220 and a standard deviation of 30. The shape of the distribution is unspecified. What is the probability that the sampling error made in estimating the population mean by the mean of a random sample of 50 test scores will be at most 5 points?

A) 0.762 B) 0.135 C) 0.881 D) Cannot be determined, because the distribution of the population is not known to be normal.

59)

60) The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a standard deviation of 0.18 ounce. What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

A) 0.7330 B) 0.0938 C) 0.8665 D) 0.0876

60)

61) The monthly expenditures on food by single adults in one city are normally distributed with a mean of $410 and a standard deviation of $70. What is the probability that the sampling error made in estimating the mean monthly expenditure of all single adults in that city by the mean of a random sample of 90 such adults will be at most $10?

A) 0.9131 B) 0.8262 C) 0.9990 D) 0.1114

61)

15

62) Scores on a biology final exam are normally distributed with a mean of 220 and a standard deviation of 24. Determine the percentage of samples of size 9 that will have mean scores within 12 points of the population mean score of 220.

A) 13.36% B) 86.64% C) 38.30% D) 93.32%

62)

63) Scores on a chemistry final exam are normally distributed with a mean of 280 and a standard deviation of 50. Determine the percentage of samples of size 4 that will have mean scores within 35 points of the population mean score of 280.

A) 91.92% B) 51.60% C) 83.84% D) 99.48%

63)

64) The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are normally distributed with a mean of $370 and a standard deviation of $45. Determine the percentage of samples of size 9 that will have mean monthly expenditures on food within $27 of the population mean expenditure of $370.

A) 96.41% B) 92.82% C) 46.41% D) 63.18%

64)

65) The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are normally distributed with a mean of $410 and a standard deviation of $105. Determine the percentage of samples of size 9 that will have mean monthly expenditures on food within $28 of the population mean expenditure of $410.

A) 98.36% B) 91.92% C) 57.62% D) 21.28%

65)

66) The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a standard deviation of 0.18 ounce. Determine the percentage of samples of size 16 that will have mean amounts of coffee within 0.1 ounce of the population mean of 8.2 ounces.

A) 97.36% B) 98.68% C) 71.23% D) 42.46%

66)

Provide an appropriate response.

67) The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5,190. The distribution of incomes is skewed to the right. For samples of size 30, which of the following statements best describes the sampling distribution of the mean?

67)

A) Nothing can be said about the distribution of x.

B) x is approximately normally distributed.

C) x is normally distributed.

D) The distribution of x is skewed to the right.

68) Let x represent the number which shows up when a balanced die is rolled. Then x is a random variable with a uniform distribution. Let x denote the mean of the numbers obtained when the die is rolled 32 times. For samples of size 32, which of the following statements concerning the sampling distribution of the mean is true?

A) The distribution of x is uniform.

B) x is approximately normally distributed.

C) x is normally distributed.

D) None of the above statements is true.

16

68)

69) Let x represent the number which shows up when a balanced die is rolled. Then x is a random

69)

variable with a uniform distribution. Let x denote the mean of the numbers obtained when the die is rolled 3 times. Which of the following statements concerning the sampling distribution of the mean, x , is true?

A) x is normally distributed.

B) x is approximately normally distributed.

C) x has a uniform distribution.

D) None of the above statements is true.

70) For the population of one town, the number of siblings is a random variable whose relative

70)

frequency histogram has a reverse J-shape. Let x denote the mean number of siblings for a random sample of size 30. For samples of size 30, which of the following statements concerning the sampling distribution of the mean is true?

A) x is normally distributed.

B) The distribution of x has a reverse J-shape.

C) x is approximately normally distributed.

D) None of the above statements is true.

71) For the population of one town, the number of siblings is a random variable whose relative

71)

frequency histogram has a reverse J-shape. Let x denote the mean number of siblings for a random sample of size 3. For samples of size 3, which of the following statements concerning the sampling distribution of the mean is true?

A) The distribution of x has a reverse J-shape.

B) x is approximately normally distributed.

C) x is normally distributed.

D) None of the above statements is true.

72) The heights of adult women in the U.S are normally distributed. Let x denote the mean height for a random sample of 4 women. For samples of size 4, which of the following statements concerning the sampling distribution of the mean is true?

A) x has a uniform distribution.

B) x is approximately normally distributed.

C) x is normally distributed.

D) None of the above statements is true.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

73) The typical computer random-number generator yields numbers in a uniform distribution between 0 and 1, with a mean of 0.500 and a standard deviation of 0.289. Consider the following two problems, which appear at a glance to be very similar. One can be solved using the Central Limit Theorem. Which one and why? (a) Suppose a sample of size 50 is randomly generated. Find the probability that the mean is below 0.300. (b) Suppose a sample of size 15 is randomly generated. Find the probability that the mean is below 0.300.

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73)

72)

74) SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). Consider the following two problems, which appear at a glance to be very similar. Which one requires the application of the Central Limit Theorem, and in what way does the solution process differ between the two problems? (a) If a student is randomly selected, what is the probability that his or her score is above 500? (b) If a sample of 35 students is selected randomly, what is the probability that the sample mean will be above 500?

74)

75) Consider the following two problems. (a) A random-number generator yields numbers in a uniform distribution between 0 and 1 with a mean of 0.5 and a standard deviation of 0.289. You wish to find the probability that the mean of a sample of 50 random numbers is greater than 0.6. (b) Scores on an aptitude test are normally distributed with a mean of 82 and a standard deviation of 11. You wish to find the probability that the score for a randomly selected person is greater than 90.

75)

Which of these two problems requires application of the Central Limit Theorem? Explain your reasoning.

76) Do you agree with Tony's reasoning below? Explain why you do or do not agree. Refer to the Central Limit Theorem in your explanation.

Tony: "When a balanced die is rolled, each of the numbers 1, 2, 3, 4, 5, and 6 has an equal chance of showing up. So, if I roll the die 50 times and find the mean of the 50 numbers, the mean has the same chance of falling between 1 and 2 as it has of falling between 3 and 4."

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76)

Answer Key Testname: UNTITLED7

1) a. 5 b.

Sample 3, 4 3, 5 3, 6 3, 7 4, 5 4, 6 4, 7 5, 6 5, 7 6, 7 c.

3 1 d.

5 e.

x 3.5 4 4.5 5 4.5 5 5.5 5.5 6 6.5

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

7

3 5

2) a. 7.5 b.

Sample x 5, 6, 9 6.7 5, 6, 10 7 5, 9, 10 8 6, 9, 10 8.3 c.

5 d. 0 1 e.

2

5.5

6

6.5

9.5 10

19

Answer Key Testname: UNTITLED7

3) Sample A, B A, C A, D A, E B, C B, D B, E C, D C, E D, E

Weights 290, 310 290, 250 290, 255 290, 220 310, 250 310, 255 310, 220 250, 255 250, 220 255, 220

x 300 270 272.5 255 280 282.5 265 252.5 235 237.5

Probability that sample mean equals population mean = 0.1 4) Sample

Weights

x

A, B, C 290, 310,250 283.3 A, B, D 290, 310, 255 285 A, B, E 290, 310 220 273.3 A, C, D 290, 250, 255 265 A, C, E 290, 250, 220 253.3 A, D, E 290, 255, 220 255 B, C, D B, C, E

310, 250, 255 271.6 310, 250, 220 260

B, D, E

310, 255, 220 261.6

C, D, E

250, 255, 220 241.6

Probability that the sample mean will be within 15 lb of the population mean is 0.7.

5) Sample Weights A, B, C, D 290, 310, 250, 255 A, B, C, E 290, 310, 250, 220 A, B, D, E 290, 310, 255, 220 A, C, D, E 290, 250, 255, 220 B, C, D, E 310, 250, 255, 220

x 276.25 267.5 268.75 253.75 258.75

Probability that the sample mean will be within 10 lb of the population mean = 0.6.

20

Answer Key Testname: UNTITLED7

6) Sample A, B A, C A, D A, E A, F B, C B, D B, E B, F C, D C, E C, F D, E D, F E, F

Ages 32, 52 32, 43 32, 64 32, 41 32, 50 52, 43 52, 64 52, 41 52, 50 43, 64 43, 41 43, 50 64, 41 64, 50 41, 50

x 42 37.5 48 36.5 41 47.5 58 46.5 51 53.5 42 46.5 52.5 57 45.5

Probability that sample mean equals population mean = 0.

7) Sample Ages A, B, C, D 32, 52, 43, 64 A, B, C, E 32, 52, 43, 41 A, B, C, F 32, 52, 43, 50 A, B, D, E 32, 52, 64, 41 A, B, D, F 32, 52, 64, 50 A, B, E, F 32, 52, 41 ,50 A, C, D, E 32, 43, 64, 41 A, C, D, F 32, 43, 64, 50 A, C, E, F 32, 43, 41, 50 A, D, E, F 32, 64, 41, 50 B, C, D, E 52, 43, 64, 41 B, C, D, F 52, 43, 64, 50 B, C, E, F 52, 43, 41, 50 B, D, E, F 52, 64, 41, 50 C, D, E, F 43, 64, 41, 50

x 47.75 42 44.25 47.25 49.5 43.75 45 47.25 41.5 46.75 50 52.25 46.5 51.75 49.5

Probability that sample mean lies within 4 years of population mean = 0.73 8) Sample Ages A, B, C, D, E 32, 52, 43, 64, 41 A, B, C, D, F 32, 52, 43, 64, 50 A, B, C, E, F 32, 52, 43, 41, 50 A, B, D, E, F 32, 52, 64, 41, 50 A, C, D, E, F 32 ,43, 64, 41, 50 B, C, D, E, F 52, 43, 64, 41, 50

x 46.4 48.2 43.6 47.8 46 50

Probability that the sample mean will lie within 2 years of the population mean = 21

2 3

Answer Key Testname: UNTITLED7

9)

10)

11)

12)

13)

14) C 15) C 16) C 17) B 18) C 19) C 20) A 21) A 22) A 23) D 24) B 25) D 26) C 27) B 28) A 29) A 30) C 31) C 32) 268 pounds 33) 265 pounds 34) 265 pounds 35) 57 36) 47 37) 49.17 22

Answer Key Testname: UNTITLED7

38) C 39) A 40) A 41) D 42) D 43) B 44) B 45) A 46) A 47) B 48) B 49) Answers will vary. Possible answer: Sampling error is the error involved in using x to estimate the population mean, μ. x varies from one sample to the next because there is randomness involved in picking the sample. The sample contains different people each time and as a result x is different each time. The sampling error can be reduced by taking a larger sample.

50) Answers will vary. Possible answer: No. The mean of all possible sample means (for samples of size 50) is equal to 65 inches. We cannot conclude that the mean of four particular sample means will be 65 inches.

51) Answers will vary. Possible answer: The numbers recorded by Andrew will have greater variability. The standard deviation of sample means (σ/ n) is smaller than the standard deviation of individual observations (σ).

52) B 53) D 54) C 55) C 56) B 57) A 58) A 59) A 60) A 61) B 62) B 63) C 64) B 65) C 66) A 67) B 68) B 69) D 70) C 71) D 72) C 73) The first may be solved using the Central Limit Theorem. The second has too small a sample size. x-μ 74) The first problem involves the formula z = , whereas the second involves the Central Limit Theorem and the σ formula z =

x-μ since it concerns a sample. σ n

23

Answer Key Testname: UNTITLED7

75) The first problem requires application of the Central Limit Theorem because we need to rely on the fact that the sample mean, x, has a normal distribution even though x does not. The second problem does not require application of the Central Limit Theorem since it does not concern a sample mean.

76) Tony's reasoning is not correct. Even though the distribution of the individual observations is uniform, by the Central Limit Theorem, the distribution of the mean of 50 numbers is approximately normal. So the mean of 50 numbers is more likely to fall between 3 and 4 than it is to fall between 1 and 2, since the interval [3, 4] is closer to the mean.

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