Deck 10: Inference About Means and Proportions With Two Populations

Question 1

Salary information regarding male and female employees of a large company is shown below. ​ The standard error of the difference between the two sample means is

A) 4.
B) 7.46.
C) 4.24.
D) 2.0.

Answer 1

2.0.

Question 2

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. ​
The null hypothesis to be tested is H₀: μd = 0. The test statistic is

A) -1.96.
B) 1.77.
C) 0.
D) 1.00.

Answer 2

0.

Question 3

The sampling distribution of - is approximated by a

A) normal distribution.
B) t distribution with n₁ + n₂ degrees of freedom.
C) t distribution with n₁ + n₂ - 1 degrees of freedom.
D) - distribution.

Answer 3

normal distribution.

Question 4

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____ samples.

A) proportional
B) matched
C) independent
D) pooled

Question 5

To compute an interval estimate for the difference between the means of two populations, the t distribution

A) is restricted to small sample situations.
B) is not restricted to small sample situations.
C) can be applied when the populations have equal means.
D) can be applied only when the populations have equal standard deviations.

Question 6

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2) _____ degrees of freedom.

A) (n₁ + n₂)
B) (n₁ + n₂ - 1)
C) (n₁ + n₂ - 2)
D) (n₁ - 1)

Question 7

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. ​
The point estimate for the difference between the means of the two populations is

A) -1.
B) -2.
C) 0.
D) 1.

Question 8

Salary information regarding male and female employees of a large company is shown below. ​ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, the p-value is

A) .0228.
B) .0455.

Question 9

Salary information regarding male and female employees of a large company is shown below. ​ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, at α = .05, the conclusion is that the population

A) average salary of males is significantly greater than females.
B) average salary of males is significantly lower than females.
C) salaries of males and females are equal.
D) average salary of males is greater than females cannot be proved.

Question 10

When developing an interval estimate for the difference between two population means with sample sizes of n₁ and n₂,

A) n₁ must be equal to n₂.
B) n₁ must be smaller than n₂.
C) n₁ must be larger than n₂.
D) n₁ and n₂ can be of different sizes.

Question 11

Salary information regarding male and female employees of a large company is shown below. ​ At 95% confidence, the margin of error is

A) 1.960.
B) 1.645.
C) 3.920.
D) 7.839.

Question 12

The standard error of - is the

A) pooled estimator of - .
B) variance of the sampling distribution of - .
C) standard deviation of the sampling distribution of - .
D) margin of error of - .​

Question 13

Salary information regarding male and female employees of a large company is shown below. ​ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females at an α = .05, the test statistic is

A) 2.0.
B) 1.5.
C) 1.96.
D) 1.645.

Question 14

Two independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n₁ = 31 and n₂ = 40. The correct distribution to use is the t distribution with _____ degrees of freedom.

A) 73
B) 72
C) 71
D) 69

Question 15

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed. ​
Given that the null hypothesis to be tested is H₀: μd = 0,

A) the null hypothesis should be rejected.
B) the null hypothesis should not be rejected.
C) the alternative hypothesis should be revised.
D) the null hypothesis should be revised.

Question 16

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

A) null hypothesis should state p₁ - p₂ < 0.
B) alternative hypothesis should state p₁ - p₂ = 0.
C) alternative hypothesis should state p₁ - p₂ < 0.
D) alternative hypothesis should state p₁ - p₂ > 0.

Question 17

Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n₁ = 25 and n₂ = 30. The correct distribution to use is the t distribution with _____ degrees of freedom.

A) 57
B) 53
C) 54
D) 56

Question 18

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

A) can be approximated by any distribution.
B) will have a variance of one.
C) can be approximated by a normal distribution.
D) will have a mean of one.

Question 19

Salary information regarding male and female employees of a large company is shown below. ​ The 95% confidence interval for the difference between the means of the two populations is

A) 0 to 6.92.
B) -2 to 2.
C) -1.96 to 1.96.
D) 0.08 to 7.92.

Question 20

Salary information regarding male and female employees of a large company is shown below. ​ The point estimate of the difference between the means of the two populations is

A) -28.
B) 3.
C) 4.
D) -4.

Question 21

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. ​ A 95% confidence interval estimate for the difference between the average purchases of all customers using the two different credit cards is

A) 13.31 to 16.69.
B) 11.68 to 18.32.
C) 12.22 to 17.78.
D) 16.68 to 23.32.

Question 22

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ The 98% confidence interval for the difference between the two population means is

A) -9.92 to -2.08.
B) -10.66 to -1.34.
C) -13.84 to -1.16.
D) -24.77 to 12.23.

Question 23

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ The standard error of - is

A) 12.9.
B) 9.3.
C) 4.
D) 2.

Question 24

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. ​ The 98% confidence interval for the difference between the two population means is

A) -3.776 to 1.776.
B) -4.747 to 2.747.
C) -1.776 to 2.776.
D) -4.747 to 1.776.

Question 25

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ The test statistic for the difference between the two population means is

A) -.47.
B) -.65.
C) -1.5.
D) -3.0.

Question 26

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ The point estimate for the difference between the means of the two populations is

A) 58.5.
B) 9.
C) -9.
D) -6.

Question 27

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. ​ A point estimate for the difference between the mean purchases of all users of the two credit cards is

A) 20.
B) 2.
C) 260.
D) 15.

Question 28

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ The p-value for the difference between the two population means is

A) .0013.
B) .0027.
C) .4987.
D) .9987.

Question 29

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. ​ At 95% confidence, the margin of error is

A) 1.694.
B) 3.32.
C) 1.96.
D) 15.

Question 30

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. ​ A point estimate for the difference between the two population means is

A) 20.
B) .50.
C) .25.
D) 1.00.

Question 31

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. ​ A point estimate for the difference between the two population means is

A) 1.
B) 2.
C) 3.
D) 4.

Question 32

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. ​
The degrees of freedom for the t distribution are

A) 22.
B) 10.
C) 24.
D) 20.

Question 33

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. ​ The null hypothesis tested is H₀: μd = 0. The test statistic for the difference between the two population means is

A) 2.
B) 0.
C) -1.
D) -2.

Question 34

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. ​ A 95% interval estimate for the difference between the two population means is

A) .071 to 1.929.
B) .226 to 1.774.
C) 1.09 to 4.078.
D) 1.078 to 2.922.

Question 35

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. ​
The standard error of - is

A) 3.0.
B) 4.
C) 8.372.
D) 19.48.

Question 36

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. ​ If the null hypothesis H₀: μd = 0 is tested at the 5% level,

A) the null hypothesis should be rejected.
B) the null hypothesis should not be rejected.
C) the alternative hypothesis should be revised.
D) the null hypothesis should be revised.

Question 37

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. ​
The 95% confidence interval for the difference between the two population means is (use rounded standard error)

A) -5.344 to 11.344.
B) -5 to 3.
C) -4.86 to 10.86.
D) -2.65 to 8.65.

Question 38

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. ​ What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

A) There is a statistically significant difference in the average final examination scores between the two classes.
B) There is no statistically significant difference in the average final examination scores between the two classes.
C) It is impossible to make a decision on the basis of the information given.
D) The students who enrolled in statistics today are the same students who enrolled five years ago.

Question 39

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. ​ The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is

A) -1.
B) 0.
C) -4.
D) 2.

Question 40

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. ​
The point estimate for the difference between the means of the two populations is

A) 0.
B) -3.
C) 3.
D) 15.

Question 41

In hypothesis tests about p₁ - p₂, the pooled estimator of p is a​(n)

A) ​simple average of and ​ .
B) ​weighted average of and .
C) ​geometric average of and .
D) ​exponential average of and .

Question 42

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. ​ At the 5% level of significance, the null hypothesis

A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Question 43

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The standard error of - is

A) .025.
B) .044.
C) .0225.
D) .68.

Question 44

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

A) ​research samples.
B) ​pooled samples.
C) ​independent samples.
D) conditional samples.

Question 45

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. ​ The mean of the differences is

A) .5.
B) 1.5.
C) 2.0.
D) 2.5.

Question 46

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The 95% confidence interval estimate for the difference between the populations favoring the products is

A) -.024 to .064.
B) .6 to .7.
C) -.024 to .7.
D) .046 to .066.

Question 47

​The sampling distribution of - is approximated by a normal distribution if _____ are all greater than or equal to 5.

A) ​n₁p₂, p₂(1 - n₂), n₂p₁, p₁(1 - n₁)
B) ​n₁p₁, p₁(1 - n₁), n₂p₂, p₂(1 - n₂)
C) ​n₁p₂, n₁(1 - p₂), n₂p₁, n₂(1 - p₁)
D) ​n₁p₁, n₁(1 - p₁), n₂p₂, n₂(1 - p₂)

Question 48

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. ​ The test statistic is

A) .098.
B) 1.645.
C) 2.75.
D) 3.08.

Question 49

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. ​ The test statistic is

A) 1.616.
B) 1.906.
C) 2.096.
D) 2.256.

Question 50

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The point estimate for the difference between the two population proportions in favor of this product is

A) .07.
B) .68.
C) .44.
D) .02.

Question 51

Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on​

A) ​worker samples.
B) ​pooled samples.
C) ​independent samples.
D) ​matched samples.

Question 52

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. ​ The point estimate of the difference between the two population proportions is

A) -.02.
B) .048.
C) .52.
D) -.5.

Question 53

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. ​ The p-value is

A) .0010.
B) .0021.
C) .0042.
D) .9990.

Question 54

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. ​ We are interested in determining if the accident proportions differ between the two age groups. The p-value is

A) less than .001.
B) more than .10.
C) .0228.
D) .3.

Question 55

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. ​ We are interested in determining if the accident proportions differ between the two age groups. Let p_u represent the proportion under and p_o the proportion over the age of 18. The null hypothesis is

A) p_u - p_o ≤ 0.
B) p_u - p_o ≥ 0.
C) p_u - p_o ≠ 0.
D) p_u - p_o = 0.

Question 56

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. ​ We are interested in determining if the accident proportions differ between the two age groups.
The pooled estimator of the population proportion is

A) .305.
B) .300.
C) .027.
D) .450.

Question 57

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. ​ At α = .10, the null hypothesis

A) should not be rejected.
B) should be rejected.
C) should be revised.
D) should not be tested.

Question 58

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. ​ The 95% confidence interval for the difference between the two population proportions is

A) .5 to .52.
B) .48 to .5.
C) .028 to .068.
D) -.068 to .028.

Question 59

In testing the null hypothesis H₀: ₁ - ?₂ = 0, the computed test statistic is z = -1.66. The corresponding p-value is?

A) ?.0485.
B) ?.0970.
C) ?.9515.
D) ?.9030.

Question 60

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ At 95% confidence, the margin of error is

A) .064.
B) .044.
C) .0225.
D) .025.

Question 61

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.​

A) ​single, independent
B) ​independent, pooled​
C) ​matched, independent
D) ​matched, pooled

Question 62

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let α = .05.

Question 63

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. coli in organic vs. conventionally grown produce? Test at α = .10.