Deck 10: Inference About Means and Proportions With Two Populations

Question 1

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

Answer 1

69

Question 2

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.

Answer 2

can be approximated by a normal distribution.

Question 3

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 - .​

Answer 3

standard deviation of the sampling distribution of - .

Question 4

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.

Question 5

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 6

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.

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

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 9

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 10

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 11

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 12

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 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 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 14

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 15

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 16

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 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

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.

Question 19

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 20

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 21

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 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 standard error of - is

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

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 test statistic for the difference between the two population means is

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

Question 24

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 25

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 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 p-value for the difference between the two population means is

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

Question 27

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 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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 47

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 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 p-value is

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

Question 49

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 50

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 51

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 52

​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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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 61

Using the following data regarding the ages (in years) of full-time and part-time students, develop an interval estimate for the difference between the mean ages of the two populations.Use 95% confidence.The degrees of freedom for the t distribution is 106.
​

Question 62

The following information is given concerning the ACT scores of high school seniors from two local schools. ​
Develop a 98% confidence interval estimate for the difference between the two population means.Assume the two populations are normally distributed.

Question 63

In a sample of 40 Democrats, 6 opposed the President's foreign policy; while of 50 Republicans, 8 were opposed to his policy.Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Question 64

Samples of employees of Companies A and B provided the following information regarding the ages of employees. ​
Develop a 97% confidence interval for the difference between the average ages of the employees of the two companies.

Question 65

The following table shows the monthly sales (in units) of six salespersons before and after a bonus plan was introduced.Using α = .05, determine whether the bonus plan has increased sales significantly.Assume the population of differences is normally distributed.(For the following matched samples, let the difference d = After - Before.)

Question 66

The business manager of a local health clinic is interested in estimating the difference between the fees for extended office visits in her center and the fees of a newly opened group practice.She gathered the following information regarding the two offices. ​
Develop a 95% confidence interval estimate for the difference between the average fees of the two offices.

Question 67

The following information was obtained from matched samples regarding the productivity (in units per hour) of four individuals using two different methods of production. ​
Let d = Method 1 - Method 2.Is there a significant difference between the mean productivity of the two methods? Let α = .05.Assume the population of differences is normally distributed.

Question 68

A credit company has gathered information regarding the average amount (in $) owed by people under 30 years of age and by people over 30 years by taking independent random samples from both age groups.You are given the following information. ​
Construct a 95% confidence interval for the difference between the population average amounts owed by the two age groups.

Question 69

Independent random samples of managers' yearly salaries (in $1000) taken from governmental and private organizations provided the following information.At a .05 level of significance, test to determine if there is a significant difference between the average salaries of the managers in the two sectors.

Question 70

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.

Question 71

The office of records at a university has stated that the proportion of incoming female students who major in business has increased.A sample of female students taken several years ago is compared with a sample of female students this year.Results are summarized below.Has the proportion increased significantly? Test at α = .10.
​

Question 72

In a random sample of 200 Republicans, 160 opposed the new tax laws; while in a sample of 120 Democrats, 84 opposed.Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats who opposed this new law.

Question 73

The following information is gathered from random samples of day and evening students regarding the number of semester hours they take.
​ ​
Develop a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students.

Question 74

The following data present the number of computer units sold per day by a sample of 6 salespersons before and after a bonus plan was implemented. ​
Using a .05 level of significance, test to see if the bonus plan was effective.That is, did the bonus plan actually increase sales? ​Assume the population of differences is normally distributed.Let d = After - Before.

Question 75

A potential investor conducted a 144-day survey in each of the North Mall and South Mall theaters in order to determine the difference between the average daily attendance at these two theaters.The North Mall theater averaged 630 patrons per day; while the South Mall theater averaged 598 patrons per day.From past information, it is known that the variance for North Mall is 1000; while the variance for the South Mall is 1304.Develop a 98% confidence interval for the difference between the average daily attendance at the two theaters.

Question 76

In order to estimate the difference between the average age of male and female employees at the Young Corporation, the following information was gathered.Develop a 95% confidence interval estimate. ​

Question 77

Test scores on a standardized test from samples of students from two universities are given below. ​
Provide a 98% confidence interval estimate for the difference between the mean test scores of the two universities.

Question 78

The following are the results about the test scores of two samples of students from University A and University B on a national statistics examination.The population standard deviations are also shown below.Develop a 95% confidence interval estimate for the difference between the mean scores of the two populations.

Question 79

In a sample of 100 Republicans, 60 favored the President's anti-drug program.While in a sample of 150 Democrats, 84 favored his program.At α = .05, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program.

Question 80

The results of a recent poll on the preference of voters regarding presidential candidates are shown below. ​
Using α = .05, test to determine whether or not there is a significant difference between the preferences for the two candidates.