Question 1

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Accepted Answer

If the confidence interval does not include 0, then it can be concluded that there is a significant difference between the two population means at the given confidence level. In this case, the confidence interval (8.5, 11.5) does not include 0, so we can conclude that there is a significant difference between the two population means at the 95 percent confidence level.

Question 2

Assume that we are constructing a confidence interval for the difference in the means of two populations based on independent random samples.If both sample sizes $n _ { 1 } \text { and } n _ { 2 } = 10$ 
and the distributions of both populations are highly skewed,then a confidence interval for the difference in the means can be constructed using the t test statistic.

Accepted Answer

If the sample sizes are both 10 and the distributions are highly skewed, then the assumption of normality for the population distributions may not be met. In this case, the t test statistic may not be appropriate for constructing a confidence interval. Alternative methods, such as non-parametric methods, may need to be employed.

Question 3

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

Accepted Answer

In an independent samples experiment, the measurements in each sample are not related to each other. This means that the measurements in one sample do not depend on or influence the measurements in the other sample. Therefore, the correct answer is A.

Question 4

When testing the difference between two proportions selected from populations with large independent samples,the z test statistic is used.

Accepted Answer

This is true, as the z test statistic can be used to compare two proportions from large independent samples.

Question 5

In forming a confidence interval for μ₁ - μ₂,only two assumptions are required: independent samples and sample sizes of at least 30.

Accepted Answer

The assumptions are independent samples, equal variances, and either sample sizes are large or the sampled populations are normally distributed.

Question 6

The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2.The weekly sales are normally distributed.This problem should be analyzed using an independent means method.

Accepted Answer

Independent means method, also known as independent samples t-test or two-sample t-test, is used to compare the means of two independent groups. In this case, the two groups are sales of store 1 and store 2, and they are independent because the sales of one store do not affect the sales of the other store. As the weekly sales are normally distributed, we can use the independent means method to determine if there is any difference between the means of the two groups.

Question 7

There are two types of machines called type A and type B.Both type A and type B can be used to produce a certain product.The production manager wants to compare efficiency of the two machines.He assigns each of the 15 workers to both types of machines to compare their hourly production rate.In other words,each worker operates machine A and machine B for one hour each.These two samples are independent.

Accepted Answer

This is a paired sample because both machines have the same operators.

Question 8

In testing the difference between the means of two independent populations,if neither population is normally distributed,then the sampling distribution of the difference in means will be approximately normal,provided that the sum of the sample sizes obtained from the two populations is at least 30.

Accepted Answer

We need each sample to be large (at least greater than 30).

Question 9

When we are testing a hypothesis about the difference in two population proportions based on large independent samples,we compute a combined (pooled)proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

Accepted Answer

When testing a hypothesis about the difference in two population proportions based on large independent samples, if we assume that there is no difference between the two proportions in our null hypothesis, we do compute a combined (pooled) proportion from the two samples. This allows us to estimate the common underlying proportion for both populations and obtain a more precise estimate of the standard error.

Question 10

In testing for the equality of means from two independent populations,if the hypothesis of equal population means is rejected at α = .01,it will __________ be rejected at α = .05.
A)Always
B)Sometimes
C)Never

Accepted Answer

If the hypothesis of equal population means is rejected at α = .01, it means there is strong evidence to suggest that the population means are different. Therefore, at a higher level of significance (α = .05), the hypothesis of equal means is still likely to be rejected. This is because α = .05 is a less strict criterion than α = .01, and any significant result found at α = .01 would also be significant at α = .05.

Question 11

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

Accepted Answer

The alternative hypothesis indicates that there is a difference between the means of two populations, not necessarily that there is no difference.

Question 12

In testing the difference between the means of two normally distributed populations using independent random samples,we can only use a two-sided test.

Accepted Answer

In testing the difference between the means of two normally distributed populations using independent random samples, we can use a one-sided test as well as a two-sided test. The choice of which test to use depends on the research hypothesis and the direction of the expected difference between the population means.

Question 13

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 to 1.4 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Accepted Answer

The correct interpretation of the confidence interval is that we can be 95 percent confident that the true difference between the population means falls between the values of -2.6 and 1.4. This means that there is a possibility that the true difference is zero, which would indicate that there is no significant difference between the two populations. Therefore, we cannot conclude with certainty that there is a significant difference between the two population means based solely on the confidence interval.

Question 14

When comparing two independent population means,if n₁ = 13 and n₂ = 10,degrees of freedom for the t statistic is 22.

Accepted Answer

Degrees of freedom = n₁ + n₂ − 2 = 13 + 10 − 2 = 21

Question 15

In an experiment involving matched pairs,a sample of 12 pairs of observations is collected.The degrees of freedom for the t statistic is 10.

Accepted Answer

Degrees of freedom is n − 1 = 12 − 1 = 11

Question 16

When comparing two population means based on independent random samples,the pooled estimate of the variance is used when there is an assumption of equal population variances.

Accepted Answer

When comparing two population means based on independent random samples, the pooled estimate of the variance is used when there is an assumption of equal population variances.

Question 17

In testing the difference between the means of two normally distributed populations using large independent random samples,the sample sizes from the two populations must be equal.

Accepted Answer

Sample sizes do not have to be equal to test the differences of the means.

Question 18

A new company is in the process of evaluating its customer service.The company offers two types of sales: (1)Internet sales and (2)store sales.The marketing research manager believes that the Internet sales are more than 10 percent higher than store sales.The null hypothesis would be: A)P_Internet - P_store > .10 B)P_Internet - P_store < .10 C)P_Internet - P_store ≥ .10 D)P_Internet - P_store ≤ .10 E)P_Internet - P_store = .10

Accepted Answer

The null hypothesis is usually the opposite of the research hypothesis. Based on the information provided, the research hypothesis is that Internet sales are more than 10% higher than store sales. Therefore, the null hypothesis would be that there is no difference or that the difference is equal to or less than 10%. The option that best reflects this is D, which states "P_Internet - P_store ≤ .10." This means that the difference between Internet and store sales is less than or equal to 10%.

Question 19

In testing the difference between two means from two independent populations,the sample sizes do not have to be equal.

Accepted Answer

The t-test for two independent means does not require equal sample sizes. However, if the sample sizes are greatly unequal, it may affect the validity of the test and alternative methods may need to be used.

Question 20

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,9 heart patients' cholesterol levels are measured before they are given the drug.The same 9 patients use XZR for two continuous months.After two months of continuous use,the 9 patients' cholesterol levels are measured again.The comparison of cholesterol levels before versus after administering the drug is an example of testing the difference between:
A)Two means from independent populations.
B)Two population variances from independent populations.
C)Two population proportions.
D)Matched pairs from two dependent populations.

Accepted Answer

This scenario involves the same group of heart patients being measured before and after using the drug XZR. Therefore, it is a comparison of matched pairs from two dependent populations. The goal is to determine if the drug has had an effect on their cholesterol levels. Options A, B, and C do not apply to this scenario.

Quiz 10: Comparing Two Means and Two Proportions

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

When testing the difference between two proportions selected from populations with large independent samples,the z test statistic is used.

In forming a confidence interval for μ₁ - μ₂,only two assumptions are required: independent samples and sample sizes of at least 30.

The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2.The weekly sales are normally distributed.This problem should be analyzed using an independent means method.

In testing the difference between the means of two independent populations,if neither population is normally distributed,then the sampling distribution of the difference in means will be approximately normal,provided that the sum of the sample sizes obtained from the two populations is at least 30.

When we are testing a hypothesis about the difference in two population proportions based on large independent samples,we compute a combined (pooled)proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

In testing for the equality of means from two independent populations,if the hypothesis of equal population means is rejected at α = .01,it will __________ be rejected at α = .05.

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

In testing the difference between the means of two normally distributed populations using independent random samples,we can only use a two-sided test.

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 to 1.4 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

When comparing two independent population means,if n₁ = 13 and n₂ = 10,degrees of freedom for the t statistic is 22.

In an experiment involving matched pairs,a sample of 12 pairs of observations is collected.The degrees of freedom for the t statistic is 10.

When comparing two population means based on independent random samples,the pooled estimate of the variance is used when there is an assumption of equal population variances.

In testing the difference between the means of two normally distributed populations using large independent random samples,the sample sizes from the two populations must be equal.

A new company is in the process of evaluating its customer service.The company offers two types of sales: (1) Internet sales and (2) store sales.The marketing research manager believes that the Internet sales are more than 10 percent higher than store sales.The null hypothesis would be:

In testing the difference between two means from two independent populations,the sample sizes do not have to be equal.

Quiz 10: Comparing Two Means and Two Proportions

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

When testing the difference between two proportions selected from populations with large independent samples,the z test statistic is used.

In forming a confidence interval for μ1 - μ2,only two assumptions are required: independent samples and sample sizes of at least 30.

The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2.The weekly sales are normally distributed.This problem should be analyzed using an independent means method.

In testing the difference between the means of two independent populations,if neither population is normally distributed,then the sampling distribution of the difference in means will be approximately normal,provided that the sum of the sample sizes obtained from the two populations is at least 30.

When we are testing a hypothesis about the difference in two population proportions based on large independent samples,we compute a combined (pooled)proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

In testing for the equality of means from two independent populations,if the hypothesis of equal population means is rejected at α = .01,it will __________ be rejected at α = .05.

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

In testing the difference between the means of two normally distributed populations using independent random samples,we can only use a two-sided test.

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 to 1.4 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

When comparing two independent population means,if n1 = 13 and n2 = 10,degrees of freedom for the t statistic is 22.

In an experiment involving matched pairs,a sample of 12 pairs of observations is collected.The degrees of freedom for the t statistic is 10.

When comparing two population means based on independent random samples,the pooled estimate of the variance is used when there is an assumption of equal population variances.

In testing the difference between the means of two normally distributed populations using large independent random samples,the sample sizes from the two populations must be equal.

A new company is in the process of evaluating its customer service.The company offers two types of sales: (1) Internet sales and (2) store sales.The marketing research manager believes that the Internet sales are more than 10 percent higher than store sales.The null hypothesis would be:

In testing the difference between two means from two independent populations,the sample sizes do not have to be equal.

In forming a confidence interval for μ₁ - μ₂,only two assumptions are required: independent samples and sample sizes of at least 30.

When comparing two independent population means,if n₁ = 13 and n₂ = 10,degrees of freedom for the t statistic is 22.