Question 1

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females,then the test is one-tailed.

Accepted Answer

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is two-tailed because the alternative hypothesis is that there is a difference, which could be in either direction (males making more or females making more). A one-tailed test would only be appropriate if the alternative hypothesis was that one gender makes more than the other, but not specifying which one.

Question 2

The paired difference test has (n - 1)degrees of freedom.

Accepted Answer

The paired difference test uses a t-test, and the degrees of freedom for a t-test using paired differences is (n-1).

Question 3

The paired t test is especially appropriate when the sample sizes of two groups are the same.

Accepted Answer

The paired t-test is used when the same subjects are measured twice under different conditions, not necessarily when the sample sizes are the same.

Question 4

When sample sizes are less than 30,a test for the differences between two population means has n-1 degrees of freedom.

Accepted Answer

When sample sizes are less than 30, a test for the differences between two population means has degrees of freedom calculated using the formula (n1-1) + (n2-1) where n1 and n2 are the sample sizes for the two populations being compared.

Question 5

If we are testing for the difference between two population proportions,it is assumed that the two populations are approximately normal and have equal variances.

Accepted Answer

When testing for the difference between two population proportions, the normality assumption may not be necessary if both sample sizes are sufficiently large. Additionally, there is no assumption of equal variances in the comparison of proportions. Instead, we use the standard error formula for the difference between proportions, which takes into account the sample sizes and sample proportions of each group.

Question 6

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City,then the test is two-tailed.

Accepted Answer

A null hypothesis is typically two-tailed when it states that there is no significant difference or relationship between two variables being compared. In this case, the null hypothesis stating that there is no difference between the mean net income of retail stores in Chicago and New York City is a two-tailed hypothesis.

Question 7

In testing the difference between two population proportions,we pool the two sample proportions to estimate the population proportion.

Accepted Answer

When testing the difference between two population proportions, we use a pooled proportion to estimate the variance of the sampling distribution. This pooled proportion is a weighted average of the sample proportions from each group, which assumes that the true population proportions are equal.

Question 8

The paired difference test has (n₁ + n₂ - 2)degrees of freedom.

Accepted Answer

The paired difference test, such as the paired t-test, uses (n - 1) degrees of freedom, where n is the number of paired observations.

Question 9

If we are testing for the difference between two population means,it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Accepted Answer

The assumption of independence between the two populations is necessary for conducting a two-sample t-test or other methods for testing the difference between two population means. If the samples are not independent, the results of the test may not be valid.

Question 10

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,then the test has (n₁ + n₂ - 2)degrees of freedom.

Accepted Answer

This is the correct formula for the degrees of freedom when testing for the difference between two population means with equal but unknown standard deviations.

Question 11

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the standard deviations are pooled to compute the best estimated variance.

Accepted Answer

The answer of If we are testing for the difference...

Question 12

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the variances are pooled to compute the best estimated variance.

Accepted Answer

When assuming two populations have equal but unknown standard deviations, we pool their variances to compute the best estimated variance. This pooled variance is used when conducting a two-sample t-test for the difference between two population means.

Question 13

The pooled estimate of the proportion is found by dividing the total number of successes by the total number of observations.

Accepted Answer

This is true. The pooled estimate of the proportion is the combined proportion of successes from multiple samples, calculated by dividing the total number of successes by the total sample size.

Question 14

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

Accepted Answer

This statement is incorrect. The pooled estimate of the proportion is found by taking the weighted average of the individual proportions in each sample, where the weights are based on the sample sizes.

Question 15

If we are testing for the difference between two population proportions,it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

Accepted Answer

When testing for the difference between two population proportions, if the sample sizes are sufficiently large (np ≥ 10 and n(1-p) ≥ 10 for both samples), then the binomial distribution can be approximated by the normal distribution. This assumption is necessary for using the z-test to compare proportions.

Question 16

When testing for a difference between the means of two dependent samples,nS1U1B11S1U1B0 = nS1U1B12S1U1B0.

Accepted Answer

This is true because n_{and nS1U1B2 represent the sample sizes for the two dependent samples, and} represents the common sample standard deviation. The formula indicates that the product of the sample size and the sample standard deviation is the same for both samples, which is a requirement for the use of a paired t-test.

Question 17

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)- 1.

Accepted Answer

The formula provided is incorrect and not the standard way to calculate degrees of freedom when testing for the difference between two population means with equal and unknown standard deviations. The correct approach typically involves using the sample sizes of the two groups and a formula related to the pooled variance estimate, often simplified in the form of the Welch-Satterthwaite equation for unequal variances or directly calculated for equal variances.

Question 18

A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee.To find reactions regarding the proposal,120 office personnel and 160 plant personnel were selected at random.Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal.Computed z = 1.48.At the 0.05 level,it was concluded that there is sufficient evidence to support the belief that the proportion of office personnel in favor of the proposal is greater than that of the plant personnel.

Accepted Answer

The computed z-value of 1.48 does not exceed the critical value of 1.645 for a one-tailed test at the 0.05 significance level, so there is not sufficient evidence to support the belief that the proportion of office personnel in favor is greater than that of plant personnel.

Question 19

A statistics professor wants to compare grades in two different classes of the same course.This is an example of a paired sample.

Accepted Answer

A paired sample would involve comparing two sets of data from the same group or subject (i.e. before and after treatment or measuring the same variable in two different conditions). In this case, the comparison is between two different classes, which are separate groups and not paired samples. A more appropriate analysis would be an unpaired or independent sample t-test.

Question 20

If samples taken from two populations are not independent,then a test of paired differences is applied.

Accepted Answer

When samples are not independent, they are often paired or matched in some way. In such cases, a test of paired differences is used to compare the two populations.

Quiz 11: Two-Sample Tests of Hypothesis

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females,then the test is one-tailed.

The paired difference test has (n - 1)degrees of freedom.

The paired t test is especially appropriate when the sample sizes of two groups are the same.

When sample sizes are less than 30,a test for the differences between two population means has n-1 degrees of freedom.

If we are testing for the difference between two population proportions,it is assumed that the two populations are approximately normal and have equal variances.

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City,then the test is two-tailed.

In testing the difference between two population proportions,we pool the two sample proportions to estimate the population proportion.

The paired difference test has (n₁ + n₂ - 2)degrees of freedom.

If we are testing for the difference between two population means,it is assumed that the sample observations from one population are independent of the sample observations from the other population.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,then the test has (n₁ + n₂ - 2)degrees of freedom.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the standard deviations are pooled to compute the best estimated variance.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the variances are pooled to compute the best estimated variance.

The pooled estimate of the proportion is found by dividing the total number of successes by the total number of observations.

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

If we are testing for the difference between two population proportions,it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

When testing for a difference between the means of two dependent samples,n₁ = n₂.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)- 1.

A statistics professor wants to compare grades in two different classes of the same course.This is an example of a paired sample.

If samples taken from two populations are not independent,then a test of paired differences is applied.

Quiz 11: Two-Sample Tests of Hypothesis

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females,then the test is one-tailed.

The paired difference test has (n - 1)degrees of freedom.

The paired t test is especially appropriate when the sample sizes of two groups are the same.

When sample sizes are less than 30,a test for the differences between two population means has n-1 degrees of freedom.

If we are testing for the difference between two population proportions,it is assumed that the two populations are approximately normal and have equal variances.

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City,then the test is two-tailed.

In testing the difference between two population proportions,we pool the two sample proportions to estimate the population proportion.

The paired difference test has (n1 + n2 - 2)degrees of freedom.

If we are testing for the difference between two population means,it is assumed that the sample observations from one population are independent of the sample observations from the other population.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,then the test has (n1 + n2 - 2)degrees of freedom.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the standard deviations are pooled to compute the best estimated variance.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,the variances are pooled to compute the best estimated variance.

The pooled estimate of the proportion is found by dividing the total number of successes by the total number of observations.

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

If we are testing for the difference between two population proportions,it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

When testing for a difference between the means of two dependent samples,n1 = n2.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n1)(n2)- 1.

A statistics professor wants to compare grades in two different classes of the same course.This is an example of a paired sample.

If samples taken from two populations are not independent,then a test of paired differences is applied.

The paired difference test has (n₁ + n₂ - 2)degrees of freedom.

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations,then the test has (n₁ + n₂ - 2)degrees of freedom.

When testing for a difference between the means of two dependent samples,n₁ = n₂.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)- 1.