Question 1

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than average price-to-earnings ratio in banking industry.The alternative hypothesis is:

Accepted Answer

The alternative hypothesis should state that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry, which is represented by option C. Option A is unclear because it combines the mean and standard deviation into one equation. Option B states that the two means are equal or that the consumer industry has a lower price-to-earnings ratio than the banking industry, which is not consistent with the hypothesis being tested. Option D is the opposite of the alternative hypothesis, as it states that the price-to-earnings ratio in the consumer industry is lower than the banking industry. Option E is unclear and unnecessarily complicated, as it includes the symbol for "not equal to" without providing any additional meaning.

Question 2

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

Accepted Answer

The answer of Given the following information about a hypothesis...

Question 3

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 vs.after administering the drug is an example of testing the difference between:

Accepted Answer

This is an example of matched pairs or paired samples as the same group of patients are being measured before and after the administration of the drug. Therefore, we are comparing the means of the same group (dependent population) before and after the administration of the drug XZR.

Question 4

A new company is in the process of evaluating its customer service.The company offers two types of sales: 1.Internet sales;2.Store sales.The marketing research manager believes that the Internet sales are more than 10% higher than store sales.The alternative hypothesis for this problem would be stated as:

Accepted Answer

The alternative hypothesis for this problem should state that the Internet sales are more than 10% higher than store sales, which is expressed as P_internet- P_store > .10. Therefore, the best choice is E.

Question 5

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

Accepted Answer

The distribution of the difference in sample means will be normally distributed if both populations are normally distributed and if the samples are independent. The Central Limit Theorem also ensures that the distribution of the difference will be approximately normal, regardless of sample sizes or population variances. Therefore, option C is the best choice.

Question 6

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

Accepted Answer

The null hypothesis represents the statement of no effect or no difference. In this case, it would be that the difference between Internet sales and store sales is less than or equal to 10%.

Question 7

In testing the difference between the means of two normally distributed populations using large,independent random samples with known variances,the correct test statistic to use is:

Accepted Answer

When comparing the means of two populations with known variances using large samples, the Z statistic is appropriate because it assumes normal distribution and known population variances.

Question 8

If the Z statistic (critical value)is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of rejecting the null hypothesis __________.

Accepted Answer

The answer of If the Z statistic (critical value)is incorrectly...

Question 9

When testing the difference between two population proportions using large independent random samples,__________ test statistic is used.

Accepted Answer

When testing the difference between two population proportions using large independent random samples, we use the Z-test statistic. The Z-test is appropriate when the sample size is large and the population standard deviation is known.

Question 10

In testing the difference between the means of two normally distributed populations using small independent random samples,the most appropriate test statistic is the _________ statistic.

Accepted Answer

When the sample sizes are small and the population standard deviations are unknown, the appropriate test statistic is the t-statistic.

Question 11

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

Accepted Answer

The answer of Given the following information about a hypothesis...

Question 12

In testing for the equality of means from two independent populations,if the null hypothesis is rejected,the test could result in:

Accepted Answer

If the null hypothesis is rejected, it means that the test has found a statistically significant difference between the means of the two populations. However, this does not necessarily mean that the difference is real. It is possible that the difference is due to chance, and that the null hypothesis is actually true. This is known as a Type I error.

Question 13

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples rather than the actual observations themselves?

Accepted Answer

In a test of hypothesis about the mean of a population of paired differences selected from two related samples, the variable of interest is the difference between the values of the observations from the two samples, rather than the actual observations themselves. This is because the two samples are related and the focus is on the difference between the paired values, rather than the individual values themselves. The other options involve testing the means, proportions, or variances of two independent samples, which focus on the actual observations themselves.

Question 14

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

Accepted Answer

If the null hypothesis is rejected at a significance level of 0.01, it means the test statistic is in the critical region for both 0.01 and the less stringent 0.05 level, so it will always be rejected at 0.05.

Question 15

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

Accepted Answer

The degrees of freedom for a paired t-test is equal to the number of pairs minus 1. In this case, we have 10 paired samples, so the degrees of freedom is 10-1 = 9. Therefore, the answer is C.

Question 16

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

Accepted Answer

Since the sample sizes are both less than 30 and we do not know the population variances, we should use a t-test. At a significance level of .05 with a two-tailed test, the critical t-value with 21 degrees of freedom (the smaller of the two sample sizes minus 1) is 1.721. Therefore, we should reject the null hypothesis if the calculated t-value is greater than 1.721.

Question 17

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

Accepted Answer

When comparing the variances of two normally distributed populations using independent random samples, the correct test statistic to use is the F-test. The F-test compares the ratios of the sample variances and follows an F-distribution. Z and t-tests are used for comparing means, while the chi-square test is used for testing categorical data.

Question 18

If the Z statistic (critical value)is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of committing a Type II error __________.

Accepted Answer

When comparing two means from independent populations using small samples, the appropriate test statistic is the t statistic. If the Z statistic is used instead, it results in wider confidence intervals and a greater chance of committing a Type II error (failing to reject a false null hypothesis). Therefore, the chance of committing a Type II error increases.

Question 19

If we are testing the difference between the means of two normally distributed independent populations with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

Accepted Answer

Degrees of freedom = n₁ + n₂ − 2 = 10 + 10 − 2 = 18

Question 20

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is:

Accepted Answer

When testing a hypothesis about the mean of a population of paired differences, we have dependent or correlated samples. In this case, we use the paired t-test, which compares the mean difference between pairs to 0 (the null hypothesis). Therefore, the correct test statistic to use is t. Options A, C, and D are not applicable in this scenario.

Quiz 10: Statistical Inferences Based on Two Samples

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than average price-to-earnings ratio in banking industry.The alternative hypothesis is:

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

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

In testing the difference between the means of two normally distributed populations using large,independent random samples with known variances,the correct test statistic to use is:

If the Z statistic (critical value) is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of rejecting the null hypothesis __________.

When testing the difference between two population proportions using large independent random samples,__________ test statistic is used.

In testing the difference between the means of two normally distributed populations using small independent random samples,the most appropriate test statistic is the _________ statistic.

In testing for the equality of means from two independent populations,if the null hypothesis is rejected,the test could result in:

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples rather than the actual observations themselves?

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

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

If the Z statistic (critical value) is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of committing a Type II error __________.

If we are testing the difference between the means of two normally distributed independent populations with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is:

Quiz 10: Statistical Inferences Based on Two Samples

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than average price-to-earnings ratio in banking industry.The alternative hypothesis is:

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

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

In testing the difference between the means of two normally distributed populations using large,independent random samples with known variances,the correct test statistic to use is:

If the Z statistic (critical value) is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of rejecting the null hypothesis __________.

When testing the difference between two population proportions using large independent random samples,__________ test statistic is used.

In testing the difference between the means of two normally distributed populations using small independent random samples,the most appropriate test statistic is the _________ statistic.

In testing for the equality of means from two independent populations,if the null hypothesis is rejected,the test could result in:

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples rather than the actual observations themselves?

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

If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 10,n2 = 10,the degrees of freedom for the t statistic is ____.

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? HA: µA> µB, 1 = 12, 2 = 9,s1 = 4,s2 = 2,n1 = 13,n2 = 10.

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

If the Z statistic (critical value) is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of committing a Type II error __________.

If we are testing the difference between the means of two normally distributed independent populations with samples of n1 = 10,n2 = 10,the degrees of freedom for the t statistic is ____.

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is:

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

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

If we are testing the difference between the means of two normally distributed independent populations with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.