Question 1

In testing the difference between the means of two normally distributed populations using independent random samples with equal variances, the correct test statistic to use is the
A) z statistic.
B) t statistic.
C) F statistic.
D) chi-square statistic.
E) None of the other choices is correct.

Accepted Answer

This is because we used the pooled estimate of the variance.

Question 2

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels, the cholesterol levels of 9 heart patients 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 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

Since it is the same 9 patients, the measurements are not independent. They are related, and thus you need to use matched pairs.

Question 3

The F statistic can assume either a positive or a negative value.

Accepted Answer

The F statistic can only have values greater than or equal to 1.

Question 4

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

Since you are trying to prove that Internet sales are greater than the store sales, the null would be the opposite, where the difference between the Internet and store sales would be less than 0.10 or equal to 0.10.

Question 5

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 alternative hypothesis for this problem would be stated as A) P_Internet − P_store > 0. B) P_Internet − P_store < 0. C) P_Internet − P_store ≥ .10. D) P_Internet − P_store ≤ .10. E) P_Internet − P_store > .10.

Accepted Answer

Since you want to prove the difference between Internet and store sales to be greater than 0.10, the alternative needs to read as P_Internet − P_store > .10.

Question 6

When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ________. A) z B) t C) F D) t²

Accepted Answer

We pool the variances and estimate the standard deviation.

Question 7

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 the average price-to-earnings ratio in the banking industry. The alternative hypothesis is A) μ_consumer = μ_banking. B) μ_consumer ≤ μ_banking. C) μ_consumer > μ_banking. D) μ_consumer < μ_banking. E) μ_consumer ≠ μ_banking.

Accepted Answer

In this case, the alternative hypothesis should illustrate that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry.

Question 8

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 ________.
A) z
B) t
C) F
D) chi-square
E) None of the other choices is correct.

Accepted Answer

This is because we estimate the population standard deviation with the pooled sample variances.

Question 9

In testing the difference between two means from two normally distributed independent populations, the distribution of the difference in sample means will be
A) normally distributed only if sample sizes are equal.
B) normally distributed only if both population standard deviations are known.
C) normally distributed.
D) normally distributed if both sample sizes are very large.
E) normally distributed only if both population variances are equal.

Accepted Answer

If they come from normally distributed population, then their differences will also be normally distributed.

Question 10

The value of F_α in a particular situation depends on the size of the right-hand tail area and the numerator degrees of freedom.

Accepted Answer

The F distribution is used when comparing two independent samples and as such it will also depend on the denominator degrees of freedom.

Question 11

The exact shape of the curve of the F distribution depends on two parameters, df₁ and df₂.

Accepted Answer

df₁ is the numerator degrees of freedom and df₂is the denominator degrees of freedom.

Question 12

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 ________. A) 19 B) 18 C) 9 D) 8 E) 20

Accepted Answer

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

Question 13

An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n) ________ experiment.
A) paired difference
B) equal variances
C) independent samples
D) dependent samples

Accepted Answer

In this case, we look at the paired differences since the populations are dependent and related.

Question 14

When testing the difference between two population proportions using large independent random samples, the ________ test statistic is used.
A) z
B) t
C) F
D) chi-square
E) None of the other choices is correct.

Accepted Answer

We know the standard deviation so therefore we can use the z test.

Question 15

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. A) Reject H₀ if t > 1.96. B) Reject H₀ if t > 1.645. C) Reject H₀ if t > 1.721. D) Reject H₀ if t > 2.08. E) Reject H₀ if t > 1.782.

Accepted Answer

Need to select a t distribution for α = .05 and df = 21.

Question 16

When testing the difference between two population proportions, the ________ test statistic is used. A) z B) t C) F D) t²

Accepted Answer

This is because we know the standard deviation.

Question 17

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

Since you are going from a stringent alpha to a less stringent alpha, and it was rejected at the more stringent alpha, it will always be rejected at the less stringent alpha.

Question 18

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?
A) a test of hypothesis about the mean of a population of paired differences selected from two related samples
B) a test of hypothesis about the difference between the means of two normally distributed populations using independent samples
C) a test of hypothesis about the difference between two population proportions, using large independent random samples
D) a test of hypothesis about the difference between the variances of two normally distributed populations using independent samples

Accepted Answer

In selection A, we are strictly concerned with looking at the difference (or the before and after) between these two related (dependent) samples. We take the difference between each pair and then look at that difference.

Question 19

An experiment in which there is no relationship between the measurements on the different samples is a(n) ________ experiment.
A) paired difference
B) equal variances
C) independent samples
D) dependent samples

Accepted Answer

If there is no relation, then the samples are said to be independent, and the one sample does not affect the other.

Question 20

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 ________. A) 19 B) 18 C) 9 D) 8 E) 10

Accepted Answer

Degrees of freedom = n − 1 = 10 − 1 = 9 for the paired difference test.

Quiz 11: Statistical Inferences Based on Two Samples

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

The F statistic can assume either a positive or a negative value.

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

When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ________.

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 the average price-to-earnings ratio in the banking industry. The alternative hypothesis 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 the difference between two means from two normally distributed independent populations, the distribution of the difference in sample means will be

The value of Fα in a particular situation depends on the size of the right-hand tail area and the numerator degrees of freedom.

The exact shape of the curve of the F distribution depends on two parameters, df1 and df2.

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 ________.

An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n) ________ experiment.

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

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 testing the difference between two population proportions, the ________ test statistic is used.

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 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?

An experiment in which there is no relationship between the measurements on the different samples is a(n) ________ experiment.

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 ________.

The value of F_α in a particular situation depends on the size of the right-hand tail area and the numerator degrees of freedom.

The exact shape of the curve of the F distribution depends on two parameters, df₁ and df₂.

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 ________.

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 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 ________.