Question 1

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

The distribution of the difference between two means from two normally distributed independent populations is normally distributed, regardless of sample size or whether population standard deviations are known, as long as the sample sizes are large enough (i.e. the Central Limit Theorem applies).

Question 2

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 that there is enough evidence to reject the null hypothesis at a significance level of .01. Since a significance level of .05 is less strict than .01, there is a higher chance of rejecting the null hypothesis at α = .05. Therefore, it will always be rejected at α = .05 if it is rejected at α = .01.

Question 3

In testing the difference between the means of two normally distributed populations using independent random samples,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

The t statistic is used when comparing the means of two independent samples, especially when the population standard deviations are unknown and the sample sizes are small.

Question 4

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

Accepted Answer

The F distribution curve shape depends on the two parameters df1 and df2, which represent the degrees of freedom for the numerator and denominator, respectively.

Question 5

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

A paired difference experiment involves taking two different measurements on the same units, which allows for a direct comparison of the differences between pairs. This is the best choice for this scenario as it specifically describes the type of experiment being conducted. The other options (B) equal variances, (C) independent samples, and (D) dependent samples, do not necessarily imply the use of paired measurements.

Question 6

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

The degrees of freedom for a paired t-test is calculated as df = n - 1, where n is the number of pairs. In this case, we have 10 pairs, so the degrees of freedom is 9.

Question 7

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

This is an example of testing the difference between matched pairs from two dependent populations, as the same group of patients' cholesterol levels are measured before and after they use the drug, creating a dependent relationship between the two sets of measurements. This requires a dependent samples t-test to determine if there is a significant difference in cholesterol levels before and after using the drug.

Question 8

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, = 12, = 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

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

Question 9

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

When comparing two independent population means with equal variances, we use the two-sample t-test. Therefore, the correct test statistic to use is the t-statistic.

Question 10

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

When testing a hypothesis about the mean of a population of paired differences, we use the t-test for paired samples. This is because the sample of paired differences follows a distribution that is approximately normal, but with slightly different properties than independent samples. Therefore, the correct test statistic to use is t, not z or any other option.

Question 11

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 ³ .10. D) P_Internet − P_store £ .10. E) P_Internet − P_store = .10.

Accepted Answer

The null hypothesis is that there is no difference between the two types of sales, so the difference between Internet sales and store sales should be less than or equal to 10 percent. Therefore, the correct choice is P_Internet − P_store £ .10.

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

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 a test of hypothesis about the mean of a population of paired differences selected from two related samples, we are interested in the difference between the values of the observations from the two samples. This is because each observation in one sample is paired with a corresponding observation in the other sample, and we are interested in whether there is a significant difference between the two samples in terms of the differences between their paired observations. The other options listed all involve comparing the actual observations themselves between two samples, rather than the differences between them.

Question 14

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 ³ 0. D) P_Internet − P_store £ .10. E) P_Internet − P_store > .10.

Accepted Answer

The alternative hypothesis should indicate that the Internet sales are higher than store sales. Choice E is the only one that meets this requirement and also explicitly states that the difference between the two types of sales is greater than 10%.

Question 15

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

Independent samples are a type of experiment where the measurements taken from one sample have no impact or relation to the measurements taken from another sample. This is in contrast to paired difference experiments, where the measurements of one sample are directly related to the measurements of the other sample. Equal variances and dependent samples are not appropriate choices for an experiment with no relationship between measurements.

Question 16

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

The alternative hypothesis is designed to test whether the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry. Therefore, the alternative hypothesis should state that μ_consumer > μ_banking. Choice C is the only option that matches this requirement.

Question 17

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

The z test statistic is used when testing the difference between two population proportions using large independent random samples. The other options are used for different types of hypothesis tests.

Question 18

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

Accepted Answer

The z-test is used for testing the difference between two population proportions when the sample size is large and/or when the population standard deviation is known.

Question 19

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

Accepted Answer

The answer of The value of F_α in a particular...

Question 20

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

Accepted Answer

The F statistic is always non-negative.

Quiz 10: Statistical Inferences for Means and Proportions

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

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 correct test statistic to use is the

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

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.

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, = 12, = 9,s₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

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 ______.

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 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

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 ______.

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.

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

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

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

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

Quiz 10: Statistical Inferences for Means and Proportions

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

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 correct test statistic to use is the

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

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.

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, = 12, = 9,s1 = 4,s2 = 2,n1 = 13,n2 = 10.

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 ______.

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 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

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 ______.

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.

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

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

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

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

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

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, = 12, = 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 ______.

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