Question 1

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15. The degrees of freedom for the F distribution when testing the equality of the two population variances are A) 10 and 15. B) 11 and 16. C) 9 and 14. D) 8 and 13.

Accepted Answer

n − 1 = df₁ and n − 2 = df₂ 10 − 1 = 9 15 − 1 = 14

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. A) 1.792 B) 1.679 C) 2.823 D) 3.210 E) 1.478

Accepted Answer

s_p²= [(n₁− 1)s₁²+ (n₂− 1)s₂²]/(n₁ + n₂ − 2) = [(12)(25) + (9)(9)]/21 = (300 + 81)/21 = 18.143 Standard deviation of difference == 1.792

Question 3

In comparing the difference between two independent population means, the sampling distributions of the population means are at least approximately ________.
A) skewed right
B) skewed left
C) normal
D) binomial

Accepted Answer

These population means need to have a normal distribution in order to use the t test.

Question 4

Construct a 95 percent confidence interval for μ₁ − μ₂, where ₁ = 34.36, ₂= 26.45, s₁ = 9, s₂ = 6, n₁ = 10, n₂ = 16. (Assume equal population variances.)

Accepted Answer

The answer of Construct a 95 percent confidence interval for...

Question 5

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8, n₂ = 8, the degrees of freedom for the t statistic is ________. A) 16 B) 7 C) 14 D) 9

Accepted Answer

Paired differences degrees of freedom = n − 1 = 8 − 1 = 7

Question 6

When comparing the variances of two normally distributed populations using independent random samples, 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

You divide the larger variance by the smaller variance and then compare to the critical value.

Question 7

In testing the difference between two independent population means, if the assumption is of unequal variances, the critical value of the t statistic is obtained by calculating the ________. A) degrees of freedom B) sum of the two sample sizes (n₁ + n₂) C) p-value D) pooled variance

Accepted Answer

As the degrees of freedom increase, then the curve starts to approximate the normal distribution.

Question 8

When comparing two independent population variances, the correct test statistic to use is ________. A) z B) t C) F D) t ²

Accepted Answer

The null states that the variances are equal.

Question 9

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, = 12, = 9, s₁ = 5, s₂ = 3, n₁ = 13, n₂ = 10. A) t = 1.96 B) t = 1.5 C) t = 2.823 D) t = 1.674 E) t = 1.063

Accepted Answer

s_p²= [(n₁− 1)s₁²+ (n₂− 1)s₂²]/(n₁ + n₂ − 2) = [(12)(25) + (9)(9)]/21 = (300 + 81)/21 = 18.143 t = [(−) − 0]/= (12 − 9)/= 3/= 3/1.792 = 1.674

Question 10

In testing the difference between the means of two independent populations, the variances of the two samples can be pooled if the population variances are assumed to ________.
A) be unequal
B) be greater than the mean
C) sum to 1
D) be equal

Accepted Answer

This means we expect variance 1 to equal variance 2 to the population variance.

Question 11

The test of means for two related populations matches the observations (matched pairs) in order to reduce the ________ attributable to the difference between individual observations and other factors.
A) means
B) test statistic
C) degrees of freedom
D) variation

Accepted Answer

In this situation, we are strictly concerned with the differences and not the individual measurements.

Question 12

When testing the difference for the 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) t²

Accepted Answer

We use t since we do not have thestandard deviation of the population.

Question 13

Given the following information about a hypothesis, and the test of the difference between two variances based on independent random samples, what is the critical value of the test statistic at a significance level of 0.05? Assume that the samples are obtained from normally distributed populations. H_A: σ²_A > σ²_B, ₁ = 12, ₂ = 9, s₁ = 5, s₂ = 3, n₁ = 13, n₂ = 10. A) 3.87 B) 2.67 C) 3.07 D) 2.80 E) 2.38

Accepted Answer

F distribution for .05, numerator df = 12, denominator df = 9

Question 14

In testing the equality of population variance, what assumption(s) should be considered?
A) independent samples
B) equal sample sizes
C) normal distribution of the populations
D) independent samples and equal sample sizes
E) independent samples and normal distribution of the populations

Accepted Answer

The two samples need to not be related in any way and these samples need to have a normal distribution.

Question 15

In testing the difference between the means of two normally distributed populations, if μ₁ = μ₂ = 50, n₁ = 9, and n₂ = 13, the degrees of freedom for the t statistic equals ________. A) 22 B) 21 C) 19 D) 20

Accepted Answer

n₁ + n₂ − 2 = 9 + 13 − 2 = 20

Question 16

Parameters of the F distribution include A) n₁. B) degrees of freedom for the numerator and the denominator. C) n₂. D) n₁ and n₂. E) None of the other choices is correct.

Accepted Answer

The larger variance is in the numerator and the smaller variance in the denominator.

Question 17

In testing the difference between two independent population means, it is assumed that the level of measurement is ________.
A) a ratio variable
B) a qualitative variable
C) an interval variable
D) a categorical variable

Accepted Answer

This is the only variable that is continuous.

Question 18

Given two independent normal distributions with s₁² − s₂²= 100, μ₁ = μ₂ = 50, and n₁ = n₂ = 50, the sampling distribution of the mean difference ₁ − ₂ will have a mean of ________. A) 100 B) 1 C) 0 D) 50 E) 10

Accepted Answer

Because they are normal distributions, the distribution of the difference will be a normal distribution. Therefore, the mean is 0.

Question 19

In general, the shape of the F distribution is ________.
A) skewed right
B) skewed left
C) normal
D) binomial

Accepted Answer

The tail is skewed to the right.

Question 20

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 the administration of the drug is an example of testing the difference between two ________.
A) samples of equal variances
B) independent samples
C) paired samples
D) samples of unequal variances

Accepted Answer

These are paired samples because they were taken on the same 9 patients as before and after. These measurements are related and dependent.

Quiz 11: Statistical Inferences Based on Two Samples

Two independent samples selected from two normally distributed populations have variances of σ12 and σ22 with n1 = 10 and n2 = 15. The degrees of freedom for the F distribution when testing the equality of the two population variances are

In comparing the difference between two independent population means, the sampling distributions of the population means are at least approximately ________.

Construct a 95 percent confidence interval for μ1 − μ2, where 1 = 34.36, 2 = 26.45, s1 = 9, s2 = 6, n1 = 10, n2 = 16. (Assume equal population variances.)

If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 8, n2 = 8, the degrees of freedom for the t statistic is ________.

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

In testing the difference between two independent population means, if the assumption is of unequal variances, the critical value of the t statistic is obtained by calculating the ________.

When comparing two independent population variances, the correct test statistic to use is ________.

In testing the difference between the means of two independent populations, the variances of the two samples can be pooled if the population variances are assumed to ________.

The test of means for two related populations matches the observations (matched pairs) in order to reduce the ________ attributable to the difference between individual observations and other factors.

When testing the difference for the 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 equality of population variance, what assumption(s) should be considered?

In testing the difference between the means of two normally distributed populations, if μ1 = μ2 = 50, n1 = 9, and n2 = 13, the degrees of freedom for the t statistic equals ________.

Parameters of the F distribution include

In testing the difference between two independent population means, it is assumed that the level of measurement is ________.

Given two independent normal distributions with s12 − s22= 100, μ1 = μ2 = 50, and n1 = n2 = 50, the sampling distribution of the mean difference 1 − 2 will have a mean of ________.

In general, the shape of the F distribution is ________.

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15. The degrees of freedom for the F distribution when testing the equality of the two population variances are

Construct a 95 percent confidence interval for μ₁ − μ₂, where ₁ = 34.36, ₂= 26.45, s₁ = 9, s₂ = 6, n₁ = 10, n₂ = 16. (Assume equal population variances.)

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8, n₂ = 8, the degrees of freedom for the t statistic is ________.

In testing the difference between the means of two normally distributed populations, if μ₁ = μ₂ = 50, n₁ = 9, and n₂ = 13, the degrees of freedom for the t statistic equals ________.

Given two independent normal distributions with s₁² − s₂²= 100, μ₁ = μ₂ = 50, and n₁ = n₂ = 50, the sampling distribution of the mean difference ₁ − ₂ will have a mean of ________.