Question 1

A researcher wants to test whether the mean length of marriages in California differs from the mean length of marriages in Texas. Which of the following best describes the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$

Question 2

Suppose a 95% confidence interval for $$\mu_1$ - \mu_2$ between two population means is given as (196, 234). What does this interval imply?

Accepted Answer

We are 95% confident that $$\mu_1$ - \mu_2$ lies between 196 and 234.

Question 3

Given two independent samples with $$\bar{x}_1 = 15.9$$, $$s_1 = 12$, n_1$ = 12$$, $$\bar{x}_2 = 12.5$$, $$s_2 = 8$, n_2$ = 15$$, and a right-tailed hypothesis test using $$\alpha = 0.05$$, which of the following is correct if the test statistic is 1.082 and the critical value is 1.761?

Accepted Answer

Fail to reject $$H_0$$ because the test statistic does not exceed the critical value.

Question 4

A researcher is interested in comparing the amount of time spent watching television by women and by men. Independent samples of 14 women and 17 men yield $$\bar{x}_1 = 12.5$$, $$s_1 = 4.2$, n_1$ = 14$$ for women and $$\bar{x}_2 = 17.7$$, $$s_2 = 4.8$, n_2$ = 17$$ for men. What is the correct formula for the 95% confidence interval for $$\mu_1$ - \mu_2$ using the pooled t$-interval procedure?

Accepted Answer

$$ (\bar{x}_1 - \bar{x}_2) \pm t^* \sqrt{ s_p^2$ \left( \frac{1}{n_1$} + \frac{1}{n_2$} \right) } $$

Question 5

Which of the following is a correct interpretation of a two-tailed test for the difference in means?

Accepted Answer

We are testing whether the means of the two populations are different, regardless of direction.

Question 6

A variable of two populations has a mean of 70 and a standard deviation of 10 for one of the populations. If a random sample of 25 is selected from this population, what is the standard error of the mean?

Accepted Answer

$$ \frac{10}{\sqrt{25}} = 2 $$

Question 7

Suppose you are comparing the mean weekly television watching times of women and men. The sample means are $$\bar{x}_1 = 11.1 ($$women) and $$\bar{x}_2 = 16.9 ($$men), with $$s_1 = 4.5$, n_1$ = 14$$, $$s_2 = 4.7$, n_2$ = 17. $$What is the pooled variance $$s_p^2$?

Accepted Answer

$$ s_p^2$ = \frac{(n_1$-1)s_1$^2 + (n_2$-1)s_2$^2}{n_1$ + n_2$ - 2} $$

Question 8

A summary of two independent samples yields $$\bar{x}_1 = 12.7$$, $$s_1 = 4.4$, n_1$ = 14$$, $$\bar{x}_2 = 17.8$$, $$s_2 = 4.4$, n_2$ = 17. $$What is the point estimate for $$\mu_1$ - \mu_2$?

Accepted Answer

$$ 12.7 - 17.8 = -5.1 $$

Question 9

Which of the following is NOT an assumption for using the pooled $$t-$$test for the difference between two means?

Accepted Answer

The two population means are equal.

Question 10

A researcher performs a hypothesis test to determine whether the mean length of marriages in California differs from the mean length of marriages in Texas. What is the alternative hypothesis ($$H_a) $$for this test?

Accepted Answer

$$H_a: \mu_1$ 
eq \mu_2$

Question 11

In a study comparing two means, the sample sizes are $$n_1 = 14$ and n_2$ = 17. $$What is the degrees of freedom for the pooled $$t-$$test?

Accepted Answer

$$ n_1$ + n_2$ - 2 = 29 $$

Question 12

A researcher is interested in comparing the mean time spent watching television by women and men. If the 95% confidence interval for $$\mu_1$ - \mu_2$ is (-8.2, -2.1), what can be concluded?

Accepted Answer

Women spend significantly less time watching television than men.

Hypothesis Testing and Confidence Intervals for Two Populations – Study Guide

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