Question 1

Which of the following is a requirement for conducting a hypothesis test comparing two population proportions?

Accepted Answer

Each sample must have at least 5 successes and 5 failures.

Question 2

Given two independent samples with sample proportions $$\hat{p}_1$$ and $$\hat{p}_2$$, what is the formula for the pooled sample proportion $$\bar{p}$$?

Accepted Answer

$$\bar{p} = \frac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 3

A researcher wants to test if the mean height of people in 1988 is less than in 2012 using two independent samples. Which hypothesis should be used?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$; $$H_1$$: \$$mu_1$$ \u003c \$$mu_2$$

Question 4

Which formula is used to calculate the test statistic for comparing two independent sample means when population variances are unknown and not assumed equal?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

Question 5

In a study comparing measured and reported weights of individuals, which type of sample is being used?

Accepted Answer

Matched pairs (dependent samples)

Question 6

What is the formula for the test statistic when testing the mean of the differences in matched pairs?

Accepted Answer

$$t = \frac{\bar{d} - \mu_d}{s_d / \sqrt{n}}$$

Question 7

Which of the following is a strict requirement for using the F test to compare two population variances?

Accepted Answer

Both populations must be normally distributed.

Question 8

If the calculated F statistic for comparing two variances is close to 1, what does this suggest about the population variances?

Accepted Answer

The population variances are likely equal.

Question 9

A medical researcher compares the effectiveness of two treatments using the difference in proportions of success. The confidence interval for $$p_1$$ - $$p_2 is (0.0363$$, 0.127). What can be concluded?

Accepted Answer

There is a significant difference between the two treatments.

Question 10

Which of the following statements is TRUE regarding the equivalence of methods for testing two population proportions?

Accepted Answer

The P-value method and the critical value method are equivalent.

Question 11

In a hypothesis test for two independent means, which formula is used to estimate the degrees of freedom for the test statistic?

Accepted Answer

$$df = \min(n_1$ - 1, n_2$ - 1)$$

Question 12

A study finds that the P-value for a two-tailed test comparing two proportions is 0.00045, and the significance level is $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is a significant difference.

Question 13

Which formula gives the margin of error $$E$$ for the confidence interval of the difference between two proportions?

Accepted Answer

$$E = z_{\alpha/2} \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1$} + \frac{\hat{p}_2 \hat{q}_2}{n_2$}}$$

Question 14

In a matched pairs study, the sample mean of the differences is $$\bar{d} = 1.425 lb$$, the sample standard deviation is $$s_d = 5.18 lb$$, and $$n = 8. $$What is the value of the test statistic for testing $$H_0$$: \mu_d = 0$$?

Accepted Answer

$$t = \frac{1.425 - 0}{5.18 / \sqrt{8}} = 0.778$$

Question 15

When conducting a hypothesis test for two variances using the F test, which sample variance should be placed in the numerator?

Accepted Answer

The larger of the two sample variances.

Question 16

A confidence interval for the mean difference in a matched pairs study is $$(-2.05, 4.90) lb. $$What does this interval suggest?

Accepted Answer

There is no significant difference between measured and reported weights.

Question 17

Which of the following is NOT a requirement for using the methods for inferences about two independent means?

Accepted Answer

The two samples must be matched pairs.

Question 18

In the context of two-sample inference, which scenario best describes a real-world example of matched pairs?

Accepted Answer

Measuring blood pressure before and after treatment in the same patients.

Chapter 9: Inferences from Two Samples – Proportions and Means

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