Question 1

A researcher wants to compare the effectiveness of two medications in reducing blood pressure. She randomly assigns 100 patients to each medication and measures the proportion of patients whose blood pressure drops below a certain threshold. Which statistical test should she use to compare the two proportions?

Accepted Answer

A 2-proportion z-test

Question 2

Suppose you are testing the claim that the proportion of defective products from Factory A is greater than that from Factory B. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Question 3

In a study, 40 out of 200 patients given Drug X recovered, while 60 out of 250 patients given Drug Y recovered. Construct a 95% confidence interval for the difference in proportions ($$p_1$$ - $$p_2). $$Which of the following interpretations is correct if the interval is $$-0.15 \u003c p_1$ - p_2$ \u003c 0.05$$?

Accepted Answer

There is no significant difference in effectiveness between Drug X and Drug Y.

Question 4

Which formula is used to calculate the test statistic for comparing two population means from independent samples with unknown but assumed equal variances?

Accepted Answer

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

Question 5

A 99% confidence interval for the difference in means ($$\mu_1$ - \mu_2$) is calculated as 2$$ \u003c \$$mu_1$$ - \$$mu_2$$ \u003c 10$$. What does this interval suggest?

Accepted Answer

The mean of population 1 is significantly greater than that of population 2.

Question 6

In a matched pairs design, which of the following is the correct formula for the confidence interval for the mean difference $$\mu_d$$?

Accepted Answer

$$\bar{d} \pm t^* \frac{s_d}{\sqrt{n}}$$

Question 7

A study finds that among 343 infants using bednets, 15 developed malaria, and among 294 infants not using bednets, 27 developed malaria. What is the sample proportion of malaria cases among infants using bednets?

Accepted Answer

$$\frac{15}{343}$$

Question 8

Which of the following best describes the advantage of using matched pairs in experimental design?

Accepted Answer

It reduces extraneous variation by controlling for confounding variables.

Question 9

If the significance level for a hypothesis test is $$\alpha = 0.05$$, what is the corresponding confidence level for a two-tailed confidence interval?

Accepted Answer

95%

Question 10

In the context of hypothesis testing for two means, what does it mean if the confidence interval for $$\mu_1$ - \mu_2$ contains zero?

Accepted Answer

There is no significant difference between the two means.

Question 11

A researcher is testing whether the mean number of words spoken per day by men is less than that for women. Which is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \$$mu_1$$ \u003c \$$mu_2$$

Question 12

Which of the following is the correct formula for the test statistic in a two-proportion z-test?

Accepted Answer

$$z = \frac{p_1$ - p_2$}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1$} + \frac{1}{n_2$})}}$$

Question 13

In a study of drive-through order accuracy, Burger King had 264 accurate and 54 inaccurate orders, while McDonald's had 329 accurate and 33 inaccurate orders. What is the null hypothesis for testing if the accuracy rates are the same?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Question 14

Which of the following best describes the area under the standard normal curve?

Accepted Answer

The area is equal to 1.

Question 15

A 90% confidence interval for the mean difference in taxi-out and taxi-in times for flights is calculated. What does it mean if the interval is entirely positive?

Accepted Answer

Taxi-out times are significantly greater than taxi-in times.

Inferences from Two Samples: Proportions, Means, and Matched Pairs

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