Q: A pharmaceutical company claims that their new drug is effective in reducing blood pressure. To test this, researchers set up a hypothesis test. Which of the following correctly identifies the null and alternative hypotheses?

$$H_0$$: \text{The drug has no effect on blood pressure}$$; H_A$$: \text{The drug reduces blood pressure}$$

Q: A sign test is performed on paired data and the p-value is found using a z-test for a proportion. Which null hypothesis is being tested?

$$H_0$$: p = 0.5$$, \text{ where } p \text{ is the probability that the first member of the pair is greater}$

Question 1

A pharmaceutical company claims that their new drug is effective in reducing blood pressure. To test this, researchers set up a hypothesis test. Which of the following correctly identifies the null and alternative hypotheses?

Accepted Answer

$$H_0$$: 	ext{The drug has no effect on blood pressure}$$; H_A$$: 	ext{The drug reduces blood pressure}$$

Question 2

A researcher performs a one-proportion z-test and obtains a p-value of $$0.03 at a $$significance level of $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is significant evidence against $$H_0.$$

Question 3

Which of the following best describes the difference between a one-sided and a two-sided hypothesis test?

Accepted Answer

A one-sided test considers deviations in only one direction from the null hypothesis, while a two-sided test considers deviations in both directions.

Question 4

Suppose you calculate a z-score of $$2.1$$ for a one-proportion z-test. What is the two-sided p-value?

Accepted Answer

$$2 	imes P(Z \u003e 2.1)$$

Question 5

Which assumption must be checked before performing a one-proportion z-test?

Accepted Answer

The sample size is large enough so that $$np \geq 10$$ and $$n(1-p) \geq 10.$$

Question 6

A study reports a 95% confidence interval for the mean systolic blood pressure as $$(120, 130). $$Which of the following is the correct interpretation?

Accepted Answer

We are 95% confident that the true mean systolic blood pressure is between 120 and 130.

Question 7

Which of the following is an assumption for constructing a confidence interval for a sample mean using the t-distribution?

Accepted Answer

The data are approximately normally distributed or the sample size is large.

Question 8

A researcher wants to compare the mean cholesterol levels between two independent groups. Which test should be used?

Accepted Answer

Two-sample t-test

Question 9

Which of the following is NOT an assumption for a two-sample t-test?

Accepted Answer

The samples are paired.

Question 10

A 95% confidence interval for the difference between two means is $$(-2, 5). $$What does this suggest about the hypothesis test for no difference?

Accepted Answer

Fail to reject the null hypothesis; zero is included in the interval.

Question 11

A paired t-test is most appropriate in which scenario?

Accepted Answer

Comparing pre- and post-treatment scores for the same individuals.

Question 12

Which of the following is a correct condition for applying a Wilcoxon rank sum test?

Accepted Answer

The two samples are independent and the data are at least ordinal.

Question 13

A sign test is performed on paired data and the p-value is found using a z-test for a proportion. Which null hypothesis is being tested?

Accepted Answer

$$H_0$$: p = 0.5$$, 	ext{ where } p 	ext{ is the probability that the first member of the pair is greater}$

Question 14

Which of the following scenarios would most likely require a non-parametric test?

Accepted Answer

The data are highly skewed and contain outliers.

Question 15

Which of the following statements about Type I and Type II errors is correct?

Accepted Answer

A Type I error is rejecting a true null hypothesis; a Type II error is failing to reject a false null hypothesis.

Question 16

A researcher is analyzing the effect of a new teaching method on student performance. She collects scores from the same students before and after the intervention. Which test should she use?

Accepted Answer

Paired t-test

Question 17

Which of the following is the correct formula for a one-sample t-test statistic?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s / \sqrt{n}}$$

Question 18

A Wilcoxon signed rank test is most appropriate when:

Accepted Answer

The data are paired and not normally distributed.

Question 19

Which of the following best describes the p-value in hypothesis testing?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Question 20

A researcher is deciding between a paired t-test and a two-sample t-test. Which factor is most important in making this decision?

Accepted Answer

Whether the samples are paired or independent.

Statistical Hypothesis Testing and Confidence Intervals: Key Concepts and Applications

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