Question 1

Which of the following best describes the null hypothesis ($$H_0) $$for the Lipitor clinical test example?

Accepted Answer

$$H_0$$: p = 0.019$$

Question 2

What is the correct alternative hypothesis ($$H_1) $$for testing if the percentage of treated patients with flu symptoms is greater than 1.9%?

Accepted Answer

$$H_1$$: p \u003e 0.019$$

Question 3

Given $$n = 863$$ and $$x = 19$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{19}{863} \approx 0.0220$$

Question 4

Which formula is used to calculate the test statistic $$z$$ for a one-proportion z-test?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$ (1 - p_0$)}{n}}}$$

Question 5

If the P-value is $$0.2582$$ and the significance level $$\alpha is$$ $$0.01$$, what is the correct conclusion?

Accepted Answer

Fail to reject $$H_0$$; there is not enough evidence to support the claim.

Question 6

Which of the following best describes the meaning of 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 $$H_0 is $$true.

Question 7

Suppose the significance level $$\alpha$$ was changed to $$0.05. $$With a P-value of $$0.2582$$, what would the conclusion be?

Accepted Answer

Fail to reject $$H_0.$$

Question 8

Which of the following is a correct interpretation of 'failing to reject the null hypothesis' in the context of the Lipitor study?

Accepted Answer

There is not enough evidence to conclude that Lipitor increases the rate of flu symptoms.

Question 9

If the sample size were much smaller but the sample proportion stayed the same, what would likely happen to the P-value?

Accepted Answer

The P-value would likely decrease.

Question 10

Which of the following is a possible Type I error in the context of this hypothesis test?

Accepted Answer

Concluding that Lipitor increases flu symptoms when it actually does not.

Question 11

A researcher claims that a new medication causes a side effect in more than 2% of patients. Which is the correct set of hypotheses for a one-proportion z-test?

Accepted Answer

$$H_0$$: p = 0.02,\ $$H_1$$: p \u003e 0.02$$

Question 12

Which step comes immediately after calculating the test statistic in the P-value approach to hypothesis testing?

Accepted Answer

Determine the P-value.

Question 13

If the sample proportion $$\hat{p} is $$much larger than $$p_0$$, what effect does this have on the test statistic $$z$$?

Accepted Answer

The test statistic $$z$$ becomes more positive.

Question 14

Which of the following best describes the significance level $$\alpha in $$hypothesis testing?

Accepted Answer

The probability of making a Type I error.

Question 15

A hospital administrator wants to test if the infection rate after surgery is less than 5%. What is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: p \u003c 0.05$$

Question 16

Which of the following is NOT a step in the P-value approach to hypothesis testing?

Accepted Answer

Calculate the confidence interval.

Question 17

If the calculated P-value is exactly equal to $$\alpha$$, what is the correct decision?

Accepted Answer

Reject $$H_0.$$

Question 18

Which of the following scenarios would require a two-tailed test?

Accepted Answer

Testing if the proportion is different from a specified value.

Question 19

A researcher wants to test if the rate of a side effect is less than 3%. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: p = 0.03$$

Question 20

Which of the following best describes the purpose of hypothesis testing in statistics?

Accepted Answer

To make inferences about a population parameter based on sample data.

Hypothesis Testing for One Proportion: P-value Approach

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