Question 1

Which of the following best describes the null hypothesis ($$H_0) in a $$hypothesis test for a population proportion?

Accepted Answer

It is a statement that the population parameter is equal to a specified value.

Question 2

A medical researcher wants to test if the proportion of patients responding to a new drug is higher than 0.60. Which is the correct formulation of the null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.60$$; H_A$$: p \u003e 0.60$$

Question 3

Which of the following is a Type I error in the context of a pregnancy test?

Accepted Answer

Concluding a patient is pregnant when she is not.

Question 4

What is the formula for the test statistic $$z in a $$hypothesis test for one population proportion?

Accepted Answer

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

Question 5

A researcher finds a $$p-$$value of 0.03 when testing $$H_0$$: p = 0.5$$ at a significance level of $$\alpha = 0.05$$. What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is statistically significant evidence against $$H_0.$$

Question 6

Which of the following conditions must be satisfied to use the normal approximation for the $$p-$$value in a population proportion hypothesis test?

Accepted Answer

$$np_0$$ \geq 10$$ and n(1$$-$$p_0$$) \geq 10$$

Question 7

In a two-tailed hypothesis test for a population proportion, which alternative hypothesis is correct?

Accepted Answer

$$H_A: p 
eq p_0$

Question 8

A city council wants to know if the proportion of voters favoring increased library funding is different from 0.50. In a random sample of 250 voters, 140 favor increased funding. What is the value of $$\hat{p}$$?

Accepted Answer

$$\hat{p} = 0.56$$

Question 9

Which of the following statements about statistical and practical significance is TRUE?

Accepted Answer

A result can be statistically significant but not practically meaningful.

Question 10

If the significance level $$\alpha is $$set very low, what is the likely consequence?

Accepted Answer

Type II error rate increases.

Question 11

In a hypothesis test comparing two population proportions, what is the formula for the test statistic $$z$$?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1$ - p_2$)}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1$} + \frac{1}{n_2$})}}$$

Question 12

A clinical trial tests whether a new treatment reduces the proportion of patients developing prostate cancer compared to a placebo. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: p_{drug} = p_{placebo}$$

Question 13

Why is it important to write down the null and alternative hypotheses before analyzing the data?

Accepted Answer

To prevent bias and ensure the integrity of the test.

Question 14

Which of the following is NOT a required condition for using the normal approximation in a two-proportion hypothesis test?

Accepted Answer

Both samples must have the same mean.

Question 15

A researcher conducts a hypothesis test and obtains a $$p-$$value greater than the significance level $$\alpha. $$Which is the correct way to state the conclusion?

Accepted Answer

"There is insufficient evidence to reject the null hypothesis."

Question 16

In a hypothesis test, what does the $$p-$$value represent?

Accepted Answer

The probability of observing a test statistic as extreme or more extreme, assuming $$H_0 is $$true.

Question 17

Suppose a test statistic $$z = 2.54 is $$calculated for a one-tailed test. What does this value indicate?

Accepted Answer

The observed proportion is 2.54 standard deviations above the null hypothesis value.

Question 18

Which of the following strategies can increase the power of a hypothesis test without increasing the significance level?

Accepted Answer

Increase the sample size.

Chapter 8-A

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