Question 1

Which of the following is the correct formula for the test statistic when testing a claim about a population proportion using the normal approximation method?

Accepted Answer

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

Question 2

A clinical trial tests the claim that fewer than 10% of patients experience headaches from a drug. In a sample of 863 patients, 47 experienced headaches. What is the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: p = 0.10$$

Question 3

Which of the following conditions must be satisfied to use the normal approximation for hypothesis testing about a proportion?

Accepted Answer

$$np \geq 5$$ and $$nq \geq 5$$

Question 4

In a survey of 510 people, 53% said we should replace passwords with biometric security. What is the sample proportion ($$\hat{p}$$)?

Accepted Answer

$$\hat{p} = 0.53$$

Question 5

A hypothesis test yields a P-value of 0.1840 and a significance level of 0.05. What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 6

Which of the following best describes the difference between the P-value method and the confidence interval method for testing a proportion?

Accepted Answer

The P-value method uses the claimed proportion for standard deviation, while the confidence interval method uses the sample proportion.

Question 7

A Pew Research poll of 4581 Americans found 47% prefer to watch the news. Test the claim that fewer than half prefer to watch the news at $$\alpha = 0.01. $$What is the alternative hypothesis ($$H_a$$)?

Accepted Answer

$$H_a: p \u003c 0.5$$

Question 8

In a MythBusters experiment, 48 slices of buttered toast were dropped, and 19 landed buttered side down. Test the claim that toast lands buttered side down 50% of the time. What is the value of $$p$$ used in the null hypothesis?

Accepted Answer

$$p = 0.5$$

Question 9

A test statistic for a proportion test is calculated as $$z = 1.3284$$ with a critical value of $$\pm 1.96. $$What is the correct interpretation?

Accepted Answer

The test statistic does not fall in the rejection region; fail to reject $$H_0.$$

Question 10

In a clinical trial, 52 out of 227 OxyContin users developed nausea. Test the claim that more than 20% develop nausea. What is the sample proportion ($$\hat{p}$$)?

Accepted Answer

$$\hat{p} = \frac{52}{227}$$

Question 11

A USA Today survey tests the claim that half of people support biometric security. The P-value is 0.1840. What does this mean at $$\alpha = 0.05$$?

Accepted Answer

There is not sufficient evidence to reject the claim.

Question 12

Which of the following is NOT a requirement for using the normal approximation to test a population proportion?

Accepted Answer

The population must be normally distributed.

Question 13

In a hypothesis test about a proportion, what does a left-tailed test indicate?

Accepted Answer

The alternative hypothesis is $$p \u003c p_0$.

Question 14

A football overtime rule is tested: 252 out of 460 games were won by the coin toss winner. Test the claim that the coin toss is fair ($$p = 0.5). $$What is the alternative hypothesis?

Accepted Answer

$$H_a: p 
eq 0.5$$

Question 15

If the P-value is less than the significance level $$\alpha$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following real-world scenarios is best suited for a hypothesis test about a population proportion?

Accepted Answer

Testing if more than 60% of voters support a new law.

Hypothesis Testing for a Population Proportion – Step-by-Step Study Guide

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