Q: Suppose a sample of 800 voters yields a sample proportion $$\hat{p} = 0.54$$ supporting a candidate. If the null hypothesis is $$p = 0.5$$, what is the value of the test statistic $$z$$?

$$z = \dfrac{0.54 - 0.5}{\sqrt{\dfrac{0.5 \times 0.5}{800}}}$$

Question 1

Which of the following is the correct formula for the standard deviation of the sample proportion $$\hat{p}$$ when testing a hypothesis about a population proportion $$p$$?

Accepted Answer

$$\sqrt{\dfrac{p(1-p)}{n}}$$

Question 2

A researcher wants to test if the proportion of Americans who support a new policy is greater than 0.5. Which of the following is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: p = 0.5$$, H_a$$: p \u003e 0.5$$

Question 3

Which of the following is NOT a required condition for performing a hypothesis test about a population proportion $$p$$?

Accepted Answer

The sample size $$n$$ must be greater than 30.

Question 4

Suppose a sample of 800 voters yields a sample proportion $$\hat{p} = 0.54$$ supporting a candidate. If the null hypothesis is $$p = 0.5$$, what is the value of the test statistic $$z$$?

Accepted Answer

$$z = \dfrac{0.54 - 0.5}{\sqrt{\dfrac{0.5 	imes 0.5}{800}}}$$

Question 5

A pharmaceutical company tests a new drug for rheumatoid arthritis. Out of 700 subjects, 410 report improvement. If the null hypothesis is $$p = 0.5$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{410}{700}$$

Question 6

Which of the following best describes the meaning of a P-value in hypothesis testing?

Accepted Answer

The probability of obtaining a sample statistic as extreme or more extreme than the observed, assuming the null hypothesis is true.

Question 7

If a hypothesis test yields a P-value of 0.03 and the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis because the P-value is less than $$\alpha.$$

Question 8

A two-tailed test is being performed at the $$\alpha = 0.01$$ significance level. Which of the following P-values would lead to rejecting the null hypothesis?

Accepted Answer

0.005

Question 9

Which of the following statements is TRUE regarding statistical significance?

Accepted Answer

A result is statistically significant if the P-value is less than or equal to the significance level $$\alpha.$$

Question 10

In a hypothesis test for a population proportion, which of the following scenarios requires using the binomial probability distribution instead of the normal approximation?

Accepted Answer

When $$np \u003c 10 or$$ $$n(1-p) \u003c 10$$

Question 11

A 2009 survey found that 3% of teenagers sent text messages daily. In a random sample of 1500 teenagers, 54 reported sending texts daily. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{54}{1500}$$

Question 12

Which of the following best describes how to use a confidence interval to make a decision about the null hypothesis in a two-tailed test?

Accepted Answer

If the hypothesized value of $$p is $$not contained in the confidence interval, reject the null hypothesis.

Question 13

A Pew Research Center survey finds that 51% of Americans believe that gun laws should be stricter. In a random sample of 481 Americans with a bachelor's degree, 247 believe gun laws should be stricter. What is the null hypothesis for testing if the proportion differs from the general population?

Accepted Answer

$$H_0$$: p = 0.51$$

Question 14

Which of the following best describes the logic of hypothesis testing for a population proportion?

Accepted Answer

We assess whether the observed sample proportion is likely under the assumption that the null hypothesis is true.

Question 15

If the P-value for a hypothesis test is 0.12, which of the following is the correct interpretation at the $$\alpha = 0.05$$ significance level?

Accepted Answer

There is not enough evidence to reject the null hypothesis.

Question 16

Which of the following is the correct formula for the test statistic $$z in a $$hypothesis test for a population proportion?

Accepted Answer

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

Section 10.2 Hypothesis Tests for a Population Proportion: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards