Question 1

A pharmaceutical company claims that 8% of patients taking a placebo experience nausea. In a clinical trial, 66 out of 705 patients taking a new drug report nausea. Test the hypothesis that the drug increases the proportion of patients experiencing nausea at the $$\alpha = 0.05$$ significance level. What is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: p = 0.08,\quad $$H_1$$: p \u003e 0.08$$

Question 2

Which of the following is the correct formula for the test statistic $$z_0$$ when testing a hypothesis about a population proportion $$p$$?

Accepted Answer

$$z_0$$ = \dfrac{\hat{p} - $$p_0$$}{\sqrt{\dfrac{$$p_0(1$$-$$p_0$$)}{n}}}$$

Question 3

A random sample of 1000 voters yields a sample proportion $$\hat{p} = 0.534 in $$favor of a policy. If the null hypothesis is $$p = 0.5$$, what is the standard deviation of the sampling distribution of $$\hat{p}$$?

Accepted Answer

$$\sigma_{\hat{p}} = \sqrt{\dfrac{0.5(1-0.5)}{1000}} \approx 0.016$$

Question 4

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

Accepted Answer

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

Question 5

Suppose you conduct a right-tailed hypothesis test for a population proportion and obtain a test statistic $$z_0 = 1.37$ with a critical value z$$_{0.05} = 1.645$$. What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

Do not reject the null hypothesis because $$1.37 \u003c 1.645.$$

Question 6

A Pew Research Center survey finds that 457 out of 780 Americans with at least a Bachelor's degree believe gun laws should be stricter. If the proportion in the general population is 0.53, what is the value of the test statistic for testing $$H_0$$: p = 0.53$$ vs H_1$: p 
eq 0.53$$?

Accepted Answer

$$z_0$$ = \dfrac{0.586 - 0.53}{\sqrt{\dfrac{0.53(1-0.53)}{780}}} \approx 3.13$$

Question 7

Which of the following is NOT an assumption required for hypothesis testing about a population proportion?

Accepted Answer

The population must be normally distributed.

Question 8

If the P-value for a hypothesis test is 0.018 and the significance level is $$\alpha = 0.1$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis because $$0.018 \u003c 0.1.$$

Question 9

A 95% confidence interval for the proportion of teens who text while driving is $$(0.268, 0.320). $$The 2009 value was $$p_0 = 0.34$. What does this interval suggest?

Accepted Answer

There is sufficient evidence to conclude the proportion has changed since 2009.

Question 10

Which of the following best describes a Type I error in the context of hypothesis testing for a population proportion?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 11

In a left-tailed test for a population proportion, which of the following would lead you to reject the null hypothesis at significance level $$\alpha$$?

Accepted Answer

If $$z_0$$ \u003c -z_{\alpha}$$

Question 12

A sample proportion is considered statistically significant if:

Accepted Answer

It is unlikely to occur under the assumption that the null hypothesis is true.

Question 13

Which of the following is the correct interpretation if a P-value is greater than the significance level $$\alpha$$?

Accepted Answer

Do not reject the null hypothesis.

Question 14

A sample of 1200 teens found that 353 had texted while driving. If the 2009 proportion was $$p_0 = 0.34$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{353}{1200} \approx 0.294$$

Question 15

Which of the following is NOT a correct way to structure the alternative hypothesis $$H_1$$ for a test about a population proportion?

Accepted Answer

$$H_1$$: p = $$p_0$$

Question 16

If the sample size $$n is $$not sufficiently large so that $$np_0(1$$-$$p_0$$) \u003c 10$$, what is the main consequence for hypothesis testing about a population proportion?

Accepted Answer

The normal approximation may not be valid.

Question 17

A right-tailed test for a population proportion yields a P-value of 0.085. If $$\alpha = 0.05$$, what is the correct interpretation?

Accepted Answer

There is not sufficient evidence to reject the null hypothesis.

Question 18

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

Accepted Answer

Testing whether the proportion of Americans with a Bachelor's degree who support stricter gun laws is different from the general population.

Hypothesis Testing for Population Proportion: Concepts, Methods, and Examples

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