Question 1

Which of the following is the correct null hypothesis ($$H_0) $$for a one-sample proportion test if you want to test whether the proportion of smokers in a city is different from 20%?

Accepted Answer

$$H_0$$: p = 0.20$$

Question 2

A researcher wants to compare the effectiveness of two medications in preventing heart attacks. Which hypothesis formulation is appropriate for a two-sample proportion test?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Question 3

Which of the following is a necessary condition for using the normal approximation in a one-sample proportion hypothesis test?

Accepted Answer

$$np \geq 10$$ and $$n(1-p) \geq 10$$

Question 4

Suppose you are testing $$H_0$$: p = 0.25$$ against H_a$$: p \u003e 0.25$$ with a sample of 250 and 75 successes. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{75}{250} = 0.30$$

Question 5

In a two-sample proportion test, which formula is used to calculate the pooled proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 6

A clinical trial compares the death rates between a therapy group ($$n_1 = 937$, x_1$ = 377) $$and a placebo group ($$n_2 = 932$, x_2$ = 431). $$What is the correct formula for the standard error (SD) of the difference in proportions?

Accepted Answer

$$SD = \sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1$} + \frac{1}{n_2$}\right)}$$

Question 7

A poll found that 47% of 1003 adults in Country A believe global warming is fact, while 45% of Province A residents believe the same. Test the hypothesis that the proportions are different at $$\alpha = 0.05. $$What is the correct null hypothesis?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Question 8

If the calculated p-value in a hypothesis test is 0.034 and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$ because $$p-$$value $$\u003c \alpha$$

Question 9

A fish market tests 300 fish and finds 50 have dangerous mercury levels. Test if this sample is from a population with $$p = 0.18 at$$ $$\alpha = 0.05. $$What is the test statistic $$z$$?

Accepted Answer

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

Question 10

A company claims 60% of college students use Kijiji. A sample of 150 finds 102 students use Kijiji. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{102}{150} = 0.68$$

Question 11

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

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value under $$H_0$$

Question 12

A researcher tests whether a new ad is equally liked by males and females. The sample results are 57 males and 47 females liked the ad. What is the correct formula for the test statistic?

Accepted Answer

$$z = \frac{\hat{p}_1 - \hat{p}_2}{SD}$$

Question 13

In a one-sample proportion test, which step comes immediately after checking the CLT conditions?

Accepted Answer

Compute the test statistic

Question 14

A statistics student surveys 95 students and finds that 14 attend Mama Mia weekly. She surveys another sample of 100, and 26 attend. What is the pooled proportion $$\hat{p}$$ for a two-sample test?

Accepted Answer

$$\hat{p} = \frac{14 + 26}{95 + 100} = \frac{40}{195} \approx 0.205$$

Question 15

Which of the following is NOT a correct step in the hypothesis testing process for proportions?

Accepted Answer

Calculate the median of the sample

Question 16

A 2010 article reports that 659 of 3305 men taking a drug developed prostate cancer, while 858 of 3424 taking placebo developed cancer. What is the sample proportion for the drug group?

Accepted Answer

$$\hat{p}_1 = \frac{659}{3305} \approx 0.20$$

Question 17

If a hypothesis test results in a p-value of 0.09 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Fail to reject $$H_0$$

Question 18

A company expects a salesperson to make sales on more than 15% of calls. In a sample of 400 calls, 76 sales are made. What is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{76}{400} = 0.19$$

Question 19

Which of the following best describes the alternative hypothesis ($$H_a) in a $$test to determine if a new therapy reduces the proportion of deaths compared to placebo?

Accepted Answer

$$H_a: p_1$ \u003c p_2$

Chapter 8-B

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드