Q: Suppose a researcher tests $$H_0$$: p = 0.40$$ against H_1$: p \neq 0.40$$ using a sample proportion of $$\hat{p} = 0.45$$ from a sample of $$n = 200. $$What is the formula for the test statistic $$z$$?

$$z = \frac{0.45 - 0.40}{\sqrt{\frac{0.40 \times 0.60}{200}}}$$

Question 1

A researcher wants to test whether the mean price of a single-family home has increased from last year’s mean price of $243,714. She collects a random sample of home prices. What is the appropriate null hypothesis for this scenario?

Accepted Answer

$$H_0$$: \mu = 243,714$$

Question 2

Suppose a researcher tests $$H_0$$: p = 0.40$$ against H_1$: p 
eq 0.40$$ using a sample proportion of $$\hat{p} = 0.45$$ from a sample of $$n = 200. $$What is the formula for the test statistic $$z$$?

Accepted Answer

$$z = \frac{0.45 - 0.40}{\sqrt{\frac{0.40 	imes 0.60}{200}}}$$

Question 3

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true

Question 4

A sociologist wants to estimate the mean age of death-row inmates. She selects a random sample and calculates a 95% confidence interval for the mean age. What does this interval mean?

Accepted Answer

If many samples were taken, about 95% of the calculated intervals would contain the true mean age

Question 5

Twenty years ago, 40% of parents believed high school students were not being taught enough math and science. A recent survey finds that 52% of parents now believe this. Which test would be most appropriate to determine if the proportion has changed?

Accepted Answer

A one-sample $$z$$ test for proportions

Question 6

What is the P-value in hypothesis testing?

Accepted Answer

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

Question 7

A fast-food restaurant wants to reduce the mean waiting time at the drive-through. The current mean is 7.3 minutes. After implementing a new system, a sample of waiting times is collected. Which alternative hypothesis should be used?

Accepted Answer

$$H_1$$: \mu \u003c 7.3$$

Question 8

A golf association claims that golf balls have a diameter of 1.68 inches. A random sample is tested. Which test is most appropriate to determine if the golf balls conform to the standard?

Accepted Answer

A one-sample $$t$$ test for means

Question 9

A researcher wants to compare preferred study hours of mathematics and non-mathematics students. She selects a random sample of each group. What type of sampling method is this?

Accepted Answer

Stratified sampling

Question 10

In a survey, respondents are asked if they would pay a higher tax if the tax revenue were directly used to reduce adult education debt. The survey compares full-time and part-time employees. What is the null hypothesis for comparing the proportions?

Accepted Answer

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

Question 11

A researcher wants to test if the mean daily volume of a computer stock has changed from 2.1 million shares. She collects a sample and constructs a 95% confidence interval for the mean. If the interval does not contain 2.1, what should she conclude?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence the mean has changed

Question 12

Which of the following is a qualitative variable?

Accepted Answer

Political philosophy (Conservative, Liberal, Moderate)

Question 13

A manager wants to test if the mean diameter of water pump pistons is different from the standard of 5.00 cm. Which alternative hypothesis should be used?

Accepted Answer

$$H_1$$: \mu 
eq 5.00$$

Question 14

Which formula is used to construct a confidence interval for the difference between two population proportions, $$p_1$$ - $$p_2$$?

Accepted Answer

$$(\hat{p}_1 - \hat{p}_2) \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1$} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2$}}$$

Question 15

A researcher studies water clarity at the same location over five years. She wants to test if the mean depth has changed. Which test should she use?

Accepted Answer

A paired $$t$$ test for means

Question 16

Which of the following statements about the critical value in hypothesis testing is correct?

Accepted Answer

The critical value is the value of the test statistic that separates the rejection region from the non-rejection region

Question 17

A researcher wants to test $$H_0$$: \mu = 4.2$$ versus H_1$: \mu \u003e 4.2$$ with a sample mean $$\bar{x} = 4.7$$, $$s = 1.2$$, and $$n = 16. $$What is the formula for the test statistic $$t$$?

Accepted Answer

$$t = \frac{4.7 - 4.2}{1.2/\sqrt{16}}$$

Question 18

Which of the following is a correct interpretation of a 95% confidence interval for a mean?

Accepted Answer

If the process is repeated many times, 95% of the intervals will contain the true mean

Hypothesis Testing, Confidence Intervals, and Inference in Statistics: Study Guide

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