Q: A golf association claims that golf balls have a diameter of 1.68 inches. A random sample of golf balls is measured. Which null and alternative hypotheses should be used to test if the golf balls conform to the standard?

$$H_0$$: \mu = 1.68$$, H_1$: \mu \neq 1.68$$

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 from this year. What is the appropriate null hypothesis for this scenario?

Accepted Answer

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

Question 2

Suppose a test for the mean waiting time at a fast-food drive-through yields a P-value of 0.03 at a 0.05 level of significance. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence that the mean waiting time has changed.

Question 3

Which formula is used to calculate the test statistic for a population proportion?

Accepted Answer

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

Question 4

A sociologist wants to estimate the mean age at death for victims of a certain disease. She collects 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

In hypothesis testing, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 6

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 appropriate to determine if the proportion has changed?

Accepted Answer

A one-sample z-test for proportions

Question 7

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

Accepted Answer

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

Question 8

A golf association claims that golf balls have a diameter of 1.68 inches. A random sample of golf balls is measured. Which null and alternative hypotheses should be used to test if the golf balls conform to the standard?

Accepted Answer

$$H_0$$: \mu = 1.68$$, H_1$: \mu 
eq 1.68$$

Question 9

A researcher wants to compare the mean 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

Which formula is used to construct a confidence interval for the difference between two population means when both samples are independent and normally distributed?

Accepted Answer

$$(\bar{x}_1 - \bar{x}_2) \pm z^* \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 11

A polling organization reports that 27% of adults in a region consider themselves to be liberal. A survey of 220 respondents finds that 35% consider themselves liberal. What is the correct null hypothesis for testing if the proportion is higher than reported?

Accepted Answer

$$H_0$$: p = 0.27$$

Question 12

Which of the following statements about the interpretation of a 95% confidence interval is correct?

Accepted Answer

If the study were repeated many times, 95% of the calculated intervals would contain the true parameter.

Question 13

A researcher tests $$H_0$$: \mu = 4.2$$ versus H_1$: \mu 
eq 4.2$$ with a sample mean of $$4.7$$, sample standard deviation $$0.8$$, and sample size $$16. $$What is the value of the test statistic?

Accepted Answer

$$z = \frac{4.7 - 4.2}{0.8 / \sqrt{16}} = 2.5$$

Question 14

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. What statistical test is appropriate to compare the proportion of full-time and part-time employees willing to pay higher taxes?

Accepted Answer

A two-sample z-test for proportions

Question 15

A researcher wants to test if the mean daily volume of a computer stock has changed from 2.1 million shares. She collects a random sample and calculates a 95% confidence interval for the mean. The interval is (1.8, 2.3). What is the correct conclusion?

Accepted Answer

There is not sufficient evidence that the mean daily volume has changed.

Question 16

Which of the following is a qualitative variable?

Accepted Answer

Political philosophy (Conservative, Liberal, Moderate)

Question 17

A researcher studies water clarity at the same location in a lake over five years. What statistical test is appropriate to determine if the mean depth has changed?

Accepted Answer

A paired t-test for means

Question 18

Which formula is used to calculate the test statistic for the difference between two population proportions?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1$ - p_2$)}{\sqrt{\frac{\hat{p}(1-\hat{p})}{n_1$} + \frac{\hat{p}(1-\hat{p})}{n_2$}}}$$

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

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