Q: In a survey, 27% of adults in a region consider themselves to be liberal. A random sample of 220 adults in the region finds that 70 identify as liberal. What is the test statistic for testing if the proportion is higher than the polling organization's claim? Use $$p_0 = 0.27$.

$$z = \frac{0.318 - 0.27}{\sqrt{\frac{0.27 \times 0.73}{220}}}$$

Q: A sociologist wants to know if the mean age at death from one year has changed from the previous year's mean of 41.8 years. She samples 30 death records and finds a sample mean of 41.2 years with a standard deviation of 2.5 years. What is the 95% confidence interval for the mean age? (Use $$t^* = 2.045$$ for 29 degrees of freedom.)

$$41.2 \pm 2.045 \times \frac{2.5}{\sqrt{30}}$$

Question 1

A researcher wants to test whether the mean price of a single-family home has increased from last year's mean of $$243,714. She collects a random sample of home prices and finds a sample mean of 250$$,000. Which of the following correctly states the null and alternative hypotheses for this scenario?

Accepted Answer

$$H_0$$: \mu = 243,714$$; H_a$$: \mu \u003e 243,714$$

Question 2

Suppose a hypothesis test is conducted at the $$\alpha = 0.05$$ level of significance. The P-value is calculated to be $$0.03. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis because $$0.03 \u003c 0.05$$

Question 3

In a survey, 27% of adults in a region consider themselves to be liberal. A random sample of 220 adults in the region finds that 70 identify as liberal. What is the test statistic for testing if the proportion is higher than the polling organization's claim? Use $$p_0 = 0.27$.

Accepted Answer

$$z = \frac{0.318 - 0.27}{\sqrt{\frac{0.27 	imes 0.73}{220}}}$$

Question 4

A Type I error occurs when:

Accepted Answer

We reject the null hypothesis when it is true.

Question 5

Twenty years ago, 40% of parents believed high school students were not being taught enough math and science. In a recent survey, 220 out of 500 parents believe this today. What is the null hypothesis for testing if the proportion has changed?

Accepted Answer

$$H_0$$: p = 0.40$$

Question 6

A sociologist wants to know if the mean age at death from one year has changed from the previous year's mean of 41.8 years. She samples 30 death records and finds a sample mean of 41.2 years with a standard deviation of 2.5 years. What is the 95% confidence interval for the mean age? (Use $$t^* = 2.045$$ for 29 degrees of freedom.)

Accepted Answer

$$41.2 \pm 2.045 	imes \frac{2.5}{\sqrt{30}}$$

Question 7

Which of the following best describes a P-value?

Accepted Answer

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

Question 8

A fast-food restaurant wants to test if a new system reduces the mean waiting time below the current average of 137 seconds. A random sample of 40 waiting times yields a sample mean of 130 seconds and a standard deviation of 15 seconds. What is the appropriate test statistic?

Accepted Answer

$$t = \frac{130 - 137}{15/\sqrt{40}}$$

Question 9

A golf association requires that golf balls have a diameter of 1.680 inches. A random sample of 6 balls has diameters: 1.682, 1.678, 1.681, 1.679, 1.680, 1.681. What is the sample mean diameter?

Accepted Answer

$$\bar{x} = \frac{1.682 + 1.678 + 1.681 + 1.679 + 1.680 + 1.681}{6}$$

Question 10

Which of the following statements about confidence intervals is correct?

Accepted Answer

A 95% confidence interval means that if we took many samples, about 95% of the intervals would contain the true parameter.

Question 11

A stock analyst believes the daily volume of a stock has decreased from the 2017 mean of 9.1 million shares. A random sample of 30 trading days in 2021 yields a sample mean of 8.2 million shares and a standard deviation of 1.1 million shares. What is the null hypothesis?

Accepted Answer

$$H_0$$: \mu = 9.1$$

Question 12

Which of the following is a correct interpretation of a Type II error?

Accepted Answer

Failing to reject the null hypothesis when the alternative hypothesis is true.

Question 13

A researcher wants to compare the mean scores of two independent groups. Which test should be used?

Accepted Answer

Two-sample t-test for independent means

Question 14

Which of the following is NOT an assumption for using a one-sample t-test?

Accepted Answer

The population standard deviation is known.

Question 15

A 95% confidence interval for the difference between two means is $$(-2.1, 0.5). $$What can you conclude?

Accepted Answer

There is not sufficient evidence to conclude the means are different at the 0.05 significance level.

Question 16

Which of the following best describes the alternative hypothesis in a two-tailed test?

Accepted Answer

$$H_a: \mu 
eq \mu_0$

Question 17

A researcher is testing $$H_0$$: \mu = 50$$ vs H_a$$: \mu \u003e 50$$ with a sample mean of 53, sample standard deviation of 4, and sample size of 16. What is the value of the test statistic?

Accepted Answer

$$t = \frac{53 - 50}{4/\sqrt{16}} = 3.0$$

Question 18

Which of the following is a correct statement about the significance level $$\alpha$$?

Accepted Answer

$$\alpha is $$the probability of making a Type I error.

Question 19

A normal probability plot is used to:

Accepted Answer

Assess whether sample data come from a population that is approximately normal.

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

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