9. Hypothesis Testing for One Sample

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

To support a claim, state it so that it becomes the null hypothesis.

In Exercises 1–5, (f) interpret the decision in the context of the original claim.

[APPLET] The table shows the sales prices for a random sample of apartment condominiums and cooperatives in four U.S. regions. At , can you conclude that the distribution of the sales prices in at least one region is different from the others? (Adapted from National Association of Realtors)

In Exercises 9–12, refer to the sample data from the given exercises in Section 13-2. Use the Wilcoxon signed-ranks test for the claim about the median of a population.

 Exercise 15 “Cotinine in Smokers”

Which of the following is a correct interpretation of a $p$-value that is not very small in the context of hypothesis testing?

What are the two types of hypotheses used in a hypothesis test? How are they related?

A null hypothesis can only be rejected at the $5\%$ significance level if and only if which of the following is true?

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: p = 0.25

H0: p ≠ 0.25

Performing a Runs Test In Exercises 15 – 20, (e) interpret the decision in the context of the original claim. Use α = 0.05

Coin Toss A coach records the results of the coin toss at the beginning of each football game for a season. The results are shown, where H represents heads and T represents tails. The coach claimed the tosses were not random. Test the coach’s claim.

H T T T H T H H T T T T H T H H

"In Exercises 1–5, (b) decide which nonparametric test to use,

[APPLET] The table shows the sales prices for a random sample of apartment condominiums and cooperatives in four U.S. regions. At , can you conclude that the distribution of the sales prices in at least one region is different from the others? (Adapted from National Association of Realtors)

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: μ ≥ 5.2

H0: μ < 5.2

Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha,

Social Media A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

In a certain hypothesis test, $H_0:p=0.4$, $H_a:p$ < $0.4$. You collect a sample and calculate a test statistic $z=-1.32$. Find the $P$-value.

In the context of hypothesis testing, what does the $\mathrm{level of significance}$ represent?

A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At α=0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.