9. Hypothesis Testing for One Sample

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.95, n = 20

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Video Game Systems A researcher claims that the percentage of U.S. gamers that are women is not 50%.

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

μ < 128

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

σ ≠ 5

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Right-tailed test, α=0.01, n=31

In your own words, explain why the hypothesis test discussed in this section is called the sign test.

Explain why the Kruskal-Wallis test is always a right-tailed test.

Performing a Runs Test In Exercises 15 – 20, (c) find the test statistic. 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

Performing a Runs Test In Exercises 15 – 20, (d) decide whether to reject or fail to reject the null hypothesis. 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

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

Performing a Runs Test In Exercises 15 – 20, (b) find the critical values. 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, (a) identify the claim and state H0 and Ha,

[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 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)

In Exercises 1–5, (d) find the test statistic,

[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 1–5, (e) decide whether to reject or fail to reject the null hypothesis,

[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)