9. Hypothesis Testing for One Sample

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)

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)

Pump DesignThe piston diameter of a certain hand pump is 0.5 inch. The quality-control manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.004 inch. The machine that controls the piston diameter is recalibrated in an attempt to lower the standard deviation. After recalibration, the quality-control manager randomly selects 25 pistons from the production line and determines that the standard deviation is 0.0025 inch. Was the recalibration effective? Use the α = 0.01 level of significance.