9. Hypothesis Testing for One Sample

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)

Reading Rates (See Problem 22 in Section 10.3.) Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the course, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages after the course.

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a. The goal of the research is to determine if the words read per minute has increased as a result of the reading course. Based on this research objective, state the null and alternative hypotheses.

Premature Birth and Education Does the length of term of pregnancy play a role in the level of education of the baby? Researchers in Norway followed over 1 million births between 1967 and 1988 and looked at the educational attainment of the children. The following data are based on the results of their research. Note that a full-term pregnancy is 38 weeks. Is gestational period independent of completing a high school diploma? Use the α = 0.05 level of significance.

Does It Matter Where I Sit? Does the location of your seat in a classroom play a role in attendance or grade? To answer this question, professors randomly assigned 400 students * in a general education physics course to one of four groups. Source: Perkins, Katherine K. and Wieman, Carl E, “The Surprising Impact of Seat Location on Student Performance” The Physics Teacher, Vol. 43, Jan. 2005.

The 100 students in group 1 sat 0 to 4 meters from the front of the class, the 100 students in group 2 sat 4 to 6.5 meters from the front, the 100 students in group 3 sat 6.5 to 9 meters from the front, and the 100 students in group 4 sat 9 to 12 meters from the front.

a. For the first half of the semester, the attendance for the whole class averaged 83%. So, if there is no effect due to seat location, we would expect 83% of students in each group to attend. The data show the attendance history for each group. How many students in each group attended, on average? Is there a significant difference among the groups in attendance patterns? Use the alpha=0.05 level of significance.

You Explain It! ESP Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month, then the proportion of correct birth months should exceed 1/12, the rate one would expect from simply guessing.

a. State the null and alternative hypotheses for this experiment.