Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 20 19 18 24 21 16 19 16 Without Caffeine 24 24 22 26 26 20 24 15 Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho: μd=2: Ha: μd⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯2 Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. Step 3 of 3: Draw a conclusion and interpret the decision.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2.

Numbers of Nights of Restful Sleep in a Four-Week Period