Question

1. 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 cutting out caffeine. 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 no caffeinated beverages for the following 28 days. During each period, the participants record the number of nights of restful sleep they had. Test Sarah’s claim at the 0.05 level of significance.

Numbers of Nights of Restful Sleep in 4-week Period
With Caffeine	21	20	26	20	24	21	18	15
Without Caffeine	22	24	27	23	21	26	22	23

Hypotheses:

Test Statistic and value:                                                                  P-value:

Conclusion:

Example of answer: Hypotheses: 1.5 points = To receive full points, hypotheses must be stated correctly, either in words or in symbols. Examples: “µ ≥ 35” or “Population mean is greater than or equal to 35”.

Test stat and value: 1 point = Correct test statistic (i.e. T, Z, Chi-Square) is identified and its value is correct.

P-value: 1 point = Correct p-value of test is given.

Conclusion: 1.5 points = State how you decided and whether you reject or fail to reject null hypothesis. Then, include a full sentence description of what this means in this particular problem.

Answer 1