Question 13.8 Assume that, on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, x, of 88 minutes and a sample standard deviation, 5, of 9 minutes. Part (a) Use at to test the null hypothesis at the .05 level of significance. Answer: Research problem: We are attempting to research the effects that drinking coffee will have on how long a person will dream for each night. Although I think that the age of the test subjects, one might consider testing \"energy drinks\" also as these tend to have more popularityf with that age group. Hypotheses: The consumption of an energy drink or coffee will cause a decrease in the amount of \"dream\" time one will have when sleeping. Rejection region/ decision rule: Ho; Iu=90 H1;I11u90 Tiest statistic: t=88-90/ (Bx/28) =-2/1.701 = -1.1759 rounded to -1.176 Decision: df=28-1=27 p-value= P(t27> -1.1759) =0.12495 rounded to 0.125 p=2 * 0.125=0.25 p-value=0.25 Conclusion / interpretation: When calculated the p value > 0.05 at 5% significance level, therefore, we do not reject Ho (them hypothesis) and conclude that drinking coffee (or energy drinks as I suggest be added to the testing) does not seem to impact the average amount of dream time for the test subjects

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