Question

We have developed a new drug and we wish to test its impact on the amount of sleep. We wish to know whether it will change (i.e., increase or decrease) the amount of sleep in patients.   Suppose for a population of adults, we know the average amount of sleep is 8.57 hours per day and a population standard deviation of 0.96 hours. We sample 50 patients in a clinical trial of the new drug and get an average amount of sleep of 8.84 hours per day. With α = 0.05, complete a Hypothesis Test - all steps (including defining mu, Null and Alternative Hypotheses; calculate test statistic and p-value; formalize the decision, conclusion, and any interpretations).

Answer 1

H0: = 8.57

Ha: 8.57

Test statistics

z = - / / sqrt(n)

= 8.84 - 8.57 / 0.96 / sqrt(50)

= 1.99

p-value = 2 * P( Z > z)

= 2 * P( Z > 1.99)

= 2 * 0.0233

= 0.0466

Decision = Since p-value < 0.05 level, we have sufficient evidence to reject H0.

Conclusion - We conclude at 0.05 level that we have enough evidence to support the claim.