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.

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