Hi i would like the answers to this task Thank you for your

Hi i would like the answers to this task. Thank you for your help,

A scientist was interested in the effect of two sleeping pills, labeled A and B. He gave 20 subjects drug A for a week, and asked them to record the number of hours sleep they managed. After waiting a week to make sure the first drug had been flushed from their systems, he gave the same patients drug B for a week, again asking them to calculate the number of hours sleep they managed that week. The scientist calculated the difference in sleeping times for each patient after taking the two drugs. The sample statistics for these 20 differences are: The scientist gives you this data and asks you to calculate whether there is a significant difference in the average amount of sleep people get when taking drug A or B. State the null and alternative hypotheses. Calculate the test-statistic and appropriate degrees-of-freedom. Find the appropriate p-value for a paired hypothesis test. Interpret the p-value with respect to the study. Explain why this study design is more likely to detect a difference in the effect of the two drugs than a study where one group is given drug A, and another group is given drug B.

Solution

H0: Xa = Xb

Ha: Xa not equals Xb

b) Test statistic = -10.6/18.45

= -0.5745

df = 20-1 = 19

c) p value = 0.5727

d) p >0.05 and hence we accept null hypothesis that there is no difference between the two means.

e) Paired test has advantages as the same group is tested hence difference due to other external factors are minimised.