Estimation: Comparing Two Populations

Please give me a full answer for the question.

The managing director of a pharmaceutical copany that has recently developed a new non-prescription sleeping pill wants to measure its effectiveness. Her assistant recruits five individuals selected ant random to participate in a preliminary experiment. The experiment is performed over 2 nights. On 1 night the subject takes the sleeping pill, and on the other he or she takes a placepo. The order in which the pills are taken by each individual is random.

Number of hours of sleep

Subject Sleeping pill (X1)Placebo (X2) Difference (X_D)

17.3 6.8 0.5

28.57.90.6

36.4 6.0 0.4

4 9.08.40.6

56.96.5 0.4

Table 11.1 Number of hours slept by subjects in preliminary experiment and their differences Number of hours of sleep Subject Sleeping pill Placebo Difference (X = X - X) 7.3 6.8 0.5 2 8.5 79 0.6 LJ 6.4 6.0 0.4 9.0 8.4 0.6 5 6.9 6.5 0.4 The managing director of a pharmaceutical company that has recently developed a new non-prescription sleeping pill wants to measure its effectiveness. Her assistant recruits five individuals selected at random to participate in a preliminary experiment. The experiment is performed over two nights. On one night the subject takes the sleeping pill, and on the other he or she takes a placebo (a pill that looks like a sleeping pill but contains no medication). The order in which the pills are taken by each individual is random. The hours of sleep in each case are shown in the second and third columns of Table 1