Insomnia has become an epidemic in the United States. Much research has been don
ID: 3371862 • Letter: I
Question
Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Use the appropriate t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05. Show all work in SPSS calculations.
Relaxation Pharmaceutical 20 35 130 83 157 138 49 142 157 39 46 194 94 95 161 154 75 57 34 118 98 51 28 65 107 90 105 73 53 20 50 92 112 71 96 86 92 75 145 148 102 24 96 108 102 35 46 74 119 186 61 75Explanation / Answer
Answer
Assumptions:-
Ho: The relaxation treatment is no effective than the pharmaceutical treatment
Ha:The relaxation treatment is more effective than the pharmaceutical treatment
The test statistic is shown as below:-
t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)
=(74.7-102.3)/sqrt(28.95^2/30+53.6^2/30)
=-2.48
Given a=0.05, the critical value is t(0.05, df=n1+n2-2=58) =-1.67 (from student t table)
Since t=-2.48 is less than -1.67, we reject Ho.
So we can conclude that
the relaxation treatment is more effective than the pharmaceutical treatment