Martha believes that a relaxation technique involvingvisualization will help peo

Question

Martha believes that a relaxation technique involvingvisualization will help people with mild insomnia fall asleepfaster. She randomly selects a sample of 20 participants from agroup of mild insomnia patients and randomly assigns 10 to receivevisualization therapy. The other 10 participants recieve notreatment. Each participant is then measured to see how long (inminutes) it takes him or her to fall asleep. Martha's dateare below. The numbers represent the number of minutes eachparticipant took to fall asleep. No Treatment(X1)                                                 Treatment (X2) 22                                                                                    19 18                                                                                    17 27                                                                                    24 20                                                                                    21 23                                                                                   27 26                                                                                   21 27                                                                                   23 22                                                                                    18 24                                                                                   19 22                                                                                    22 a. Should Martha use an independent-samples t-test or arelated samples t-test? Explain. b. What are the independent and dependent variables? c. Using the fact that Martha believes the treatment willreduce the amount of time to fall asleep, state the null andalternate hypothesis. d. Would you use a one-tailed or two-tailed test?Explain. e. What is the df? f. Consider that a = .05. determine the critical value,state the value, and how you found it. g. Consider that t obt =1.49. Report the statistical resultsunsing the correct format. h. What should Martha conclude? Martha believes that a relaxation technique involvingvisualization will help people with mild insomnia fall asleepfaster. She randomly selects a sample of 20 participants from agroup of mild insomnia patients and randomly assigns 10 to receivevisualization therapy. The other 10 participants recieve notreatment. Each participant is then measured to see how long (inminutes) it takes him or her to fall asleep. Martha's dateare below. The numbers represent the number of minutes eachparticipant took to fall asleep. No Treatment(X1)                                                 Treatment (X2) 22                                                                                    19 18                                                                                    17 27                                                                                    24 20                                                                                    21 23                                                                                   27 26                                                                                   21 27                                                                                   23 22                                                                                    18 24                                                                                   19 22                                                                                    22 a. Should Martha use an independent-samples t-test or arelated samples t-test? Explain. b. What are the independent and dependent variables? c. Using the fact that Martha believes the treatment willreduce the amount of time to fall asleep, state the null andalternate hypothesis. d. Would you use a one-tailed or two-tailed test?Explain. e. What is the df? f. Consider that a = .05. determine the critical value,state the value, and how you found it. g. Consider that t obt =1.49. Report the statistical resultsunsing the correct format. h. What should Martha conclude?

Explanation / Answer

(a) independent-samples t-test      Reason: there is no relationship betweeneach person in no treatment group and treatment group. (b) Independent variable: the therapy      Dependent variable: the score (c) Let 1: mean with no treatment           2: meanwith treatment Ho:1-20 (alternative hypothesis) (d) One-tailed test      Reason: only interested in reducing theamount of time. (e) df=n1+n2-2=18 (f) Given =0.05, |t(0.05, df=n1+n2-2=18)|=1.73 (checkstudent t table)     The critival value is 1.73 (g) Since t=1.49

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