Q6. An investigator theorizes that people who participate in a regular program o
ID: 3306753 • Letter: Q
Question
Q6. An investigator theorizes that people who participate in a regular program of exercise will have levels of systolic blood pressure that are significantly different from that of people who do not participate in a regular program of exercise. To test this idea the investigator randomly assigns 21 subjects to an exercise program for 10 weeks and 21 subjects to a non-exercise comparison group. After ten weeks the mean systolic blood pressure of subjects in the exercise group is 137 and the standard deviation of blood pressure values in the exercise group is 10. After ten weeks, the mean systolic blood pressure of subjects in the non-exercise group is 127 and the standard deviation on subjects in the non-exercise group is g.0. Please test the investigator's theory using an alpha level of .o5. As part of your answer please: a. State both the null and alternative hypotheses b. Include the critical value of the appropriate statistic as part of a decision rule for rejecting the null hypothesis c. Show all of your work involved in reaching a decision as to whether the investigator d. State the conclusion the investigator is entitled to draw on the basis of these results. should reject the null hypothesis or notExplanation / Answer
a)
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
b)
tCRIT is ±2.021 for 40 DF and 0.05 as alpha level
c)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test. We take it as S1 being the SD for subjects who belong to exercise group and S2 as SD of subjects who do not belong to the exercise group.
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (21-1)*10^2+(21-1)*9^2/20+20
= 3620/40
=90.5
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(137-127)-0/90.5(1/21+1/21)
=3.4062
d)
tCRIT is ±2.021 and hence reject the null hypothesis because tSTAT>tCRIT and hence tSTAT lies in the rejection region
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.