Question

7. Dr. Henry believes that if he gives couples a measure of relationship satisfaction (0-8) before he provide them couples therapy and then the same measure of relationship satisfaction (0-8) after therapy his patients will be less likely to divorce. He give his 41 clients the satisfaction measure then therapy for one month and gives the same 41 clients the satisfaction measure after therapy. (Total 18 pts)

A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)?

   Independent:________________________   Scaling:_____________________________

   Dependent:__________________________   Scaling:_____________________________

B. What test should Dr. Henry use (2 pts)?__________________________________________________

C. Why that test (1 pts)?

D. What are the null and alternative hypotheses for that test (2 pts)?

E. What is the critical value for p=.05 (1 pts)? _________________________

G. If Dr. Henry calculates a test statistic of 2.11, should he (2 pts)?         Retain H0       Reject H0

H. Interpret the findings (6 pts):

Answer 1

A.

Independent: measure of relationship before therapy

Scaling:satisfaction (0-8)

Dependent:measure of relationship after therapy

Scaling: satisfaction (0-8)

B. Since the sample size is large enough i.e. 41, so we assume (x_i,y_i) follows bivariate normal distribution where x_i=measure of relationship of ith couple before therapy, y_i=measure of relationship of ith couple after therapy.

Hence we use pair t test for comparing the satisfaction level before and after therapy.

C.

Since we want to measure the satisfaction level before and after therapy, so we

define D_i=y_i-x_i=difference between the measures of relationship after and before of ith couple.

E.

H. Since we reject null hypothesis, so we conclude that after therapy his patients will be less likely to divorce.