Last Name 3

Firstname LastnameInstructors NameCourse Number24 March 2014Problem 2One hundred and fifty subjects who completed a weight-reduction program at a fitness center were divided into three equal groups. Subjects in Group 1 were assigned to a support group that met weekly. Subjects in Group 2 were assigned to a support group that met monthly. Subjects in Group 3 did not participate in support group activities. At the end of the year a determination was made as to whether each subject met their weight loss goal. The results are in the table below. Perform an appropriate test to determine if there is a significant difference in the proportion that met their weight loss goal among the three groups. Group 1Group 2Group 3

Met Goal 342812

Did not Meet Goal162238

a. present a contingency tableThe Contingency Table is a two-way frequency table. There is a row for each factor level and a column for each response level. List all the levels of goals as rows in a table and the levels of Groups as columns, the find the joint or cell frequency for each cell.

Group 1Group 2Group 3

Met Goal34281274

Did not meet Goal1676

505050150

b. State the appropriate null and the alternative hypothesis Ho: Meeting the weight loss was independent of the group assignedHa: Meeting the weight loss was dependent of the group assignedc. Determine a critical valueThe critical value is determined using the 95% of the mean and the standard error of the sample. 95% from the chi-square table is represented by 1.96. The 1.96=0.0250. Since it is a two tailed test then our critical value will be 0.02502=0.05 (5%)d. Present a test statistic

X2=(Oij-Eij)2 EijEij=RC NRow 1= (7450150), (7450150), (7450150)= 24.67, 24.67, 24.67Row 2= (7650150), (7650150), (7650150)= 25.33, 25.33, 25.33X2= ((34-24.67)224.67) + ((23-24.67)224.67) + ((12-24.67)224.67) +((16-25.33)225.33)+ ((22-25.33)225.33) + ((38-25.33)225.33)=20.3604

e. Present a p-valueThe P-value for the chi-square test is P ( >X), the probability of observing a value at least as extreme as the test statistic for a chi-square distribution with (r-1)(c-1) degrees of freedom.

Degree of freedom= (R-1)(C-1)= (2-1)(3-1)=12=2P-value= 10.597f. Interpret the p-value

The p-value is highly significant indicating that some association between the variables is present.g. State your decision

Reject the Ho (Meeting the weight loss was independent of the group assigned) and accept the Ha (Meeting the weight loss was dependent of the group assigned)h. State your conclusion

The weight loss of the 150 subjects depended on the group assigned with those without a grop meeting likely to miss their weight loss goal while those assigned to the group that met weekly likely to meet their weight loss goal.