3. In a study, 29 girls with anorexia received cognitive behavioral therapy. Thi

Question

3. In a study, 29 girls with anorexia received cognitive behavioral therapy. This form of psychotherapy stresses identifying the thinking that causes the undesirable behavior and replacing it with thoughts designed to help improve this behavior. The table gives the weights before and after therapy. Determine if the women gained a statistically significant amount of weight from treatment using a 4C's analysis. Girl 16 17 18 Girl Before After 82.2 85.6 81.4 81.9 76.4 103.6 98.4 93.4 73.4 82.1 96.7 95.3 82.4 72.5 90.9 Before 80.6 83.3 87.7 84.2 86.4 83.0 76.5 80.2 87.8 83.3 79.7 84.5 80.8 After 80,5822 71.3 84.9 81.5 82.6 79.9 88.7 94.9 76.3 81 80.5 85 89.2 81.3 76.5 85.4 89.1 83.9 82.7 81.6 75.7 82.6 100.4 85.2 83.6 84.6 20 21 24 25 26 27 28 10 12 13 14 15 87.4 86.7 Context Conditions Calculations (using MiniTab) Conclusion

Explanation / Answer

Solution: We have to use Paired t test:

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: D = 0

Ha: D 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

Rejection Region

Based on the information provided, the significance level is =0.05, and the degrees of freedom are df=28.

Using MINITAB,

Paired T for Before - After

                  N      Mean     StDev   SE Mean

Before           29     82.70      4.84      0.90

After            29     85.70      8.35      1.55

Difference       29     -3.00      7.32      1.36

95% CI for mean difference: (-5.78, -0.22)

T-Test of mean difference = 0 (vs not = 0): T-Value = -2.21 P-Value = 0.036

Decision about the null hypothesis:

Using the P-value approach: The p-value is p=0.036, and since p=0.036<0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean is different than , at the 0.05 significance level.

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