Question

3. Very-low-calorie diet (VLCD) Treatment Table gives B (before) and A (after) treatment data for obese female patients in a weight-loss program Table of Weight Loss Data 86.2 Before 99.5 126.3 91.7 121.4 111.4 108.6 114.3 115.4 73.9 79 After 72.7 87.7 93.3 92.3 96.9 84.8 92.9 Weight(kg) of Obese Women Before and After 12-Week VLCD Treatment Can we conclude, at the 95 % confidence level, that the treatment is effective in causing weight reduction in these people. That is, test the hypothesis that u,>0 at a 0.05. This is paired test State the null and alternative hypothesis. Ho: H,: b. Specify the level of significance and identify the degrees of freedom if needed. a 0.OS 9-1 df Sketch the sampling distribution, determine the critical value(s), and c. determine the rejection region(s). Compute d 22.4 and s5S d. Find the standardized test statistic. Make a decision to reject or fail to reject the null hypothesis e fInterpret the decision in the context of the original claim using a complete sentence. level of significance, At the

Answer 1

a) H₀: $\mu_{d} \leq 0$

    H₁: $\mu_{d} > 0$

b) $\alpha$ = 0.05

   df = 9 - 1 = 8

c) At alpha = 0.05, the critical value is t_0.95,8 = 1.860

t = 1.86

$\bar d$ = (33 + 24.5 + 23.8 + 21.4 + 23.1 + 23.7 + 19 + 20.5 + 12.3)/9 = 22.37

s_d = sqrt(((33 - 22.37)^2 + (24.5 - 22.37)^2 + (23.8 - 22.37)^2 + (21.4 - 22.37)^2 + (23.1 - 22.37)^2 + (23.7 - 22.37)^2 + (19 - 22.37)^2 + (20.5 - 22.37)^2 + (12.3 - 22.37)^2)/8) = 5.4667

d) The test statistic t = ($\bar d - D$)/(s_d/$\sqrt n$)

                                  = (22.37 - 0)/(5.4667/$\sqrt 9$)

                                  = 12.276

e) Reject the null hypothesis, since the test statistic value is greater than the critical value(12.276 > 1.860).

f) At the 0.05 level of significance, we can conclude that the treatment is effective in causing weight reduction in these people.