Please answer the question below: 4. Suppose a study in which middle-aged partic

Question

Please answer the question below:

4. Suppose a study in which middle-aged participants (mean age 55years) with impaired glucose tolerance (IGT) were randomized to either an intervention or a control group. People in the intervention group were encouraged to (a) reduce weight, (b) reduce fat in-take, (c) increase fiber intake, and (d) increase hours per week of exercise. People in the control group received pamphlets with general information concerning diet and exercise but did not receive individual counseling. Table 1 presents weight changes ([follow-up weight] - [baseline weight]) in the two groups after 1 year Table 1 Intervention Control Group n2-250 Group n1-255 Change in weight (kg) over 1 year (mean sd) -4.3+5.8-0.947 (a) Is there a significant weight loss in the intervention group during the 1-year follow-up (b) Is there a significant weight loss in the control group during the 1-year follow-up period? period? (c) Describe what procedure you would follow in order to test whether the mean weight changes are different between the two groups. Hint: Clearly describe the procedure without performing any test (d) [ONLY PHP2510 Perform the hypothesis test in part (c). What is your conclusion about the intervention?

Explanation / Answer

Questio 4(a)

Here for intervention group during the 1 year follow group.

Here mean weight loss xint= -4.3 kg

standard deviation of weight loss sint =  5.8 kg

Here test statistic to check that there is significant loss.

t = (xint -0)/ (s /sqrt(n) = -4.3/ (5.8/ sqrt(255))= 11.84

so tcritical for dF = 254 and alpha = 0.05 ,

t254,0.05 = 1.9693

so here t >  tcritical so we can conclude that there is significant weight loss due to intervention program.

(b)

Here for Control group during the 1 year follow up group period

Here mean weight loss xctrl= -0.9 kg

standard deviation of weight loss sint = 4.7 kg

Here test statistic to check that there is significant loss.

t = (xctrl -0)/ (s /sqrt(n) = -0.9/ (4.7/ sqrt(250))= 3.03

so tcritical for dF = 249 and alpha = 0.05

t249,0.05 = 1.9695

so here t >  tcritical so we can conclude that there is significant weight loss due to control program.

(c) We would use t test hypotheiss testing for two independent sample populations.

(d) H0 : int . = ctrl

Ha : int .   ctrl

Here pooled standard deviation

sp = [{(n1 -1)s12 + (n2 -1)s22 } /(n1 + n2 -2)]

sp = [(254 * 5.82 + 249 * 4.72) /(254 + 249)] = 5.2842

Test statistic

t = (xint - xctrl)/ sp * sqrt(1/n1 + 1/n2 ) = (-4.3 + 0.9)/ [5.2842 * sqrt(1/255 + 1/250) ] = -3.4/ 0.47031 = -7.23

so here tcritical  for dF = (255 + 250 - 2) = 503 , alpha = 0.05

tcritical = 1.9647

t >  tcritical so we shall reject the null hypothsis and can conclude that the intervention group and control group weight loss are different.

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