Question

A cohort study is conducted to assess the effectiveness of a 4-week weight-loss intervention program among overweight men. Sixty participants were randomized into two groups. Group 1 worked with a personal trainer to come up with a physical activity regimen that would best fit their lifestyle, while Group 2 worked with a dietician to co-design a diet program to which the men would most likely adhere. Mean BMI was assessed for each group at the end of the 4 weeks. The results are summarized in the table below:

Group	Sample Size	Mean BMI (s)
Physical Activity Program	31	29.1 (6.7)
Diet Program	29	25.9 (8.4)

According to this data, is there evidence at the 0.05 level of the mean BMI for the group that received the physical activity program being significantly higher than the mean BMI for the diet program group?

Part A) true or false; We have statistcally significant evidence at the 5% level to show that the mean BMI for group 1 is significantly higher than the mean BMI for group2.

PartB) Indicate the most accurate p-value associated with the above-mentioned conclusion.

Answer 1

Ans:

Assumption:

population variances are equal.

pooled standard deviation=SQRT(((31-1)*6.7^2+(29-1)*8.4^2)/(31+29-2))=7.5685

standard error=7.5685*sqrt((1/31)+(1/29))=1.955

Test statistic:

t=(29.1-25.9)/1.955

t=1.637

df=31+29-2=58

p-value=tdist(1.637,58,1)=0.0535

As,p-value>0.05,we fail to reject the null hypothesis.

There is not sufficient evidence at the 0.05 level of the mean BMI for the group that received the physical activity program being significantly higher than the mean BMI for the diet program group

False,as there is not statistically significant evidence.