Two weight loss clubs, A and B, were compared with respect to overall performanc

Question

Two weight loss clubs, A and B, were compared with respect to overall performance. From club A, a random sample of 100 people was selected and it was found that the average weight loss over a one month period was 20 pounds. From club B, a random sample of 100 people was selected and it was found that the average weight loss over a one month period was 26 pounds. If it is known that the population standard deviations for weight loss of these two clubs are 4 pound and 7 pound, respectively, establish a 95% confidence interval on the difference between these two population means, and answer the following questions: The Standard error of Difference is The Margin of Error (%) of Difference is

Explanation / Answer

standard errror of differnce =(s12/n1 +s22/n2)1/2 =0.806

for 95% Ci; z=1.96

hence margin of error =z*std error =1.5802

point estinate of differnece =x2-x1 =26-20 =6

hence confidence interval =point estimate +/- z*std error =4.420 ; 7.580

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