Twenty volunteers agree to participate in a study on the effectiveness of a new

Question

Twenty volunteers agree to participate in a study on the effectiveness of a new diet on weight loss. The volunteers are weighed prior to beginning the diet and after six weeks on the diet. The sample mean weight loss (weight before the diet minus weight after six weeks on the diet) is 7 pounds and the sample standard deviation of the weight losses is 13 pounds.

We would like to conduct a hypothesis test to determine if the diet is successful in reducing weight. What is the P-value for the appropriate test of significance? What is the interpretation of the P-value obtained?

Explanation / Answer

null hypothesis: Ho: mean wseight loss =0

alternate hypothesis:Ha" mean weight loss>0

here std error =std deviation/(n)1/2 =2.9069

hence test stat t=(X-mean)/std error =(7-0)/2.9069 =2.408

for 19 df ,for above tstat ; p value =0.0132

as p value is less then 0.05 level; we reject null hypothesis; and accept that diet is successful in reducing weight

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