Question

# A study was conducted to determine the effectiveness of a diet program in reducing weight of...

A study was conducted to determine the effectiveness of a diet program in reducing weight of obeys people. Eight randomly selected patients were put on this diet and the amount of weight losses (in pounds) were recorded. Suppose the sample mean and the sample standard deviation of weight losses were 38 and 4.598136 pounds, respectively. Construct a 90% confidence interval for the average weight loss and based on the confidence interval constructed determine if you would expect to see an average weight loss of 35 pounds. (Assume that samples were taken independently from a normal distribution.)

90% CI: (34.91932, 41.08068), an average weight loss of 35 pounds is expected to see.

90% CI: (36.91082, 39.08918), an average weight loss of 35 pounds is expected to see.

90% CI: (36.91082, 39.08918), an average weight loss of 35 pounds is not expected to see.

90% CI: (34.91932, 41.08068), an average weight loss of 35 pounds is not expected to see.

90% CI: (35.69965, 41.08068), an average weight loss of 35 pounds is not expected to see.

90% CI: (35.69965, 41.08068), an average weight loss of 35 pounds is expected to see.

90% CI: (34.91932, 41.08068), an average weight loss of 35 pounds is expected to see.

[ explanation:-

given data are:-

sample mean () = 38

sample sd (s) = 4.598136

sample size (n) = 8

df = (n-1) = (8-1) = 7

t critical value for alpha=0.10,df=7,both tailed test be:-

[ using t distribution table ]

the 90% confidence interval for the average weight loss is:-

decision:-

as 35 is included in the 90 % confidence interval, we may expect an average we would expect an average weight loss of 35 pounds. ]

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