Atkins weight loss program In a test of weight loss program

Atkins weight loss program. In a test of weight loss program, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1lb, with a standard deviation of 4.8lb. Construct a 90% confidence interval estimate of the mean weight loss for all such subjects. Does the Atkins program appear to be effective? Does it appear to be practical?

Solution

mean weight loss = 2.1lb

standard deviation = 4.8lb

sample size n = 40

std error = stdev/sqrt(n) = 4.8/sqrt(40) = 0.76

degrees of freedom = n - 1 = 39

critical value for alpha 0.10 and df 39 = +1.68

margin of error = critical value * std error = +1.68 * 0.76 = +1.28

confidence interval = sample mean + margin of error = 2.1 +1.28 = (0.82 , 3.38)

Yes it is effective since the values > 0

Yes it is practial