A randomized trial tested the effectiveness of diets on adults. Among 41 subject

Question

A randomized trial tested the effectiveness of diets on adults. Among 41 subjects using Diet 1, the mean weight loss after a year was 3.2 lb with a standard deviation of 6.6 lb. Among 41 subjects using Diet 2, the mean weight loss after a year was 1.4 lb with a standard deviation of 5.8lb. Construct a 95% confidence interval estimate of the difference between the population means. Do not assume the population standard deviations are equal.

Does there appear to be a difference in the effectiveness of the two diets? Yes or No

Explanation / Answer

FIrst we should calculate the degrees of freedom here, where population standard deviations are equal.

dF = (s12 /n1 + s2 2 /n2 )/ [(s12 /n1)2 /(n1 -1) + (s22 /n2)2 /(n2 -1)]

dF = [ 6.62 /41 + 5.82 /41] / [ (6.62 /41 )/ 40 + (5.82 /41)/ 40 ]

dF = 40

95% confidence interval = (x1 - x2 ) +- t40,0.05 * sqrt (s12 /n1 + s22 /n2 )

= (3.2 - 1.4) +- 2.02 * sqrt (6.62 /41 + 5.82 /41)

= 1.8 +- 2.02 * 1.3722

= (-0.972, 4.572)

Here the confidence interval consisits the value of Zero so we can say that there is no difference in the effectiveness of the two diets.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.