Question

3. In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss for all such subjects. Does the confidence interval give us information about the effectiveness of the diet?

Answer 1

Answer:Yes

Step-by-step explanation:

Given

$mean \mu =2.1 lb$

$standard deviation \sigma =4.8lb$

n=40

$Standard error=\frac{\sigma }{\sqrt{n}}$

$S.E.=\frac{4.8}{\sqrt{40}}=0.76$

$\alpha =0.1$

$Z_{\frac{\alpha }{2}}=1.645$

Margin of error=$\pm Z_{\frac{\alpha }{2}}\cdot S.E.$

Margin of error=$\pm 1.645\times 0.76$

Margin of error=$\pm 1.2502$

Confidence interval $\mu \pm Z_{\frac{\alpha }{2}}\cdot S.E.$

$\left ( 0.8498,3.3502\right )$

it is effective since it is greater than zero