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In a test of the Atkins weight loss program, 40 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 lb, with a sample standard deviation of 4.8 lb.

a. What is the best point estimate of the population mean weight loss of all overweight adults who follow the Atkins program?

b. Construct a 99% confidence interval estimate of the mean weightloss for all such subjects.

c. Does the Atkins program appear to be effective? Is itpractical?

User Nixnotwin
by
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1 Answer

5 votes

Answer:

a) For this case the best point estimate of the population mean weight loss of all overweight adults who follow the Atkins program is the sample mean:


\hat \mu = \bar X = 2.1

b)
2.1-2.708(4.8)/(√(40))=0.0448


2.1+2.708(4.8)/(√(40))=4.1552

c) Since the confidence interval contains only positive values we can conclude that the program is effective and is enough evidence at 1% of significance to conclude that the true weigth loss is higher than 0.

Explanation:

Data given


\bar X=2.1 represent the sample mean for the weigth loss


\mu population mean

s=4.8 represent the sample standard deviation

n=40 represent the sample size

Part a

For this case the best point estimate of the population mean weight loss of all overweight adults who follow the Atkins program is the sample mean:


\hat \mu = \bar X = 2.1

Part b

The confidence interval for the true mean is given by the following formula:


\bar X \pm t_(\alpha/2)(s)/(√(n)) (1)

The degrees of freedom are given by:


df=n-1=40-1=39

The Confidence level is 0.99 or 99%, the significance is
\alpha=0.01 and
\alpha/2 =0.005, the critical value for this case is
t_(\alpha/2)=2.708

The confidence interval is given by:


2.1-2.708(4.8)/(√(40))=0.0448


2.1+2.708(4.8)/(√(40))=4.1552

Part c

Since the confidence interval contains only positive values we can conclude that the program is effective and is enough evidence at 1% of significance to conclude that the true weigth loss is higher than 0.

User Will Glass
by
7.7k points
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