In a test of the effectiveness of garlic for lowering choles

In a test of the effectiveness of garlic for lowering cholesterol, 42 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have a mean of 3.5 and a standard deviation of 16.6. Complete parts (a) and (b) below.

a. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic treatment?

The best point estimate is­­­ 3.5 mg/dl.

Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

What is the confidence interval estimate of the population mean mu?

________mg/dL < mu < mg/dL________

What does the confidence interval suggest about the effectiveness of the treatment?

A - The confidence interval limits do not contain 0, suggesting that the garlic treatment did not

affect the LDL cholesterol levels.

B - The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

C - The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.

D - The confidence interval limits do not contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

Solution

a)

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    3.5          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    16.6          
n = sample size =    42          
              
Thus,              
              
Lower bound =    -1.520321543          
Upper bound =    8.520321543          
              
Thus, the confidence interval is              
              
(   -1.520321543   ,   8.520321543   ) [ANSWER]

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OPTION C: C - The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels. [ANSWER]