In a test of the effectiveness of garlic for lowering cholesterol, 43 subjects w

Question

In a test of the effectiveness of garlic for lowering cholesterol, 43 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 5.3 and a standard deviation of 19.2 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 mg/dL.

b) 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?

Explanation / Answer

Here we have given that,

number of subjects (n) = 43

mean (Xbar) = 5.3

and standard deviation = 19.2

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

The best  point estimate of the population mean net change in LDL cholesterol after the garlic treatment is 5.3.

b) 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?

c = confidence level = 95% = 0.95

95% confidence interval for mean net change in LDL cholesterol after the garlic treatment is,

Xbar - E < mu < Xbar + E

where E is the margin of error.

E = (Zc*sd) / sqrt(n)

Zc is the critical value for normal distribution.

Zc we can find by using EXCEL.

syntax is,

=NORMSINV(probability)

where probability = 1 - a/2

where a = 1-c

Zc = 1.96

E = (1.96*19.2) / sqrt(43) = 5.739

lower limit = Xbar - E = 5.3 - 5.739 = -0.439

upper limit = Xbar + E = 5.3 + 5.739 = 11.039

95% confidence interval for mean net change in LDL cholesterol after the garlic treatment is (-0.439, 11.039).

We are 95% confident that the mean net change in LDL cholesterol after the garlic treatment is lies between -0.439 and 11.039.

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