in a test for effectiveness of garlic lowering cholesterol 4

in a test for effectiveness of garlic lowering cholesterol, 47 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 2.7 and a standard deviation of 17.3. A. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic treatment? B. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. C. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

Solution

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

best point estimate = sample mean = 2.7 [ANSWER]

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b. Construct a 90% 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 ?

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
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 =    0.05          
X = sample mean =    2.7          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    17.3          
n = sample size =    47          
              
Thus,              
Margin of Error E =    4.150729493          
Lower bound =    -1.450729493          
Upper bound =    6.850729493          
              
Thus, the confidence interval is              
              
(   -1.450729493   ,   6.850729493   ) [ANSWER, CONFIDENCE INTERVAL]

Thus, we are 90% confident that the true mean change in LDL cholesterol is between -1.4507 and 6.8507. As 0 is inside this interval, then there is no significant change in LDL cholesterol at 0.10 level. [CONCLUSION]