Question

The National Heart, Lung, and Blood Institute completed a large-scale study of cholesterol and heart disease, and reported that the national average for blood cholesterol level of 50-year old males was 210 mg/dl. A total of 89 men with cholesterol readings in the average range (200 – 220) volunteered for a low cholesterol diet for 12 weeks. At the end of the dieting period their average cholesterol reading was 204 mg/dl with a SD of 33 mg/dl.

a. What is the 95% confidence interval for the study described above? (submit all work)

b. Provide an interpretation of your answer to part A.

c. Does the known population mean of 210 mg/dl fall within the interval?

d. Provide an interpretation of your answer to part C.

e. How would

(1) decreasing the sample size and

(2) decreasing the confidence level affect the size of the interval calculated in part A?

Explain your answer.

Answer 1

Since sample size is 89 (> 30), we use the z-distribution      
a)   95% confidence interval for population mean      
Given      
X̅ = 204  Sample Mean    
s = 33  Sample Standard Deviation    
n = 89  Sample Size    
Confidence interval for mean is given by      
       
     
For 95%, α = 0.05, α/2 = 0.025      
From the z-tables, or Excel function NORM.S.INV(α/2)      
z = NORM.S.INV(0.025) = 1.960   (We take the positive value for calculations)   
       
       
= (197.14, 210.86)   (Rounding to two decimals)   
       
95% confidence interval is (197.14, 210.86) mg/dl      
       
b) Interpretation to answer in part (a)      
When we draw multiple samples from the population under similar conditions,       
we expect that in 95% of samples, the true mean of the population will lie within       
the lower and upper limits of the confidence interval.      
       
c) 197.4 < 210 < 210.86      
Thus the known population mean of 210 mg/dl falls within the interval      
       
d) Since the known population mean falls in the 95% confidence interval,      
we can say that our 95% confidence interval is a true representation of the       
interval for population mean      
       
e) 1) Decreasing the sample size will increase the Margin of Error      
Thus the interval will be wider.      
       
2) When we decrease the confidence level, the absolute z value will decrease,      
thus the interval will be smaller