A medical researcher treats 40 subjects with high school cho

A medical researcher treats 40 subjects with high school cholesterol with a new drug. The mean decrease in cholesterol levels is 90.7 after two months of taking the drug, and the sample standard deviation is 28.3. assume that the decrease in cholesterol levels after two months of taking the drug follows a normal distribution, with a population standard deviation of 30. Construct a 90% confidence interval for the unknown population mean decrease in cholesterol levels

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=90.7
Standard deviation( sd )=30
Sample Size(n)=40
Confidence Interval = [ 90.7 ± Z a/2 ( 30/ Sqrt ( 40) ) ]
= [ 90.7 - 1.64 * (4.743) , 90.7 + 1.64 * (4.743) ]
= [ 82.921,98.479 ]