Question

A pharmaceutical company has developed a new drug to reduce cholesterol. A regulatory agency will recommend the new drug for use if there is convincing evidence that the mean reduction in cholesterol level after one month of use is more than 20 mg/dl. The company collected data by giving the new drug to a random sample of 50 people from the population of people with high cholesterol. The sample mean reduction was 24 mg/dl and the standard deviation was 15 mg/dl.

a. Calculate and interpret a 95% confidence interval for the mean reduction in cholesterol level for the new drug.

b. Do you think the confidence interval you found in part a provides convincing evidence that the new drug is effective? Explain in one or two sentences.

please show work!

Answer 1

Ans:

a)

sample size,n=50

sample mean=24

sample standard deviation=15

df=n-1=50-1=49

t*=tinv(0.05,49)=2.010

95% confidence interval for the mean reduction

=24+/-2.010*(15/sqrt(50))

=24+/-4.26

=(19.74, 28.26)

b)

As,lower limit of above confidnece interval is lower than 20,so we can not conclude that mean reduction is more than 20,hence there is not sufficient evidence that the new drug is effective.