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 and explain!!!

Answer 1

a)

95% Confidence Interval is
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 50- 1 ) = 2.01
24 ± 2.01 * 15/√(50)
Lower Limit = 24 - 2.01 * 15/√(50)
Lower Limit = 19.7361
Upper Limit = 24 + 2.01 * 15/√(50)
Upper Limit = 28.2639
95% Confidence interval is ( 19.74 , 28.26 )

Interpretation = We are 95% confident that the mean reduction in cholesterol level for the new drug

is between 19.74 and 28.26 mg / dl

b)

Since Claimed mean 20 contained in confidence interval, we conclude that

confidence interval does not provides convincing evidence that the new drug is effective.