A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 millimole per liter. Assume the population standard deviation is σ = 0.18.

a. Construct a 98% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs.

B. Based on the confidence interval constructed in part (a), is it likely that the mean reduction in cholesterol level is less than 0.90?

Answer:

a. 98% confidence interval ( 0.92, 0.96 )

Step-by-step explanation

sample size, n = 314

mean = 0.94

σ = 0.18.

98% confidence interval

Alpha = 1 - 0.98

= 0.02

Alpha/2 = 0.01

Z_(alpha) = 2.326 from the standard normal distribution table

Margin of error = Z_(alpha)* (σ/?√?n)

= 2.326*(0.18/?√? 314)

= 0.0236

Lower bound = mean - margin of error

= 0.94 - 0.0236

= 0.92

Lower bound = mean + margin of error

= 0.94 + 0.0236

= 0.96

Confidence interval ( 0.92, 0.96 )

B. Based on the confidence interval constructed in part (a), is it likely that the mean reduction in cholesterol level is less than 0.90?

We are 98% confidence that the mean reduction in cholesterol level lies between ( 0.92, 0.96 ), however, it is also possible that it may not lie within the calculated confidence interval, which means it may be less than 0.9.