Question

9 A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol level, in milligrams per deciliter, we measured before and after treatment for each individual, with the followine re Individual Before 283 299 274 284 248 275 293 277 After 215 206 187 212 178 212 192 196 /7, Y a) Construct a 90% confidence interval for the mean reduction in cholesterol level. physician claim that the mean reduction in cholesterol level is more than 80 milligrams per deciliter. Does the confidence interval contradict this claim? b A

Answer 1

(a)

The reduction in cholesterol for 8 individuals is,

68, 93, 87, 72, 70, 63, 101, 81

Mean reduction = 79.375

Standard deviation = 13.38376

Standard error of mean reduction = 13.38376 / $\sqrt{8}$ = 4.731874

Degree of freedom = n - 1 = 8 - 1 = 7

Critical t value for 90% confidence interval and df = 7 is 1.895

90% confidence interval of the mean reduction in cholesterol level is,

(79.375 - 1.895 * 4.731874, 79.375 + 1.895 * 4.731874)

(70.4081, 88.3419)

(b)

As, the 90% confidence interval of reduction in cholesterol levels contains the values less than 80, the confidence interval contradicts the claim that the mean reduction in cholesterol levels is more than 80 milligrams per deciliter.