Suppose we want to compare fasting serum-cholesterol levels among recent Asian i

Question

Suppose we want to compare fasting serum-cholesterol levels among recent Asian immigrants to the United States with typical levels found in the general U.S. population. We assume cholesterol levels in women ages 21-40 in the United States are approximately normally distributed with mean 190 mg/dl It is unknown whether cholesterol levels among recent Asian immigrants are higher or lower than those in the general U.S. population. Let's assume that the levels among recent female Asian immigrants are normally distributed with unknown mean and standard deviation. Hence we wish to test the null hypothesis Ho: ? 190 versus Ha: ? 190 at ?-0.05. Blood tests are performed on 100 female Asian immigrants ages 21-40. If the sample standard deviation is 40 mg/dl

Explanation / Answer

Standard Error =40 / Sqrt(100) =4

tcrit for ? =0.05 and degrees of freedom = 99 is 1.9842 (can be determined from a standard t-table or using Excel function T.INV()

hence mean upper cholesterol level =mean + tcrit*std error =190 + 1.9842 * 4 = 197.9369

mean lower cholesterol level =mean - tcrit*std error =182.0631

if the sample mean is 181.52 which is outside our confidence interval. we should reject null hypothesis because the sample mean lies outside the non-critical region

for alpha =0.01 , t =2.6264

hence revised lower level =190 -4*2.6264 =179.4944

as on 0.01 alpha.181.52 falls inside confidence interval, we can not reject the null hypothesis.

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