**NEED part (e)** Consider the distribution of serum cholesterol levels for all

Question

**NEED part (e)** Consider the distribution of serum cholesterol levels for all 20- to 74-year-old males living in the United States. The mean of this population is 211 mg/dL, and the standard deviation is 46.0mg/dL. In a study of a subpopulation of such males who smoke and are hypertensive, it isassumed (not unreasonably) that the distribution of serum cholesterol levels is normally distributed, with unknown mean , but with the same standard deviation as the original population.

(b)In the study, a random sample of size n = 12 hypertensive smokers was selected, and found to have a sample mean cholesterol level of x= 217 mg/dL. Construct a 95% confidence interval for the true mean cholesterol level of this subpopulation.

(c)Calculate the p-value of this sample, at the = .05 significance level.

(d)Based on your answers in parts (b) and (c), is the null hypothesis rejected in favor of the alternative hypothesis, at the = .05 significance level? Interpret your conclusion: What exactly has been demonstrated, based on the empirical evidence?

(e) Determine the 95% acceptance region and complementary rejection region for the null hypothesis. Is this consistent with your findings in part (d)? Why?

Explanation / Answer

As only part(E) required here, i will solve only part (e)

Here null hypothesis is MEan cholestrol level is 211mg/dL

Acceptance region = +- Z95% (/sqrt(n))

= 211 +- 1.96 * (46/sqrt(12))

= 211 +- 1.96 * 13.28

= (184.97, 237.03)

Acceptance Region 184.97 < X < 237.03

Rejection region .

X< 184.97 and X > 237.03

Where X is the mean of serum cholestrol level of a sample of 12. and yes, it is consistent as per findings in part(d) as sample mean we get is in acceptance region.

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