Question

The distribution of serum cholesterol levels for the general population of adult males in the United States is normal with a mean of 211 mg/dL and a standard deviation of 46 mg/dL. A researcher wishes to know if adult males who are hypertensive and who smoke differ significantly from this general population with regards to their serum cholesterol levels. The researcher randomly selects 25 adult male hypertensive smokers, measures their serum cholesterol levels, and calculates a mean of 217 mg/dL and a standard deviation of 38 mg/dL.

(a) What is the null hypothesis for this problem? What is the alternative hypothesis?

(b) For this problem, would you perform a one- or two-tailed test? Explain how you reached that decision.

(c) Determine which procedure (you have learned five situations) is the appropriate statistical test to use, with a clear explanation for your choice.

(d) Using your calculator, test the null hypothesis, present your results. Show all your work.

(e) Using statistical language (“statistic-ese”), state your conclusion and your reasoning for reaching this conclusion. Then restate your conclusion, this time in English instead of “statistic-ese,” without including statistical symbols or the term hypothesis. (What is the answer to the researcher’s question?)

(f) State, based on your conclusion, whether you may have committed a Type I error or a Type II error, and what that means.

Answer 1

a] NULL HYPOTHESIS H0:   mg/dL

ALTERNATIVE HYPOTHESIS Ha:   mg/dL

b] TWO TAILED TEST. SINCE WE ARE TESTING  differ significantly from this general population with regards to their serum cholesterol levels..

c] Since Population standard deviation isknown.

Z= xbar-mean/sigma/sqrt(n)

Z= 217-211/46/SQRT(25)

Z= 6/46/5

Z= 0.652

Z critical value=1.96

D] REJECT H0 IF Z >1.96 .Since Z critical GREATER than Zcal therefore NOT significant

Decision: DO NOT REJECT H0.

E] Conclusion: We do not have sufficient evidence to conclude that  differ significantly from this general population with regards to their serum cholesterol levels at 0.05 level of significance.

F] WE REJECTED NULL HYPOTHESIS H0. THEREFORE WEHERE COMMITED TYPE 1 ERROR.