Question

Show all work for credit, including calculations when used.  In other words, you should show all the inputs such as invnorm(a,b,c,d) , normaldist(a,b,c,d), etc.  Those are all you need to complete the work, besides the basic Z, SD, and CI formulas provided.

2. High blood pressure has been identified as a risk factor for heart attacks and strokes. The National Health and Nutrition Examination Survey reported that 12 out of 38 randomly selected US adults had high blood pressure.

a) State the conditions and verify if they are met.

b) Draw a sketch. Find the indicated values for a 90% confidence interval showing all work and reporting 7 decimal places for all calculations.

c) Interpret our interval in the context of the problem.

d) The Center for Disease Control and Prevention reports that 32% of all US adults have high blood pressure. Based on your above confidence interval, is there evidence to support the CDC claim? Justify your answer.

Answer 1

a)
np > 5 and n*(1-p) > 5
hence conditions are met

z-value for 90% CI, 1.6448536 (=NORM.INV(0.05,0,1)
pcap = 12/38 = 0.3157895

SE = sqrt(0.3157895*(1-0.3157895)/38) = 0.0754053

b)
CI = (0.3157895 - 1.6448536*0.0754053, 0.3157895 + 1.6448536*0.0754053)
= (0.1917588, 0.4398202)

c)
For a sample of 38, one can be 90% confident that proportion of high blood pressure is between 0.1917588 and 0.4398202

d)

There is sufficient evidence to support the claim as 0.32 lies in the above interval