Question

Much discussion has appeared in the medical literature in recent years on the role of diet in the development of heart disease. The serum-cholesterol levels of a random sample of n = 24 people who eat a primarily macrobiotic diet were measured. Their average cholesterol level was found to be ¯x = 195 milligrams per deciliter with standard deviation of s = 35 milligrams per deciliter. The cholesterol levels in the general population in this age group have mean of 230 milligrams per deciliter. Assume that serum-cholesterol levels are normally distributed. Show work for full credit.

(a) Conduct a hypothesis test to determine if the true mean cholesterol level in the macrobiotic diet population is di↵erent from 230 milligrams per deciliter. Use pvalue.

b) Interpret your answer from part (a).

Answer 1

Solution :

= 230

= 195

s = 35

n = 24

Df = n -1 =24-1 = 23

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 230

Ha : 230  

Test statistic = t

= ( - ) / s/ n

= (195 - 230 ) / 35 / 24

= -4.90

P (Z < -4.90 ) = 0.0001

P-value = 0.0001