Question

Cholesterol: An article in the Archives of Internal Medicine reported that in a sample of 250 men, 55 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 210 women, 50 had elevated cholesterol levels. Can you conclude that the proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels? Let p1 denote the proportion of men with elevated cholesterol levels and p2 denote the proportion of women with elevated cholesterol levels. Use the α=0.05 level of significance and the P-value method with the TI-84 Plus calculator.

a) State the appropriate null and alternate hypotheses.

b) p-value

c) reject or not

d) conclusion

Answer 1

a)

Null Hypothesis: The proportion of men with elevated cholesterol levels is not less than the proportion of women with elevated cholesterol levels.

Alternate Hypothesis: The proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels.

b)

For one tailed test, for test statistic, Z = −0.461, the p-value =0.3225

c)

Since the p-value of 0.3225 > 0.05 significance level, we do not reject the null hypothesis.

d)

Conclusion: Since the null hypothesis is not rejected, we do not have sufficient evidence to claim that the proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels.

Z-test for two proportions: