Question

An article in the Archives of Internal Medicine reported that in a sample of 244 men, 73 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 232 women, 44 had elevated cholesterol levels. use the a=0.05

a) Write the hypotheses for the test.

b) Calculate the difference in sample proportions between groups.

c) Using 2PropZTest, calculate a P-value.

d) Fill in the blanks to explain what the P-value means: If there is __________________________ between the proportions of high cholesterol, then there is a ___ % chance that there is a _______ or ______________ percentage point difference between the high cholesterol rates.

e) What is your decision about the null hypothesis? Why?

f) Statistically, is there a significant difference between high cholesterol rates of men and women? Support your answer.

g) Calculate a 95% confidence interval for the difference in high cholesterol rates. Does the confidence interval strengthen or weaken your conclusions in parts e) and f)? Why?

Answer 1

a) H₀: P1 = P2

    H₁: P1 P2

b) p1 = 73/244 = 0.299

   p2 = 44/232 = 0.190

The difference in sample proportion is p1 - p2 = 0.299 - 0.190 = 0.109

The pooled sample proportion(P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                                     = (0.299 * 244 + 0.190 * 232)/(244 + 232)

                                                     = 0.25

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

      = sqrt(0.25 * (1 - 0.25) * (1/244 + 1/232))

      = 0.0397

The test statistic z = (p1 - p2)/SE

                             = 0.109/0.0397 = 2.75

P-value = 2 * P(Z > 2.75)

             = 2 * (1 - P(Z < 2.75))

             = 2 * (1 - 0.9970)

             = 0.006

If there is a statistical significance difference between the the proportions of high cholesterol , then there is 0.6% chance that there is a 5% or more percentage of point difference between the high cholesterol rates.

e) Since the P-value is less than (0.006 < 0.05), we should reject the null hypothesis.

f) Yes, there is a statistical difference between high cholesterol of men and women.

g) The 95% confidence interval is

(p1 - p2) +/- z_0.025 * SE

= 0.109 +/- 1.96 * 0.0397

= 0.109 +/- 0.0778

= 0.0312, 0.1868

Since the confidence interval does not cointain 0, there is a statistical difference between high cholesterol of men and women.

So the confidence interval strengthen the conclusions in parts e) and f).