7 test Compute the PValue Cholesterol An article in the Arch

7 test

Compute the P-Value

Cholesterol: An article in the Archives of Intern a! Medicine reported than in a sample of 242 men, 69 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 236 women. 40 had elevated cholesterol levels. Can you conclude that the proportion of people with elevated cholesterol levels differs between men and women? Let p 1 denote the proportion of men with elevated cholesterol levels. Use the a = 0.05 level of significance and the P-value method with the TI-84 calculator.

Solution

p1=69/242 =0.285124

p2=40/236 =0.1694915

The test hypothesis:

Ho: p1=p2 (i.e. null hypothesis)

Ha: p1 not equal to p2 (i.e. alternative hypothesis)

The test statistic is

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.285124-0.1694915)/sqrt(0.285124*(1-0.285124)/242+0.1694915*(1-0.1694915)/236)

=3.05

It is a two-tailed test.

So the p-value= 2*P(Z>3.05) =0.0023 (from standard normal table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can conclude that the proportion of people with elevated cholesterol levels differs between men and women.