Question

A study of randomly selected Americans found that of 1,792 men, 244 had cardiovascular disease (CVD) and of 2,007 women, CVD was prevalent in 135 of them. Conduct a hypothesis test to see if CVD prevalence is higher among men than women in America.

Let men be group 1 and women be group 2.

1.Write the hypotheses for this test.

2.What is the test statistic?

3.What is the p-value?

4.Using α = 0.05, decide whether or not to reject the null hypothesis.

5.Based on your decision, is there evidence that CVD prevalence is higher among men than women in America?

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

2)

p1cap = X1/N1 = 244/1792 = 0.1362
p1cap = X2/N2 = 135/2007 = 0.0673
pcap = (X1 + X2)/(N1 + N2) = (244+135)/(1792+2007) = 0.0998

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1362-0.0673)/sqrt(0.0998*(1-0.0998)*(1/1792 + 1/2007))
z = 7.07

3)

P-value Approach
P-value = 0

4)

As P-value < 0.05, reject the null hypothesis.

5)

yes, There is sufficient evidence to conclude that CVD prevalence is higher among men than women in America