Question

A recent study examined the association between high blood pressure and increased risk of death from cardiovascular disease. There were 2676 men with low blood pressure and 3338 men with high blood pressure. In the low-blood-pressure group, 21 men died from cardiovascular disease; in the high-blood-pressure group, 55 died. a. Compute the 95% confidence interval for the difference in proportions. b. Do the study data confirm that death rates are higher among men with high blood pressure? State hypotheses, carry out a significance test, and give your conclusions.

Answer 1

To answer the student's question, the 95% confidence interval for the difference in proportions is calculated using the formula for two proportions. Additionally, a hypothesis test is performed to determine if death rates from cardiovascular disease are higher among men with high blood pressure, involving setting hypotheses, calculating a test statistic, and making a conclusion based on the results.

Step-by-step explanation:

Calculating 95% Confidence Interval for the Difference in Proportions

To calculate the 95% confidence interval for the difference between the observed proportions of deaths from cardiovascular disease in the low and high blood pressure groups, we will use the following formula:

(p1 - p2) ± z* sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2)

Where p1 and p2 are the observed proportions in the low and high blood pressure groups, n1 and n2 are the total number of individuals in the groups, and z* is the z-value corresponding to the 95% confidence level (approximately 1.96).

First, we calculate the proportions:
p1 = 21/2676 and p2 = 55/3338.

Next, we input these into the formula with the respective group sizes to find the confidence interval.

Hypothesis Testing for Difference in Proportions

To test the hypothesis that death rates from cardiovascular disease are higher among men with high blood pressure, we perform a test of significance for the difference in proportions. The null hypothesis (H0) states there is no difference in death rates, while the alternative hypothesis (H1) suggests that the death rate is higher for the high blood pressure group. The steps involve calculating the test statistic and comparing it to a critical value or using a p-value approach. A conclusion is drawn based on this comparison.

For this case, details of the test calculation are not provided, but a general process has been outlined.

Answer 2

Find the odds of a man with high blood pressure dying from cardiovascular disease. 55 p .0165 3338 = p .0165 .0165 .0168 1 p 1 .0165 .9835

Do the same for a man with low blood pressure. 21 p .0079 2676 = = p .0079 .0079 .00796 1 p 1 .0079 .9921 = = = − − ----->

Calculate the odds ratio with the odds for the high blood pressure group in the numerator. Describe the result in words. HBP LBP odds .0168 odds ratio 2.11 odds .00796 = = = Men with high blood pressure are 2.11 times more likely to die from cardiovascular disease.