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Chapter 6: Problem 165

Physician's Health Study In the Physician's Health Study, introduced in Data 1.6 on page 37 , 22,071 male physicians participated in a study to determine whether taking a daily low-dose aspirin reduced the risk of heart attacks. The men were randomly assigned to two groups and the study was double-blind. After five years, 104 of the 11,037 men taking a daily low-dose aspirin had had a heart attack while 189 of the 11,034 men taking a placebo had had a heart attack. \({ }^{39}\) Does taking a daily lowdose aspirin reduce the risk of heart attacks? Conduct the test, and, in addition, explain why we can infer a causal relationship from the results.

Short Answer

Expert verified
Based on the hypothesis testing procedure, we will reach a decision and it is likely that a daily low-dose aspirin does reduce the risk of heart attacks given the data. This conclusion can make us infer a causal relationship due to the double-blind randomized assignment in this study.

Step by step solution

01

Understanding the problem

In this problem, we are asked to test whether a daily low-dose aspirin reduces the risk of heart attacks. We have two groups: one taking aspirin and the other taking placebo. We need to use this data to run a hypothesis test.
02

Formulating the Hypotheses

In this case, our null hypothesis (H0) is that there is no difference in the risk of heart attacks between aspirin and placebo groups. Accordingly, the alternative hypothesis (Ha) is that the risk of heart attacks is lower in the aspirin group. So, in mathematical terms it would be - H0: P1 = P2, Ha: P1 < P2, where P1 is the proportion of heart attacks in the aspirin group and P2 in the placebo group.
03

Calculating the test statistics

First, calculate the proportions of heart attacks in each group: p1=104/11037 (aspirin) and p2=189/11034 (placebo). Then calculate the pooled proportion (pooled), which is (x1+x2) / (n1+n2). Here, x1 and x2 are the number of heart attacks in each group and n1 and n2 are the total number in each group. The test statistic (z) is then calculated as (P1-P2) - 0 / sqrt( pooled(1 - pooled)((1/n1) + (1/n2)).
04

Find the p-value and make a decision

The p-value is the chance of getting our observed data or more extreme under the null hypothesis. If the p-value is less than our significance level (usually 0.05), we reject the null hypothesis. Use the normal distribution to find the p-value of our calculated z-score. Then make decision based on our p-value.
05

Infer a Causal Relationship

Since this is a randomized controlled study and all other variables are held constant, any differences in heart attack rates between the two groups can be attributed to the treatment (aspirin or placebo). Thus, if the result of our test is statistically significant, we can infer a causal relationship between daily low-dose aspirin and reduced risk of heart attacks.

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Most popular questions from this chapter

Do Ovulating Women Affect Men's Speech? Studies suggest that when young men interact with a woman who is in the fertile period of her menstrual cycle, they pick up subconsciously on subtle changes in her skin tone, voice, and scent. A study introduced in Exercise \(\mathrm{B} .23\) suggests that men may even change their speech patterns around ovulating women. The men were randomly divided into two groups with one group paired with a woman in the fertile phase of her cycle and the other group with a woman in a different stage of her cycle. The same women were used in the two different stages. For the men paired with a less fertile woman, 38 of the 61 men copied their partner's sentence construction in a task to describe an object. For the men paired with a woman at peak fertility, 30 of the 62 men copied their partner's sentence construction. The experimenters hypothesized that men might be less likely to copy their partner during peak fertility in a (subconscious) attempt to attract more attention to themselves. Use the normal distribution to test at a \(5 \%\) level whether the proportion of men copying sentence structure is less when the woman is at peak fertility.

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