Artificial intelligent assistant

Equality of two binomial parameters I am having some trouble with this problem of Ross. Can anyone please help me out. In a famous experiment to determine the efficacy of aspirin in preventing heart attacks, 22,000 healthy middle-aged men were randomly divided into two equal groups, one of which was given a daily dose of aspirin and the other a placebo that looked and tasted identical to the aspirin. The experiment was halted at a time when 104 men in the aspirin group and 189 in the control group had had heart attacks. Use these data to test the hypothesis that the taking of aspirin does not change the probability of having a heart attack. Thanks in advance.

**Hint:** You need to perform a test for equality of sample proportions from two independent populations. The test statistic for testing the difference in two population proportions, that is, for testing the null hypothesis $$H_0:p_1−p_2=0$$ is:

$$Z=\dfrac{(\hat{p}_1−\hat{p}_2)−0}{\sqrt{\hat{p}(1−\hat{p})\left(\dfrac{1}{n_1}+\dfrac{1}{n_2}\right)}} \sim N(0,1)$$

where: $\hat{p}=\dfrac{Y_1+Y_2}{n_1+n_2}$ is the proportion of "successes" in the two samples combined. In your case

* $n_1=n_2=11000$ and
* $Y_1=104, Y_2=189$.



You only need to specify the significance level $α$ at which you will perform the test. If not given by the exercise you can choose $α=5%$ or $α=1%$.

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