Question

Some pharmaceutical companies suggest there are health benefits to taking low doses of aspirin daily. Medical researchers monitoring two independent groups of physicians over a 6-yer period found that, of 3429 doctors (group 1) who took aspirin daily, 148 died from a heart attack or stroke during this period. For 1710 doctors (group 2) who received a placebo instead of aspirin, 79 deaths were recorded. Test whether the proportion of deaths due to heart attack or stroke is lower for those taking aspirin compared to placebo. Test at the 1% significance level

1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. What is the critical value of the z statistic?
4. What is the test statistic?
5. What decision can be drawn from the test?
6. What conclusion can be drawn from the test?

Answer 1

Here we can use ti-83 calculator.

x1 = 148

n1 = 3429

x2 = 79

n2 = 1710

Null hypothesis :

H0: p1 = p2

Alternative hypothesis :

Ha: p1 < p2

Alpha = 1% = 0.01 then critical value is Zc= -2.33

Test statistic :

Z = -0.499

Decision :

Z= -0.499 > Zc=-2.33 then conclude that fail to reject H0.

P-value :

P = 0.3088

Conclusion :

P-value is greater than alpha=0.01 then conclude that fail to reject H0.

Therefore there is not enough evidence to support the claim.