A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin
Is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend
Aspirin. The value of the test statistic in this problem is approximately equal to:
A) - 4.12
B) - 2.33
C) - 1.86
D) - 0.07

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion: $ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $, where $\hat{p} = 0.83$, $p_0 = 0.90$, and $n = 100$. Plugging in these values gives a z-score of approximately -2.33.

A Survey Claims That 9 Out of 10 Doctors Recommend