A company claims that 9 out of 10 doctors (i.e., $90 \%$ ) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than $90 \%$, a random sample of 100 doctors was chosen which resulted in 87 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately:
A) $- 1.00$
B) $- 0.50$
C) $- 0.66$
D) $1.00$

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 $\hat{p} = 0.87$, $p_0 = 0.90$, and $n = 100$. Plugging in these values gives approximately $-1.00$.

A Company Claims That 9 Out of 10 Doctors (I 90%90 \%90%

A Company Claims That 9 Out of 10 Doctors (I $90 \%$