Test Hypotheses about a Population Proportion
-A survey claims that 9 out of 10 doctors (i.e., $90 \%$ ) recommend brand $Z$ for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand $Z$ is less than $90 \%$, a random sample of 100 doctors results in 85 who indicate that they recommend brand $Z$. The test statistic in this problem is approximately:
A) $- 1.67$
B) $1.67$
C) $- 1.17$
D) $- 1.33$

Question

Quizplus · Accepted Answer

The test statistic for a hypothesis test about a population proportion is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{85}{100} = 0.85$, $p_0 = 0.90$, and $n = 100$. Plugging these values into the formula gives $z \approx -1.67$, indicating that the test statistic is approximately $-1.67$.

Test Hypotheses About a Population Proportion -A Survey Claims That 90%90 \%90%

Test Hypotheses About a Population Proportion
-A Survey Claims That $90 \%$