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 doctors was taken. Suppose the test statistic is $\mathrm { z } = - 1.95$. Can we conclude that $\mathrm { H } _ { 0 }$ should be rejected at the a) $\alpha = 0.10$, b) $\alpha = 0.05$, and c) $\alpha = 0.01$ level?
A) a) yes; b) yes; c) no
B) a) yes; b) yes; c) yes
C) a) no; b) no; c) no
D) a) no; b) no; c) yes

Question

Quizplus · Accepted Answer

For a two-tailed test, the critical z-values for $\alpha = 0.10, 0.05,$ and $0.01$ are approximately $1.645, 1.96,$ and $2.576$ respectively. Since the test statistic is $-1.95$, it falls within the rejection region for $\alpha = 0.10$ and $\alpha = 0.05$ but not for $\alpha = 0.01$.

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

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