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 doctors was taken. Suppose the test statistic is $z = - 1.75$. Can we conclude that $H _ { 0 }$ should be rejected at the a) $\alpha = .10$, b) $\alpha = .05$, and c) $\alpha = .01$ level?
A) a) yes; b) yes; c) no
B) a) yes; b) yes; c) yes
C) a) no; b) no; c) yes
D) a) no; b) no; c) no

Question

Quizplus · Accepted Answer

For a one-tailed z-test, the critical z-values are approximately -1.28 for $\alpha = .10$, -1.645 for $\alpha = .05$, and -2.33 for $\alpha = .01$. Since the test statistic $z = -1.75$ is less than -1.28 and -1.645, it falls in the rejection region for $\alpha = .10$ and $\alpha = .05$, but not for $\alpha = .01$, where the critical value is -2.33.

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

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