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 z= -2.23 . Can we conclude that H0 should be rejected at the a)$\alpha = 0,10 , \text { b) } \alpha = 0,05 \text {, and c) } \alpha = 0,0 ]$ 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

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  z= -2.23 . Can we conclude that  H0  should be rejected at the a)$\alpha = 0,10 , \text { b) } \alpha = 0,05 \text {, and c) } \alpha = 0,0 ]$ 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

Quizplus · Accepted Answer

The critical z-value for a one-tailed test at α = 0.10 is -1.28, and at α = 0.05 is -1.645. Since -2.23 is less than both, we reject H0 for both α = 0.10 and α = 0.05. However, for α = 0.01, the critical z-value is -2.33, and since -2.23 is greater, we do not reject H0 at α = 0.01.

A Survey Claims That 9 Out of 10 Doctors (I α=0,10, b) α=0,05, and c) α=0,0]\alpha = 0,10 , \text { b) } \alpha = 0,05 \text {, and c) } \alpha = 0,0 ]α=0,10, b) α=0,05, and c) α=0,0]

A Survey Claims That 9 Out of 10 Doctors (I $\alpha = 0,10 , \text { b) } \alpha = 0,05 \text {, and c) } \alpha = 0,0 ]$