A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90,a random sample of 100 doctors was selected.Suppose that the test statistic is -2.20.Can we conclude that H₀ should be rejected at the (α = 0.10,(α = 0.05,and (α = 0.01 level of Type I error? A) (a) yes; (b) yes; (c) yes B) (a) no; (b) no; (c) no C) (a) yes; (b) yes; (c) no D) (a) no; (b) no; (c) yes

Question

Quizplus · Accepted Answer

We need to compare the test statistic with the critical values for different levels of significance. 
For α = 0.10, the critical value is -1.645. Since -2.20 < -1.645, we reject the null hypothesis at α = 0.10 level.
For α = 0.05, the critical value is -1.96. Since -2.20 < -1.96, we reject the null hypothesis at α = 0.05 level.
For α = 0.01, the critical value is -2.576. Since -2.20 > -2.576, we fail to reject the null hypothesis at α = 0.01 level.
Therefore, we can conclude that the null hypothesis should be rejected at α = 0.10 and α = 0.05 levels, but not at α = 0.01 level. The correct choice is option C.

A Survey Claims That 9 Out of 10 Doctors Recommend