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 you conclude that H₀ should be rejected at the (a)α = 0.10,(b)α = 0.05,and (c)α = 0.01 level of Type I error? A)(a)yes; (b)yes; (c)yes B)(a)no; (b)no; (c)no C)(a)no; (b)no; (c)yes D)(a)yes; (b)yes; (c)no

Question

Quizplus · Accepted Answer

We are testing the null hypothesis H0: p=0.90 (where p is the proportion of doctors who recommend aspirin) against the alternative hypothesis Ha: p<0.90. This is a one-tailed test since the alternative hypothesis is directional.

The test statistic is -2.20. Since the sample size is large (n=100) and the normal approximation can be used, the test statistic follows a standard normal distribution under the null hypothesis.

(a) For α = 0.10, the critical value is zα = -1.28 (from the standard normal table). Since the test statistic is smaller than the critical value (i.e. -2.20 < -1.28), we reject the null hypothesis.

(b) For α = 0.05, the critical value is zα = -1.645. Again, since the test statistic is smaller than the critical value (i.e. -2.20 < -1.645), we reject the null hypothesis.

(c) For α = 0.01, the critical value is zα = -2.33. Since the test statistic (-2.20) is greater than the critical value (-2.33), we fail to reject the null hypothesis.

Therefore, the best choice is D, which states that the null hypothesis should be rejected at the 0.10 and 0.05 levels, but not at the 0.01 level.

A Survey Claims That 9 Out of 10 Doctors Recommend