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 H₀should 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) yes; (b) yes; (c) no C) (a) no; (b) no; (c) yes D) (a) no; (b) no; (c) no

Question

Quizplus · Accepted Answer

We need to perform a one-tailed test with the null hypothesis being that the proportion of doctors who recommend aspirin is 0.90 or higher. The alternative hypothesis is that the proportion is less than 0.90.
(a) With a significance level of 0.10, the critical value is -1.28. Since the test statistic (-2.20) is less than the critical value, we reject the null hypothesis.
(b) With a significance level of 0.05, the critical value is -1.64. Again, since the test statistic (-2.20) is less than the critical value, we reject the null hypothesis.
(c) With a significance level of 0.01, the critical value is -2.33. The test statistic (-2.20) is greater than the critical value, so we fail to reject the null hypothesis. Therefore, we cannot conclude that the actual proportion of doctors who recommend aspirin is less than 0.90 at the 0.01 level of Type I error.

A Survey Claims That 9 Out of 10 Doctors Recommend