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) = 0.10, (b) = 0.05, and (c) = 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

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)  = 0.10, (b)  = 0.05, and (c)  = 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

Quizplus · Accepted Answer

The null hypothesis is that the proportion of doctors who recommend aspirin is 0.90. The alternative is that the proportion is less than 0.90. The test statistic is -2.20, which corresponds to a p-value of approximately 0.014.

(a) At the 0.10 level of Type I error, the critical value is -1.28. Since the test statistic (-2.20) is less than the critical value, we reject the null hypothesis. Therefore, choice (a) is yes.

(b) At the 0.05 level of Type I error, the critical value is -1.645. Since the test statistic (-2.20) is less than the critical value, we reject the null hypothesis. Therefore, choice (b) is yes.

(c) At the 0.01 level of Type I error, the critical value is -2.33. Since the test statistic (-2.20) is greater than the critical value, we do not reject the null hypothesis. Therefore, choice (c) is no.

A Survey Claims That 9 Out of 10 Doctors Recommend