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 you reject the null hypothesis. What conclusion can you reach?

Question

There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.


There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.


There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.


There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

Answer 1

When you reject the null hypothesis, it means that you have found sufficient evidence to support the alternative hypothesis. In this case, the null hypothesis (H0) is that the proportion of doctors who recommend aspirin is equal to or greater than 0.90, while the alternative hypothesis (H1) is that the proportion of doctors who recommend aspirin is less than 0.90.

Since you rejected the null hypothesis, the appropriate conclusion is:

There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.