Question

a hospital director believes that 74% of the lab reports contain errors. a sample of 390 reports found 273 errors. is there sufficient evidence at the 0.05 level to refute the hospital directors claim? state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is the statement of no - effect or the claim that is initially assumed to be true. Here, the hospital director's claim is the null hypothesis. So $H_0:p = 0.74$, where $p$ is the proportion of lab reports that contain errors.

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is the statement we are trying to find evidence for. Since we want to refute the director's claim, and there is no indication of a one - sided test (like more or less than), it is a two - sided test. So $H_a:p
eq0.74$.

Answer:

$H_0:p = 0.74$
$H_a:p
eq0.74$