QuestionA true/false test has 90 questions. Suppose a passing grade is 54 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 54 answers correct out of 90 . Use a significance level of 0.05 . Steps 1 and 2 of a hypothesis test procedure are given below. Show step 3 , finding the test statistic and the p-value and step 4 , interpreting the results.
Step 1: $H_{0}: p=0.50$ $$H_{a}: p>0.50$$
Step 2: Choose the one-proportion z-test. Sample size is large enough, because $n p_{0}$ is $90(0.5)=45$ and $n\left(1-p_{0}\right)=$ $90(.5)=45$, and both are more than 10 . Assume the sample is random. Step 3: Compute the $z$-test statistic, and the $p$-value. $z=$ $\square$ (Round to two decimal places as needed.) $p$-value $=$ $\square$ (Round to three decimal places as needed.)