Chapter 8, Problem 105CRE

Guessing on a True/False Test A true/false test has 50 questions. Suppose a passing grade is 35 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 35 answers correct out of 50. Use a significance level of $\mathrm{0.05.}$ Steps 1 and 2 of a hypothesis test procedure are given. Show steps 3 and 4, and be sure to write a clear conclusion.

Step 1: ${\text{H}}_{\text{0}}:p=0.50$

${\text{H}}_{\text{a}}:p>0.50$

Step 2: Choose the one-proportion $z\text{-test}\text{.}$ Sample size is large enough, because $n{p}_0$ is $50\left(0.5\right)=25$ and $n\left(1-p_0\right)=50\left(0.50\right)=25$, and both are more than 10. Assume the sample is random and $\alpha =\mathrm{0.05.}$