A true/false test has 8080 questions. suppose a passing grade is 5252 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 5252 answers correct out of 8080. 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.

Let p be the proportion of the correct answers.

As per given , we have

, since the alternative hypothesis is right tailed , so the test is a one -tailed test.

If the student gets 52 answers correct out of 80.

i.e. the proportion of correct answers :

Test statistic :

P-value :   [ by using p-value table for z (right-tailed)]

Since the p-value(0.0037) is less than the significance level (0.05), so we reject the null hypothesis.

Results : We have enough evidence to support the claim that a student knows more than half of the answers and is not just guessing.