A​ true/false test has 100 questions. Suppose a passing grade is 65 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 65 answers correct out of 100. 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: H0​: p=0.50 Step​ 1: Ha​: p>0.50   Step​ 2: Choose the​ one-proportion z-test. Sample size is large​ enough, because np0 is 100​(0.5)=50 and n1−p0 ​= 100​(.5) ​= 50​, and both are more than 10. Assume the sample is random. Step​ 3: Compute the​ z-test statistic, and the​ p-value.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.