Suppose a school superintendent reads an article which state

Suppose a school superintendent reads an article which states that the overall mean score for the SAT is 910. He does some research and collects data on a sample of his students. He discovered that the average is 960. The superintendent calls the local newspaper to report that his students have scored much higher than the national average.   Is he correct? Explain your reasoning. What else should be considered in his claim.

Solution

Mean = 910

Sample mean = 960

It need not be right.

A hypothesis test is to be conducted and the result depends on the sample size, std deviation and type of sample.

Only if p value happens to be less than alpha, we can accept the claim statistically.