Question

The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Please help him

Answer 1

Variable of interest: The SAT scores of all the students entering the universities in the United States this year.

Type 1 Error: The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower.

In other words:

The parameter the president is interested in is the mean SAT score of the entering students to his university this year.

The population the president is interested in is all entering students to his university this year.