The MCAT is a standardized test written by students hoping to get become medical doctors. The MCAT is designed so that themeanscore each year is 500. Suppose you take a simple random sample of test results for 50 students who wrote the MCAT in 2021. You find that the mean score for this sample was 525 with a standard deviation of 125.

(a) [4 marks] Test the claim that the population mean score in 2021 was 500. For full marks, write out the full 8-step process that you have been shown in class. Partial marks will be given for the following:

• correct null and alternative hypotheses
• correct test statistic
• correct P-value
• correct conclusion

(b) [1 mark] In regular language, what is your conclusion saying? (Is the mean score in 2021 equal to 500 or not?)