According to admissions at Blank Slate University, the average ACT score of the incoming freshman class is 23. An intrigued incoming freshman has reason to believe that the actual average ACT score at Blank Slate University is higher than 23. This student takes a simple random sample of 80 incoming freshman and computes an average ACT score of 24.2. Assume that we know the standard deviation of ACT scores of the incoming freshman class at Blank Slate University is 4.8. Consider the question: Does this survey indicate that the mean ACT score at BSU is higher than 23?
a) State the null and alternative hypotheses relative to this question.
b) Find the test statistic.
c) What is the P-value?
d) Can we reject the null hypothesis? Explain why or why not.