A test prep company has developed a new intervention to improve SAT-Verbal scores. They will conduct ...

A test prep company has developed a new intervention to improve SAT-Verbal scores. They will conduct a hypothesis test to determine if the average SAT-Verbal score of a student who has completed their program is greater than the known national average of 500. The program is very expensive at $12,000 per student. Use this scenario to answer the following questions.

A. Write out the null and alternative hypotheses using the appropriate symbols.
B. In terms of this scenario, describe what a Type I error would look like.
C. In terms of this scenario, describe what a Type II error would look like.
D. The researchers used a sample size of n= 8,000 and found a sample mean of 503.  Using your hypotheses from part A, and the known population standard deviation of 100, what is the test statistic?
E. What is the p-value associated with the test statistic you computed in part D?
F. Are the results of this study statistically significant? Explain why.