Spelman College is experiencing unprecedented applications for the 2021-22 school year. Although the college has suspended using standardized test scores for the 2021-22 academic year, the college is considering for the future a new admission standard for its SAT acceptance score raising it to 1200. To test the efficacy of this score they selected 100 current students and found that the average score to be 1150. Using the previous standard deviation SAT score of 200. Test at the .05 level whether the mean SAT score for current students is 1200.

1. Form the null and alternate hypotheses
2. Test using all three methods
3. What in terms of the narrative are the Type I and Type II errors?
4. What is the probability of making a Type I error?
5. What decision would you make if = .01?
6. For a= 1190, find (1190)