A local school district recently implemented an experimental program to improve mathematical skills for a specific high risk population. They selected 15 students to be in the initial study. After 1 year, the students in the program took a national mathematic achievement test. Students in this high risk population score an average of 35 with a standard deviation of 6. The goal of the program is for students to increase performance. Assume the data is approximately normally distributed.
The scores the students received are listed below.
40 55 50 30 33 44 25 15 53 40 65 13 58 69 78
The program is using a 5% significance level to report its results.
Answer the following questions:
1. Determine and state the mean and standard deviation for the data set.
2. State the alternative hypothesis.
3. State which hypothesis test you would use (Z Test, T Test 1 Proportion).
4. List either the p-value and alpha OR the critical value and test statistic.
5. Determine whether or not to reject the null hypothesis.
6. Using the initial study, should the school district continue to fund the program or possibly extend the program to a larger number of students? Explain why or why not.