# Statistics questions:

**Question description**

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.

**Directions**

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 this initial study, should the school district continue to fund the program and/or possibly extend the program to a larger number of students? Explain why or why not. |

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