1. Use the following information to carry out a one sample t test (5 points):

You are on the police force in a small town. During an election year, a candidate for mayor claims that fewer police are needed because the average police officer makes only 4 arrests per year. Based on your own experience, you think this number is inaccurate but you are not sure whether the true mean number of arrests should be greater or lesser. So you conduct a small research project. You ask 12 officers how many arrests they made in the past year. The average for this sample of 12 officers is 6.3, with a standard deviation of 1.5. Using this information, test the null hypothesis that the population mean for the number of arrest is equal to 4 against your alternative hypothesis that the number of arrests is DIFFERENT than four. Set your alpha level to .01. (NOTE: we use a t-test here because we have a small sample; n < 50.) Be sure to write out all 5 hypothesis testing steps clearly.