As a researcher, you are curious if income impacts the length of prison sentences for theft. The known average sentence for the general population is = 12.5 months. You have a random sample of 81 people (N = 81) whose income is below the poverty line. The average sentence for this sample of people was xbar = 16.8 months, with a standard deviation of s_x = 5.3. In this case, the critical values for an (alpha) = .05 are +/- 1.99 (6 points).

A) Please calculate and report the confidence interval for these data, including your level of confidence.

B) Based on the confidence interval, would you retain or reject the null hypothesis? Explain your reasoning.

C) Would the p-value be bigger or smaller than alpha?

D) In everyday language, what do these results tell you about the research question? What can we conclude about income and prison sentences?