5. A professor at a community college claims that a college algebra student can increase his or her score on an exam if the person is provided with a pre-test the week before the exam. To test her theory, she selected 16 college algebra students at random and gave these students a pre-test the week before an exam. She also selected a random sample of 12 students who were given the same exam but did not have access to a pre-test. The first group had a mean score of 79.4 with standard deviation 8.8. The second group had a mean score of 71.2 with standard deviation 7.9. Test to see if the population mean score of students who get a pre-test is different from the population mean score of those who do not. Use a 5% significance level. a) State the null and alternate hypotheses. b) Would you use the normal distribution (z) or Student's (1) distribution? Why? c) State the test statistic and p-value of your test. Round your answers to four decimal places. d) Explain your decision to reject or fail to reject the null hypothesis in terms of p and a. Interpret your conclusion in the context of this problem.