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) Does this problem involve independent or dependent samples? Explain.
(b) State the null and alternate hypotheses.
(c) Would you perform a left-tailed, right-tailed, or two-tailed test? Why?
(d) Would you use a t critical value or a z critical value? Why?
(e) What is the critical value?
(f) Compute the test statistic.
(g) Sketch the normal curve indicating the positions of the critical value, critical region, and test statistic.
(h) Would you reject or fail to reject the null hypothesis?
(i) Interpret your conclusion in the context of this problem.