Pen color 6.3.25 A psychology study (Rutchick, Slepian, and Ferris, 2010) inves- tigated whether using a red pen causes people to assign lower scores than using a blue pen. A group of 128 students in an introductory un- dergraduate psychology class were asked to grade an eighth grader's essay on a scale of 0-100. Some of the student graders were randomly assigned to use a red pen while grading the essay, and the rest were randomly assigned to use a blue pen. The researchers reported that the group using a red pen gave an average score of 76.20, and the SD of the scores was 12.29. For the group using blue pens, the average score was 80.00, and the SD of the scores was 9.36. a. State the null and alternative hypotheses to be tested. b. Without having access to the 128 scores that were assigned to the essays, can you feel comfortable in applying a two-sample t-test using the summary statistics? Explain. c. What additional information is needed to apply a two-sample t-test using the summary statistics? d. Make a reasonable guess for the missing information and con- duct a two-sample t-test. Report the values of the test statistic and p-value. e. Summarize your conclusion from this test. f. Is it legitimate to draw a cause-and-effect conclusion based on these data and your test result? Explain why nor why not