A computer information systems professor is interested in studying the amount of time it takes students enrolled in the Introduction to Computers course to write a program in Visual Basic. The professor hires you to analyze the following results (in minutes), stored in VB, from a random sample of nine students:
10 13 9 15 12 13 11 13 12
a. At the 0.05 level of significance, is there evidence that the population mean time is greater than 10 minutes? What will you tell the professor?
b. Suppose that the professor, when checking her results, realizes that the fourth student needed 51 minutes rather than the recorded 15 minutes to write the Visual Basic program. At the 0.05 level of significance, reanalyze the question posed in (a), using the revised data. What will you tell the professor now?
c. The professor is perplexed by these paradoxical results and requests an explanation from you regarding the justification for the difference in your findings in (a) and (b). Discuss.
d. A few days later, the professor calls to tell you that the dilemma is completely resolved. The original number 15 (the fourth data value) was correct, and therefore your findings in (a) are being used in the article she is writing for a computer journal. Now she wants to hire you to compare the results from that group of Introduction to Computers students against those from a sample of 11 computer majors in order to determine whether there is evidence that computer majors can write a Visual Basic program in less time than introductory students. For the computer majors, the sample mean is 8.5 minutes, and the sample standard deviation is 2.0 minutes. At the 0.05 level of significance, completely analyze these data. What will you tell the professor?
e. A few days later, the professor calls again to tell you that a reviewer of her article wants her to include the p-value for the "correct" result in (a). In addition, the professor inquires about an unequal-variances problem, which the reviewer wants her to discuss in her article. In your own words, discuss the concept of p-value and also describe the unequal-variances problem. Then, determine the p-value in (a) and discuss whether the unequal-variances problem had any meaning in the professor's study.