Author:
Christine Farr

Question 1Data on 200 men and 200 women were obtained from representative random samples of young men and women who applied for employment at a large U.S. corporation in 2012. During the application process, each applicant was given a Reading comprehension test, a Mathematics reasoning test, along with several other exercises which were used to generate an overall competency score. A review committee used these scores along with other factors when considering the applicants for employment. All of the applicants were between the ages of 18 and 25. The data file is posted as exam1_employment_competency.csv attached. You may read the file into JMP, or any other software package of your choice, to answer the following questions. The data file contains information on the following five variables• Subject: subject identification number• Gender: coded 1 for females and 2 for males.• Reading: score on a reading comprehension test• Mathematics: score on a mathematics reasoning test• Competency: an overall assessment of employment competency obtained from a complex combination of the scores on the reading and mathematics tests and the scores on several other tests of reasoning, communication, organization, and social skills.There is one line of data for each of the 400 individuals in the sample. To help you check if you correctly entered the data into JMP, the first five lines of the data file are shown below.Subject Gender Reading Mathematics Competency1 1 11 20 60.42 1 13 21 84.73 1 11 12 44.54 1 6 4 4.05 1 6 7 11.8Use these data to answer the following questions.(a) Do these data provide evidence that women perform better at Reading tasks than men? Set up appropriate null and alternate hypotheses to answer this question, report a formula and a value for your test statistic, and clearly indicate how you reached your conclusion. Use an α = .05 significance level, and state your conclusion in the context of this study.(b) Construct a 99 percent confidence interval for the difference between mean Mathematics performance for women and mean Mathematics performance for men. Interpret your confidence interval in the context of the employment competence tests. Using an α = .01 significance level, would you conclude that there is a significant difference between mean Mathematics performance for women and mean Mathematics performance for men? Justify you answer.(c) Do these data provide evidence that men perform better on Mathematics related tasks than they perform on Reading related tasks? Use a significance level of α = .05, and justify your answer.(d) For each of parts 1(a)–1(c) of this question, state the conditions that must be checked to validate the use of the statistical methods that you employed. What evidence can you provide regarding whether these conditions are satisfied?

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