Statistical Analysis of Gender Differences in Employment Competency Scores

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1Statistical Analysis of Gender Differences in Employment Competency ScoresQuestion 1Data on 200 men and 200 women were obtained from representative random samples of youngmen and women who applied for employment at a large U.S. corporation in 2012.During theapplication process, each applicant was given a Reading comprehension test, a Mathematicsreasoning test, along with several other exercises which were used to generate an overallcompetency score. Areviewcommittee used these scores along with other factors whenconsidering the applicants for employment. All of the applicants were between the ages of 18 and25.The data file is posted asexam1_employment_competency.csvattached.You may read thefile into JMP, or any other software package of your choice, to answer the following questions. Thedata 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 overallassessment of employment competency obtained from a complexcombination of the scores on the reading and mathematics tests and the scores on severalother 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 youcorrectly entered the data into JMP, the first five lines of the data file are shown below.SubjectGenderReadingMathematicsCompetency11112060.421132184.731111244.541644.0516711.8Use these data to answer the following questions.(a)Do these data provide evidence thatwomenperform better atReadingtasks thanmen? Set upappropriate null and alternate hypotheses to answer this question, report a formula and avalue foryour test statistic, and clearly indicate how you reached your conclusion. Use anα= .05 significancelevel, and state your conclusion in the context of this study.Here we want to test thatwomenperform better atReadingtasks thanmenthus the null andalternative hypotheses are,𝐻0:μௐ−μெ≤0𝑎𝑛𝑑𝐻𝑎:μௐ−μெ>0It can be seen that, this is a two sample test for mean, the test is one tailed (right tailed). Sohere the t-test for two sample mean would be the most appropriate test.

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2The test statistic can be calculated using the formula,T =௫̅1−௫̅మඨೄ1మ𝑛1ାೄమమ𝑛మUsing Minitab the obtained output is given below,Two-Sample T-Test and CI: Reading, GenderTwo-sampleTforReadingGenderNMeanStDevSEMean120010.633.470.2522009.033.830.27Difference=μ(1)-μ(2)Estimatefordifference:1.60095%lowerboundfordifference:0.997T-Testofdifference=0(vs>):T-Value = 4.38P-Value = 0.000DF = 394The above output indicates that the test statistic value is 4.38 with associated p-value 0.000. Asthe p-value is smaller than the significance level of 0.05 thus we are rejecting the nullhypothesis indicating that, the data gives enough evidence thatwomenperform better atReadingtasks thanmen.(b)Constructa99percentconfidenceintervalforthedifferencebetweenmeanMathematicsperformance forwomenand meanMathematicsperformance formen.Interpret your confidenceinterval in the context of theemployment competence tests.Using anα= .01 significance level,would you conclude that there is a significant differencebetween meanMathematicsperformanceforwomenand meanMathematicsperformance formen? Justify you answer.The obtained MINITAB output is given below,Two-Sample T-Test and CI: Mathematics, GenderTwo-sampleTforMathematicsGenderNMeanStDevSEMean120012.005.910.42220010.996.180.44Difference=μ(1)-μ(2)Estimatefordifference:1.00599%CIfordifference:(-0.560,2.570)T-Testofdifference=0(vs≠):T-Value = 1.66P-Value = 0.097DF = 397

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3The output gives us the 99% confidence intervalfor the difference between mean Mathematicsperformance for women and mean Mathematics performance for menas(-0.560, 2.570).The interval indicates that, we are 95% confident that the populationdifference between meanMathematics performance for women and mean Mathematics performance for menfalls in theinterval(-0.560, 2.570).As the confidence interval contains the value 0 so at 0.01 significance level we can concludethat there is no significant difference between the meanMathematics performancebetween thetwo genders.(c)Do these data provide evidence thatmenperform better onMathematicsrelated tasks than theyperform onReadingrelated tasks?Use a significance level ofα= .05, and justify your answer.Here we want to test thatmen perform better on Mathematics related tasks than they performon Reading related tasksthus the null and alternative hypotheses are(here the sample isdependent, d = mathematics score performance–reading performance),𝐻0:μ𝑑≤0𝑎𝑛𝑑𝐻𝑎:μ𝑑>0It can be seen that, this is adependentsample test for mean, the test is one tailed (right tailed).So here thepairedt-test would be the most appropriate test.The test statistic can be calculated using the formula,T =௫̅𝑑ೄ𝑑√𝑛Using Minitab the obtained output is given below,Paired T-Test and CI: Mathematics, ReadingPairedTforMathematics-ReadingNMeanStDevSEMeanMathematics20010.9956.1820.437Reading2009.0303.8300.271Difference2001.9654.6410.32895%lowerboundformeandifference: 1.423T-Testofmeandifference=0(vs>0): T-Value = 5.99P-Value = 0.000The above output indicates that the test statistic value is5.99with associated p-value 0.000. Asthe p-value is smaller than the significance level of 0.05 thus we are rejecting the nullhypothesis indicating that, the data gives enough evidencethatmen perform better onMathematics related tasks than they perform on Reading related tasks.

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