: Inference for Two Independent Samples 1. Due to the gender wage gap, a researcher believes that female professors earn less than their male counterparts. To examine this, the researcher uses information available for 52 tenure-track professors in a small college (Weisberg, 1985). The results of the analysis are presented below. Group Statistics Sid. Emo Sex (coded 1 for female) Male Academic year salary in dollars N Mean 38 24696.79 14 21357.14 Sid Deviation 5646.409 6151 873 Mean 915 968 1644.157 Female Independent Samples Tell Test Lone Test for Equality of Variances Mest for Equality of Man F Sig Mean Difference 1 d Sig tal 071 Std Emor Diference 1807.716 95% confiance intonar of me Diference LON Upper -291251 6970.550 Academic year salay in dollars 000 985 1907 50 339.547 Equal variances assumed Equal variances not assumed 1774 21.591 090 3339.547 188207 -567854 7247141 Normal 0-0 Plot of Academic year salary in dollars 10000 . 2004 Expected Normal Value 100 30 15.00 15.00 5004 15.00 5.00 100 Observed Value a) Determine the probability that the salary for women is within $5000 of that for men. b) Determine the probability that the salary for men is more than $2000 more than the salary for women. c) Construct a 99% confidence interval for the difference in the population mean salary for men and women. 2 ECON2008: STATISTICAL METHODS I : PROBLEM SETS AY: 2021-2022 d) Use the confidence interval in c) to determine whether there is a difference in salaries for men and women. e) Conduct the relevant hypothesis test and respond to the researcher. 1) Based on the necessary assumptions, was the inferential method you used appropriate. Give reasons for your answer : Inference for Two Independent Samples 1. Due to the gender wage gap, a researcher believes that female professors earn less than their male counterparts. To examine this, the researcher uses information available for 52 tenure-track professors in a small college (Weisberg, 1985). The results of the analysis are presented below. Group Statistics Sid. Emo Sex (coded 1 for female) Male Academic year salary in dollars N Mean 38 24696.79 14 21357.14 Sid Deviation 5646.409 6151 873 Mean 915 968 1644.157 Female Independent Samples Tell Test Lone Test for Equality of Variances Mest for Equality of Man F Sig Mean Difference 1 d Sig tal 071 Std Emor Diference 1807.716 95% confiance intonar of me Diference LON Upper -291251 6970.550 Academic year salay in dollars 000 985 1907 50 339.547 Equal variances assumed Equal variances not assumed 1774 21.591 090 3339.547 188207 -567854 7247141 Normal 0-0 Plot of Academic year salary in dollars 10000 . 2004 Expected Normal Value 100 30 15.00 15.00 5004 15.00 5.00 100 Observed Value a) Determine the probability that the salary for women is within $5000 of that for men. b) Determine the probability that the salary for men is more than $2000 more than the salary for women. c) Construct a 99% confidence interval for the difference in the population mean salary for men and women. 2 ECON2008: STATISTICAL METHODS I : PROBLEM SETS AY: 2021-2022 d) Use the confidence interval in c) to determine whether there is a difference in salaries for men and women. e) Conduct the relevant hypothesis test and respond to the researcher. 1) Based on the necessary assumptions, was the inferential method you used appropriate. Give reasons for your