Question

4. (Four parts; 13 marks in total) A study was conducted to assess the effect of gender on average math SAT scores for students applying to a particular math department. The "effect" of gender (or the gender effect) on average math SAT score is defined as the difference in average math SAT score between males and females (um -up). Assume all the required assumptions are satisfied. a) (2 marks) Referring to the output in Tables 1 and 2 below, is there a gender effect; in other words, is there a difference in average math SAT score between males and females? Refer to the estimated difference and the P-value to answer the question (you don't have to carry out a formal test). Table 1: Descriptive Summaries for males and females. Group Statistics Std. Error gender N Mean Std. Deviation | Mean sat Male 28 489.8919 126.35510 23.87887 Female 28 489.6025 49.60250 9.37399 Table 2: Two-Independent Sample Output for mean SAT score between males and females. Independent Samples Test t-test for Equality of Means Mean Difference 28936 of 54 sat Std. Error Difference 25.65292 Sig. 2-tailed) 991 Equal variances assumed | 011280 Suppose the study was also concerned with the effect of different types of high school (the students attended) on average math SAT score. They considered the type of high school each student attended as either a private high school or a public high school. No student attended both types of high school. fie

Answer 1

a)Male eN 28 FemalecnD 28 . Mean (M MeancF) and its mean diffeaenre o12393 6 Std.frror Mean (M) 23.87887 sld. Error Mean (F) 489.831g489.602 9. 37399 Ad. Eroy Mean tm)std.Fror MeancE) means here is more valability in Male da ta by using 4- test for Fquality of Means, t: 0.011280 ttwotoi J std.fTror Difference = 25.65292 with S4 DF. 0.991. ttable 0.062g accept null hypothesis ie. There is fro m above we difference in avera 9e math sAT SCore between maS and females. tera ttable