4. (Five parts; 18 marks in total) A study was conducted to assess the effect of

Question

4. (Five parts; 18 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 (,- ). 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 Mean Std. Deviation Mean 28 489.8919 28 489.6025 126.35510 23.87887 49.60250 9.37399 Female

Explanation / Answer

a)

From tables 1 and 2, referring to the p-value 0.991 which is quite a large value, we accept the null hypothesis and conclude that there is no significant difference in average math SAT scores between males and females.

From table 4, referring to the p-value 0 which means we reject the null hypothesis and conclude that there is significant differences among the average math SAT scores for the 4 groups.

From table 5, referring to the p-value 0.991 which means we accept the null hypothesis and conclude that there is no significant differences between the average math SAT scores of males and females(ignoring high school type).

From table 6, referring to the p-value 0.00 which means we reject the null hypothesis and conclude that there is significant differences between the average math SAT scores of public and private schools(ignoring gender).

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