n 2017, the SAT was scored out of 1600. The average SAT scores among the 925 Texas students who stated their intended major was Mathematics was 1148. The average SAT score among the 1026 Texas students who stated their intended major was History was 1031. Assume the true standard deviation for both populations is 193. (a.) Test the hypothesis at the 1% significance level that future Texas math majors had a higher SAT score on average in 2017 than future Texas history majors. (b.) Find a 98% confidence interval for the difference in their SAT scores (Let μ1 be the mean math major score and μ2 be the mean history major score).

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In 2017, the SAT was scored out of 1600. The average SAT scores among the 925 Texas students who stated their intended major was Mathematics was 1148. The average SAT score among the 1026 Texas students who stated their intended major was History was 1031. Assume the true standard deviation for both populations is 193.

(a.) Test the hypothesis at the 1% significance level that future Texas math majors had a higher SAT score on average in 2017 than future Texas history majors.

(b.) Find a 98% confidence interval for the difference in their SAT scores (Let μ1 be the mean math major score and μ2 be the mean history major score).

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