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1.1 A college professor randomly selects 25 freshman to study the mathematical background of the incoming freshman class. The average SAT score of these 25 students is 565 and the standard deviation is estimated to be 40. Using the information, can the professor theft the null hypothesis that the average test score is 550 or less? Use a 5% level of significance 1.2 suppose the college professor in question 1.1 wants to know whether the mathematical aptitude of freshman has improved over the past year. He randomly draws the 25 SAT Mathematics scores from last year's freshman class and obtains a sample mean of 560 and a sample standard deviation of 35. Compare the results from last year with the results from this year. Do the data offer enough evidence for rejecting the null hypothesis that there is no improvement? Use a 5% level of significance
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