In the past, the mean final exam score in a particular course has been 6 6 % . This year, the professor of the course believes that her students will do better than this and, in fact, a random sample of 5 0 of her students obtain a mean final exam score of 7 0 . 5 % with a standard deviation of 8 . 8 . a ) Is the professor correct about her students this year performing significantly better on the final exam than they have in previous years, using ? . 0 5 ( 8 points ) b ) If , in fact, the population of all of the professor's students this year would obtain a mean final exam score of 6 8 % , what is the probability that she would incorrectly fail to reject the null hypothesis based on the data she collected from her sample of 5 0 students in part ' ? ' ? ( 1 0 points )