Researchers found that grade 8 students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, these researchers selected a standardized mathematics achievement test that produced a normal distribution of scores with a mean of = 100 and a standard deviation ofs = 15. Next, the researchers modified the test by inserting a set of very easy problems among the standardized questions and gave the modified test to a sample of n = 40 students. If the average test score for the sample is M = 105, is this result sufficient to conclude that inserting the easy questions improves student performance? Use = .01. Show all the steps of hypothesis testing.