Montarello and Martens (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ = 100 and a standard deviation of s = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students.
If the average test score for the sample is µ = 104, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with a = .01.