"An Analysis of the Study Time-Grade Association," published in Radical Pedagogy in 2002, reported that scores on a standardized test for cognitive ability for a group of over 100 students in an Introductory Psychology course had mean 22.6 and standard deviation 5.0. For the 7 students who reported studying the most for the course (9 hours or more per week), the mean was 17.6 and standard deviation was 2.8.
a. Calculate the standardized sample mean, using 5 as the standard deviation.
b. Recall that values of z between 0 and 1 are quite common; values closer to 1 than to 2 may be considered not unusual; values close to 2 are borderline, values close to 3 are unusually large, and values considerably greater than 3 are extremely large. Based on the relative size of your z statistic, explain why there is evidence that mean cognitive ability score for those 7 students was significantly lower than for the population of students in the course.
c. Can we conclude that studying diminishes a student's cognitive ability? Explain.