Question

According to my records, the population of all past assignment grades have a mean (μ) of 42 points and standard deviation (σ) of 5 points. The new class of 81 students had a mean grade (M) of 43 points. I conducted a hypothesis test to see if the new class would perform significantly differently from the population of past students. I was interested in any type of “difference,” whether it’s an improvement or a decrease in assignment grade. The significance level for my Z test was set at α = .05.

i) Calculate the raw effect size and the standardized effect size for this test. (4 points total: 2 points for each measure: 1 for process/work, 1 for result)

j) Since the average assignment grade for the new section is numerically higher than the average assignment grade from the existing pool of past students, I could also set up a directional research hypothesis. What would the written hypotheses and the notations be? (4 points total: 1 for each notation, 1 for each written hypotheses)

k) Using the same alpha level at α = .05, determine the critical Z value

l) In this statistical test, how high does the mean assignment grade from the new class have to be, at least, to be considered “significantly” higher than the pool of past grades? Hint: In other words, when does the calculated Z equal the critical Z? What needs to be the sample mean for that to happen? (2 points total: 1 for answer, 1 for formula/work)

Answer 1