Q1. Hypothesis testing using a Z test (26 points) For my PSY230, I implemented a
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Q1. Hypothesis testing using a Z test (26 points) For my PSY230, I implemented a new guided practice so that students are guided through a problem set similar to those in the assignment before completing the assignment. The goal is to provide an additional opportunity for practicing the statistical skills and to enhance the students’ performance on the weekly assignments. In order to see if this new element was helpful to students, I compared the average assignment grade from the new section to the existing pool of past assignment grades from all my previous sections of PSY230 prior to implementing the new guided practice. In other words, the new section with the guided practice is my sample, which will be compared to the population of all past students. According to my records, the population of all past assignment grades have a mean () of 38 points and standard deviation () of 7 points. The new class of 64 students had a mean grade (M) of 40 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 = .05.
a) Identify the dependent variable for this study (1 points)
b) State your null hypothesis and alternative hypothesis using both words and statistical notation
c) Calculate standard error (SE, which is the standard deviation of the sampling distribution) (2 points total: 1 for process/work, 1 for result)
d) Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) (2 points total: 1 for process/work, 1 for result)
e) Specify whether the hypothesis test should be a two-tailed or a one-tailed test, and explain the rationale for the choice. (2 points total: 1 for chosen test, 1 for rationale)
f) Determine the critical value for Z
g) Comparison of obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly states “reject” or “fail to reject” the null hypothesis
h) Write a 1-2 sentences to conclude the results (you can simply restate the accepted hypothesis or explain it in another way) (1 point)
i) Calculate the raw effect size and the standardized effect size for this test.
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?
k) Using the same alpha level at = .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)
Explanation / Answer
a) Dependent Variable: Assigment Grades
b) H1: The new guided practice not successful
i.e. The grade points are not higher when new guided practices implimented compare to old system
H1: The new guided practice successful
i.e. The grade points are higher when new guided practices implimented compare to old system
c) SE = SD/Sqrt(n) = 7 / sqrt(64) = 0.875
d) Z = (Sample mean - Population mean)/SE
= (40-38)/0.875 = 2.28571
e) It is right tail test i.e. one tailed test
f) The critical vlaue of Z is 1.645
Here Z value > Z critical value, so we reject H0
h) Thus we conclude that the new guided practice successful
i.e. The grade points are higher when new guided practices implimented compare to old system
i) Effect Size = Difference of means / SD = 40-38 / 7 = 2/7 = 0.2857 medium effect
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