Answer Key on z-Tests
Instructions: Solve the following problem by conducting a z-test.
To test the idea that including people in the decision making process makes people more satisfied with the outcome, a researcher conducts the following study. One group of sixty students (participation group) are asked for their input on the type of course projects they think would be the most useful before a decision is finally made. Another group of sixty students (non-participation group) is simply told what the final project is going to be. Both groups are asked to rate how satisfied they are with the course project using a ten point scale when "1" represents very dissatisfied and "10" represents very satisfied. The average satisfaction rating for the students in the participation group was 7.0. The average satisfaction rating for the students in the non-participation group was 5.25. The standard error of the difference is 1.0.
State the null and research hypothesis.
Ho: Xp £ Xnp
Ha: Xp > Xnp
Calculate a z-score for the difference between these two groups.
z = (7 - 5.25 - 0)/1.0 = 1.75
Is there a significant difference between these two groups scores?
Yes
What does your finding mean?
Participation improves satisfaction with decisions.
Instructions: Conduct a z-test for the following problem.
A professor thinks that touching students when handing back an exam will have an impact on how satisfied they are with the results of their tests. So, the professor decides to do an experiment to test this hypothesis. To accomplish this, the professor randomly divides the class into two groups (touch group vs. no touch group). When handing back the exams, the professor nonchalantly touches each one of the students in the touch group and avoids touching all of the students in the no touch group. Next, the teacher asks all of students to rate how satisfied they are with their performance on the exam using a "1" to "10" scale (where "1" represents not very satisfied and "10" represents very satisfied).
The mean of the students in the touch group is 6.00.
The mean of the students in the no touch group is 4.25
s diff = 1.00
First, write out the null and research hypothesis for this experiment.
Ho: Xt = Xnt
Ha: Xt ¹ Xnt
Now, determine whether or not the groups are different from each other at p < .05 and p < .01 significance levels.
z = (6.0 - 4.25 -0)/ 1.0 = 1.75
Accept Null Hypothesis
No significant difference between groups.