Question

A psychologist examined the number of electronic devices used for communication (computers, tablets, and smartphones) in the home and reported a mean (μ) of 3.2 devices and standard deviation (σ) of 1.8 devices. But I wonder if my circle of friends has a different mean of devices in the home. To test this idea, I randomly picked 16 friends of mine and asked them how many electronic communication devices they have in their home. I would like to perform a Z test to see if the number of devices in the home among my friends is significantly different than the national average. The significance level for my Z test was set at α= .05.

Subject #	# of devices
1	2
2	3
3	4
4	3
5	5
6	3
7	4
8	3
9	2
10	2
11	4
12	4
13	3
14	5
15	4
16	7

1. What is the dependent variable in this study? (1 point)

2. What should be my null and alternative hypotheses? State each hypothesis using both words and statistical notation.

Hint: I am interested in any difference from the national average so the hypotheses would be non-directional.(4 points total. 2 for the 2 notations, 2 for the 2 written hypotheses)

3. Calculate the sample mean. (2 points total, 1 for process/work, 1 for result)

4. Calculate standard error (SE, which is the standard deviation of the sampling distribution) (2 points total, 1 for process/work, 1 for result)

5. 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)

6. 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)

7. Determine the critical value for Z(1 point)

8. Compare obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly state “reject” or “fail to reject” the null hypothesis (2 points: 1 for comparing the correct numbers and saying which one is more “extreme”; 1 for making the decision about null hypothesis.)

1. Write a 1-2 sentence conclusion interpreting the results (you can simply restate the accepted hypothesis or explain it in another way) (1 point)

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

10. If the test was done with α level of .10, using the same non-directional hypotheses, what would be the critical Z value from the Z table? What would be the result of the hypothesis test (in terms of rejecting or failing to reject the null hypothesis)? (2 points: 1 for critical Z, 1 for test result)

11. Compare the hypothesis tests result when α = .05 and when α = .10. Were the results the same? Why or why not? (1 point)

Answer 1