Question

Q2. Hypothesis Testing with a Z test (14 points total)

A research institute examined the number of smart phones and tablets connected to the internet in American households and reported a mean (μ) of 5 devices per household and a standard deviation (σ) of 1.5 devices. But I wonder if the statistics in my neighborhood, Chandler, would be different from the national average. To test this idea, I randomly picked 16 friends of mine living in Chandler and asked them how many smart phones and tablets with internet access are in their households. The data set is shown below.

I would like to perform a Z test to see if the number of mobile devices in Chandler households (represented by the sample of 16 households) are significantly different from the number of devices in the national households. The significance level for my Z test was set at α = .05. The hypotheses should be nondirectional because I am not predicting any specific direction of difference, and the test should be two-tailed.

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

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

b. What should be my null and alternative hypotheses? State each hypothesis using both words and statistical symbol notation. (2 points total. 1 for each hypothesis: .5 for written, .5 for notation)

Note: The hypotheses should be non-directional.

c. Calculate the sample mean. (1 point total: .5 if the process is correct but the result was calculated incorrectly)

d. Calculate standard error using the population standard deviation σ given in the research scenario (SE, which is the standard deviation of the sampling distribution) (2 point total: 1 if the process is correct but the result was calculated incorrectly)

e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) (2 point total: 1 if the process is correct but the result was calculated incorrectly)

f. Determine the critical Z value(s). Explain how you find the answer. (1 point: .5 for the Z value, .5 for the rationale)

g. Compare the Z statistic with the appropriate critical Z value (is the Z statistic more extreme than the critical Z?), and then draw a conclusion about the result of the hypothesis test (do you “reject” or “fail to reject” the null hypothesis?) (2 points: 1 for Z statistic comparison; 1 for hypothesis test decision)

h. Write 1-2 sentences to answer the research question (you can use the wording from the hypotheses or explain it in another way) (1 point)

i. Calculate the standardized effect size (2 point total: 1 if the process is correct but the result was calculated incorrectly)

Answer 1