Can you help me make sure that this is correct?

Q1. Hypothesis Testing with a Z test (10 points total)

A research institute examined the number of mobile devices (smart phones and tablets) in American households and reported a mean () of 4 devices per household and a standard deviation () of 2 devices. But I wonder if the statistics in my city, Tucson, would be different from the national average. Specifically, I have a hunch that household in Tucson might have more mobile devices compared to the national average.

To test this idea, I randomly picked 16 friends of mine living in Tucson and asked them how many smart phones and tablets arein their households. The data set is shown below. (The same data are also provided in an Excel file if you choose to use Excel for your calculations.)

I would like to perform a Z test to see if the numbers of mobile devices in Tucson households (represented by the sample of 16 households) are significantly higher than the numbers of mobile devices in the national households. The significance level for my Z test was set at = .05. The hypotheses should be directional because I am predicting a specific direction of difference, and the test should be one-tailed.

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

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

The dependent variable in the study is the number of devices in the household.

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)

	Written	Symbolic Symbol bank for copy & pasting: =<>m
Null	The number of mobile devices in Chandler are not significantly different from the general households nationwide.	H0:devices = national
Alternative	The number of mobile devices in Chandler are significantly different from the national number of devices in households nationwide.	H1:devices national

c. Calculate the sample mean. Round the result to the hundredth (2^nd place to the right of the decimal).(1 point total: .5 if the process is correct but the result was calculated incorrectly)

6+3+4+7+6+4+2+3+5+2+7+2+7+4+3+6=71 M = X/N

71/16 Sample Mean= 4.4375= 4.44

d. Calculate standard error using the population standard deviation given in the research scenario (SE, which is the standard deviation of the sampling distribution) Round the result to the hundredth (2^nd place to the right of the decimal).(1 point total: deduct .5 if the process is correct but the result was calculated incorrectly)

=4, =2, M=4.44 N=16 SE =s/N 2/16= 2/4= 0.5

e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) Round the result to the hundredth (2^nd place to the right of the decimal).(1 point total: deduct .5 if the process is correct but the result was calculated incorrectly)

Z = (M-m)/SE Z= (4.44-4)/0.5 =0.88

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

a = .05 and this is a one-directional test. we look to the Z table to see what the z value is when there is 5% in the tail. The closest you get to 5% is 5.05% and 4.95%which have z values of 1.64 and 1.65. Averaging these two z values. we get the z value for 5% which is 1.645.

g. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test.

- Is the Z statistic more extreme than the critical Z? (.5 point)

- Do you "reject" or "fail to reject" the null hypothesis? (.5 point)

Since the Z statistic = 0.88 it is not more extreme then the critical Z (1.645) thus we fail to reject the null hypothesis.

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

We fail to reject the null hypothesis because the number of mobile devices in Tucson are less than the devices compared to the national average.

i. Calculate the standardized effect size (1 point total: deduct .5 if the process is correct but the result was calculated incorrectly)

d = (M-m)/s d= (4.44-4)/2 = 0.22