Q1. Hypothesis Testing with a Z test (10 points total) A research institute examined the number of mobile devices (smart

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Q1 Hypothesis Testing With A Z Test 10 Points Total A Research Institute Examined The Number Of Mobile Devices Smart 1 (79.54 KiB) Viewed 157 times

Q1 Hypothesis Testing With A Z Test 10 Points Total A Research Institute Examined The Number Of Mobile Devices Smart 2 (75.3 KiB) Viewed 157 times

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 (w) of 4 devices per household and a standard deviation (C) of 2 devices. But I wonder if the statistics in my neighborhood, Flagstaff, would be different from the national average. Specifically, I have a hunch that household in Flagstaff might have more mobile devices compared to the national average. To test this idea, I randomly picked 18 friends of mine living in Flagstaff and asked them how many smart phones and tablets are in 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 Flagstaff households (represented by the sample of 18 households) are significantly higher than the numbers of mobile devices in the national households. The significance level for my Z test was set at a = .05. The hypotheses should be directional because I am predicting a specific direction of difference, and the test should be one-tailed. Househol d Number of devices 1 6 2 3 3 3 4 5 6 1 6 4 7 2 8 3 9 5 10 2 11 7 2 12 13 7

14 4 15 3 16 6 17 4 18 5 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) c. Calculate the sample mean. Round the result to the hundredth (2nd place to the right of the decimal). (1 point total: .5 if the process is correct but the result was calculated incorrectly) d. Calculate standard error using the population standard deviation o given in the research scenario (SE, which is the standard deviation of the sampling distribution) Round the result to the hundredth (2nd place to the right of the decimal). (i point total: deduct.5 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) Round the result to the hundredth (2nd place to the right of the decimal). (1 point total deduct .5 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 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) 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) i. Calculate the standardized effect size (1 point total: deduct.5 if the process is correct but the result was calculated incorrectly)