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Comparison of the mean Verizon and AT&T Cellphone: Hypothesis Test and a Confidence Interval

How does the cellphone service compare between different cities?
a. At the .05 level of significance, is there evidence of a difference in the mean cell phone service rating between Verizon and AT&T?
b. What assumption is necessary about the population distribution in order to perform this test?
c. Use a graphical method to evaluate the validity of the assumption in (a).
d. Construct and interpret a 95% confidence interval estimate of the difference in the mean cellphone service rating between Verizon and AT&T.

City Verizon AT&T T-Mobile Sprint
Atlanta 79 70 71 66
Boston 76 69 74 64
Chicago 77 71 70 65
Dallas-Ft. Worth 78 75 74 65
Denver 77 71 71 67
Detroit 79 73 77 65
Jacksonville 81 73 75 64
Las Vegas 81 72 74 68
Los Angeles 78 66 68 65
Miami 80 68 73 69
Minneapolis-St. Paul 77 68 75 66
Philadelphia 78 77 71 66
Phoenix 81 68 76 66
San Antonio 80 75 75 65
San Diego 79 69 72 68
San Francisco 75 66 73 69
Seattle 77 68 74 67
St. Louis 79 74 74 66
Washington 76 72 71 68

Solution Preview

In the accompanying Excel spread sheet I have calculated the Verizon score - the AT&T score for each city and placed that difference into column F. Then I had Excel calculate the summary statistics for column F and I will use the summary stats for column F to answer parts a. and d.
a. At the .05 level of significance, is there evidence of a difference in the mean cell phone service rating between Verizon and AT&T? Yes, there IS evidence of a significant difference in the mean cell phone service ratings between Verizon and AT&T. See the hypothesis test below.
A Paired Differences T-Test will answer this question (also known ...

Solution Summary

An investigation of the difference (if any) between the cellphone service ratings of Verizon and AT&T in a matched-pairs t-test as well as a matched pairs confidence interval

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