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Cell Phone Bills

Cell Phone Bills. Rustie Wayne Madisen Christenson Skyler Young Kathleen Harris Markell Beazer. How much are you spending?.

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Cell Phone Bills

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  1. Cell Phone Bills Rustie Wayne Madisen Christenson Skyler Young Kathleen Harris Markell Beazer

  2. How much are you spending? • For our research project, we set out to try and probe the cost of cell phone bills and find what the average cell phone bill costs consumer America, on an individual level. • J.D Power associates http://images.dealer.com/jdpa/pdf/2011146-whs2.pdf

  3. Methods and Protocols • Obtain a Sample • Hypothesis test • Estimation of the mean via confidence intervals • Estimation of population proportion • Approximation of the Population Standard Deviations • Visual Data

  4. Obtain a Sample We knew that we needed more than 30 people, so we ended up asking 80 different people what they had to pay for their individual cell phone bills.

  5. Hypothesis Test • H0 : µ=71 • H1: µ≠71 • Two-tailed test • T-Distribution (population Stdrd. Dev. Unknown) • Test Statistic (1.906) Critical Value (1.990) • P Value of .060

  6. Population Mean • Used the formula: xbar ± t (α/2) (s/√n) = • Sum of all individual monthly plans collected is 6,099. Number of plans is 80 xbar = 6,099/80 = 76.24 α=.05 α/2=.025 df=79 , so... = 1.990 • Used t-distribution

  7. Population Mean • Using the confidence interval of 95%. We are 95% confident the population mean lies between: • 76.24 - ((1.990)(24.58/√80)) = $70.77 and • 76.24 + ((1.990)(24.58/√80)) = $81.71 ($70.77 , $81.71)

  8. Population Proportion • Obtain a point estimate • Construct and interpret a confidence interval

  9. Population Proportion

  10. Population Proportion • We came up with the upper bound which was .683, and our lower bound which was .467. So we are 95% confident that the proportion of people who pay more than seventy dollars on their cell phone bills is between .467 and .683.

  11. Approximation of the Population Standard Deviation 1. compute the sample variance which was $604.3352848 2. determine the critical values with a 95% confidence interval and a=.05. We know that n=80 so we are now able to plug in this information to the equation. To compute for the lower bound we used the following equation: [(n-1)s^2/x`2~(a/2)] [(79)604.3352848/105.473] = 452.6512709 (then take the square root of the answer), square root of 452.6512709 = $21.28 3. Then we computed the upper bound with the following equation: [(n-1)s^2/x`2~(1-a/2)] We then plugged in our data into this equation as follows: [(79)604.3352848/56.309] = 847.8660161 (then take the square root of the answer), square root of 847.8660161 = $29.12 We are 95% confident that the populations standard deviation of the price of a cell phone bill in America is between $21.28 and $29.12.

  12. Histogram As this graph indicates, the majority of cell phone users pay moderate or average prices for their monthly cell phone services. Only a minority will pay above average prices.

  13. Box and Whisker Diagram The Box and Whisker diagram presents the same information, in a simpler format. The whisker on the right tail shows the minority of cell phone users paying above average prices.

  14. Conclusion As you can see from the methods we have illustrated , Statistics shows that approaching a problem from many angles proves to be beneficial. We tried to pick the most relevant methods to really scrutinize our question and make the best decisions about our data set. From our results it appears that things, as a whole, have shifted slightly today compared to experiments in the past. For example, the approximation of the proportion of the population that pays over $70 yielded a result of between 47% and 68%, with 95% confidence. This would indicate that the majority of people are paying more than $70. From the approximation of the mean, you can see that we are 95% confident that the true average of all cell phone bills lies between $70.77 and $81.77. This would only leave a slight window of 33 cents for the true mean to be $71, as was indicated back in 2011, from JD Power and Associates. Finally, the Hypothesis Test was very enlightening. Although we did not reject the Null Hypothesis, it is worth noting that our test statistic was .086 away from tipping into the Critical Region, thus allowing us to reject the Null and make the claim that there is sufficient evidence to conclude that cell phone bills are more expensive in 2013.

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