12. A Precise Quarterback The number of passes completed and the total number of passing yards recorded for the Los Angeles Chargers quarterback, Philip Rivers for each of the 15 regular season games that he played in the fall of 201713 were used to calculate the average number of yards per pass for each game.

a. Calculate the mean and standard deviation of the number of completions and the number of yards per pass.

b. Find a 95% confidence interval estimate for the variance of the number of completions. Why would you prefer a small variability in the number of completed passes?

c. Find a 95% confidence interval for 2  , the variance of the yards per pass. Use these results to find a 95%
confidence interval for  , the standard deviation of the yards per pass.

d. Test whether the standard deviation of the yards per pass for this quarterback differs from  54 with a 5.05.

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Yards per Yards per Week Completions Pass Week Completions Pass 12 3 45678 222222 28 13.8 9 13.2 11 20 11.4 12 18 17.7 13 31 11.1 14 27 16.1 15 20 12.6 16 21 17.2 17 2222222 17 12.5 15 12.2 25 10.7 21 12.3 15.8 20 11.8 31 10.7 8.7