1) The dotplot below shows the number of points scored by NBA player Tim Duncan in his 81 regular season games during the 2002-2003 season. Is the standard deviation closest to 2, 7, or 15? Explain. 09000 100 8: ..... on- 10 15 20 30 35 40 Points 2) The following data values are the points scored in each game by the 2008 Chicago Bears. 29 17 24 24 34 20 48 27 14 3 27 14 23 27 20 24 a) Calculate the mean and standard deviation of the data set. b) 3 is an outlier. What do you think would happen if you removed this low outlier from the data set? Recalculate the mean and standard deviation without the outlier to test your theory and observe what actually happened. 3) Brady Anderson was a member of the Baltimore Orioles for most of his career and was known for his tremendous performance in 1996 when he hit 50 home runs. Here are his run totals for each of his 15 seasons: 1 4 3 2 21 13 12 16 50 18 18 24 19 8 1 a) Calculate the mean and standard deviation of the data set. b) 50 is an outlier. What do you think would happen if you removed this high outlier from the data set? Recalculate the mean and standard deviation without the outlier to test your theory and observe what actually happened.4) During the 2014-2015 season, goalie Jimmy Howard of the Detroit Red Wings had the following save percentages for the first 10 games: 94.1 88.5 94.9 95.8 94.4 88.5 92.6 93.3 90.5 93.5 a) Find the mean and standard deviation of the data. Round to the nearest tenth, if necessary. (You do not need to show work.) b) If Howard saved 94.5%% of the goals in the next game, what would happen to the mean and the standard deviation? Explain. c) If Howard saved 85.9% of the goals in the next game, what would happen to the mean and standard deviation? Explain. 5) During the first 10 games of the 2014-2015 season, the Nashville Predators' goalie, Pekka Rinne, saved on average 93.1% of goals with a standard deviation of 4.0%. a) Interpret the standard deviation in this context. b) The following data values are Pekka Rinne's save percentages in the first 10 games of the 2014-2015 season. Make a dotplot of the data. 90.0 94.4 92.9 100.0 91.7 93.8 88.5 96.3 86.7 96.3 c) What percent of the data is within one standard deviation of the mean? Show work! d) Imagine we subtracted 2% from Rinne's save percentages for each of the 10 games. How would this affect the mean and the standard deviation? Explain.6) In problems 4 and 5 you were given information about the performances of Jimmy Howard and Pekka Rinne. a) Which goalie is more consistent? Explain. b) Suppose we wanted to test if Howard is more consistent than Rinne. State the hypotheses we are interested in testing. c) Find the actual value of the test statistic. d) Describe how to simulate the distribution of the test statistic using notecards. e) Here are the results of 100 trials of the simulation, assuming that both players are equally consistent. Based on the simulation, estimate the p-value. THITITT Simulated Difference in Standard Deviations f) Interpret the p-value. g) Based on your p-value, make an appropriate conclusion. h) Based on your conclusion, what type of error is it possible you made? Explain