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# Statistics assignment 6

STAT 212 – Assignment 6

Data Description and Background

In this assignment we will continue to work with the data pertaining to the Carllson brother’s competition over who is the better Strategema player. For the 100 games they played, besides indicating who was the winner/loser, the duration of the games (in seconds) was also provided. This is variable we will be focusing on for this assignment. Answer or perform the following:

1) For the games Sven won, provide an estimate of the mean time it takes Sven to beat his brother. Similarly, for the games Jens won, provide an estimate of the mean time it takes for Jens to beat his brother. – 1 pt

2) Construct two QQ-plots, one displaying the durations of the games Sven won, and another displaying the durations of the games Jens won. (Note: When making the QQ-plots, treat them as two separate datasets.) – 2 pt

3) Using the QQ-Plots in part 2, is it plausible to conclude that the distribution of duration for the games Sven won follows a Normal Distribution? Analogously, is it plausible to conclude that the distribution of duration for the games Jens won follows a Normal Distribution? – 1 pts

4) Let S denote the mean duration of games Sven wins. Similarly, let J denote the mean duration of the games Jens wins. Construct a two-sided 70% confidence interval for the quantity, = S – J. Do not assume the standard deviation of the durations are the same for both brother’s wins. – 2 pt

5) Sven won 56 out of the 100 games (see assignment 5 solutions). Based on the prior fact, one might conclude Sven is the better Strategema player. After analyzing the game durations in the previous problems, would you agree with the assessment that Sven is the better player? – 1 pts

 Game_Number Winner Loser Duration 1 Jens Sven 41 2 Sven Jens 76 3 Sven Jens 156 4 Sven Jens 151 5 Sven Jens 105 6 Jens Sven 71 7 Sven Jens 123 8 Sven Jens 111 9 Sven Jens 164 10 Sven Jens 116 11 Jens Sven 46 12 Sven Jens 88 13 Jens Sven 59 14 Jens Sven 47 15 Jens Sven 57 16 Sven Jens 108 17 Sven Jens 78 18 Sven Jens 94 19 Jens Sven 86 20 Jens Sven 60 21 Jens Sven 52 22 Jens Sven 64 23 Jens Sven 72 24 Jens Sven 56 25 Jens Sven 30 26 Sven Jens 173 27 Jens Sven 46 28 Jens Sven 80 29 Sven Jens 147 30 Jens Sven 87 31 Jens Sven 71 32 Sven Jens 146 33 Sven Jens 66 34 Jens Sven 62 35 Jens Sven 59 36 Sven Jens 173 37 Jens Sven 73 38 Jens Sven 75 39 Sven Jens 148 40 Jens Sven 73 41 Sven Jens 127 42 Sven Jens 108 43 Jens Sven 32 44 Jens Sven 61 45 Jens Sven 89 46 Jens Sven 34 47 Jens Sven 50 48 Jens Sven 62 49 Sven Jens 128 50 Sven Jens 73 51 Sven Jens 112 52 Sven Jens 125 53 Sven Jens 65 54 Sven Jens 141 55 Sven Jens 104 56 Sven Jens 123 57 Jens Sven 86 58 Jens Sven 49 59 Sven Jens 144 60 Sven Jens 103 61 Jens Sven 81 62 Sven Jens 65 63 Jens Sven 77 64 Jens Sven 64 65 Sven Jens 162 66 Sven Jens 155 67 Sven Jens 67 68 Sven Jens 91 69 Jens Sven 67 70 Sven Jens 137 71 Jens Sven 82 72 Jens Sven 86 73 Sven Jens 102 74 Sven Jens 101 75 Sven Jens 164 76 Jens Sven 31 77 Sven Jens 83 78 Sven Jens 173 79 Sven Jens 125 80 Jens Sven 49 81 Sven Jens 125 82 Sven Jens 115 83 Jens Sven 79 84 Jens Sven 64 85 Sven Jens 177 86 Sven Jens 124 87 Jens Sven 83 88 Sven Jens 162 89 Sven Jens 104 90 Sven Jens 135 91 Sven Jens 179 92 Jens Sven 88 93 Jens Sven 72 94 Sven Jens 66 95 Sven Jens 119 96 Sven Jens 177 97 Jens Sven 73 98 Sven Jens 137 99 Sven Jens 99 100 Sven Jens 159

Last Updated on March 30, 2021

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