Table 3.4 on page 174 shows the number of points scored and penalty minutes for 24 ice hockey players on the Ottawa Senators NHL team for the 2009€“2010 season. The data are also stored in OttawaSenators. Assume that we consider these players to be a sample of all NHL players.

Table 3.4

(a) Create a dotplot of the distribution of penalty minutes (PenMin) for the original sample of 24 players. Comment on the shape, paying particular attention to skewness and possible outliers.
(b) Find the mean and standard deviation of the penalty minute values for the original sample.
(c) Use StatKey or other technology to construct a bootstrap distribution for the mean penalty minutes for samples of size n = 24 NHL players. Comment on the shape of this distribution, especially compared to the shape of the original sample.
(d) Compute the standard deviation of the bootstrap means using the distribution in part (c). Compare this value to the standard deviation of the penalty minutes in the original sample.
(e) Construct an interval estimate for the mean penalty minutes of NHL players.
(f) Give a reason why it might not be reasonable to use the players on one team as a sample of all players in a league.

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34 Points Pen mins 71 53 59 49 48 29 26 24 57 32 28 26 121 26 53 20 13 22 28 22 20 54 34 18 38 Points Pen mins 13 11 3 22 175 3 24 45 18 16 14 14 38 5 40 16 20 20 107 190 12 14