Refer to the randomization test described in Exercise 5.72 for the correlation between uniform malevolence and penalty minutes for NHL teams. Suppose that a student constructs randomization samples by scrambling the NHLMalevolence variable in MalevolentUniformsNHL and computing the correlation with ZPenMin. The student repeats this process 1000 times to generate a randomization distribution and finds the standard deviation of the randomization correlations to be 0.22. Since the distribution is reasonably normal and the correlation between these variables in the original sample is r = 0.521, the student computes a 90% confidence interval for the correlation using 0.521 ± 1.645 · 0.22 = (0.159, 0.883).
(a) Identify a clear error in the process that the student has used to construct a confidence interval for the correlation in this situation.
(b) Suggest a more appropriate method for estimating the standard error to find a confidence interval for the correlation between uniform malevolence and standardized penalty minutes for NHL teams, based on the sample data in MalevolentUniformsNHL.
(c) Carry out the procedure you describe in part (b) to obtain an estimate of the standard error. Assuming that a normal distribution is appropriate, use the standard error to find (and interpret) a 90% confidence interval for the correlation in this context.
(d) Does it look like a normal distribution is appropriate in this situation? Explain why or why not.

Exercise 5.72

Data 4.3 on page 224

Frank and Gilovich4 describe a study of relationships between the type of uniforms worn by professional sports teams and the aggressiveness of the team. They consider teams from the National Football League (NFL) and National Hockey League (NHL). Participants with no knowledge of the teams rated the jerseys on characteristics such as timid/aggressive, nice/mean, and good/bad. The averages of these responses produced a €˜€˜malevolence€ index with higher scores signifying impressions of more malevolent (evil-looking) uniforms. To measure aggressiveness, the authors used the amount of penalties (yards for football and minutes for hockey) converted to z-scores and averaged for each team over the seasons from 1970 to 1986. The data are shown in Table 4.1 and stored in MalevolentUniformsNFL and MalevolentUniformsNHL.

Table 4.1

Transcribed Image Text:

NFLTeam LA Raiders Pittsburgh Malevolence 5.10 ZPenYds 1.19 NHLTeam Malevolence 533 ZPenMin 0.88 Vancouver 5.00 048 Philadelphia Boston New Jersey Pittsburgh Chicago Montreal 5.17 2.01 5.13 4.45 Cincinnati 4.97 0.27 0.42 New Orleans Chicago Kansas City Washington St Louis 4.83 a.10 -0.78 4.68 0.29 4.27 0.64 4.58 -a.19 4.18 -0.02 4.40 -0.07 4.18 -0.70 4.15 4.27 -01 Detroit 0.44 NY Jets 4.12 a.01 Edmonton 4.15 0.58 LA Rams 4.10 -0.09 Calgary LA Kings Buffalo 4.13 -0.40 Cleveland 4.05 0.44 4.05 -0.20 San Diego Green Bay Philadelphia Minnesota 4.05 0.27 4.00 -0.68 4.00 -0.73 Minnesota NY Rangers NY Islanders Winnipeg St. Louis Washington Toronto 4.00 -0.11 3.97 -0.49 3.90 -0.31 -081 3.90 3.80 -0.35 Atlanta 3.87 0.30 3.78 -0.30 Indianapolis San Francisco 3.83 -a.19 3.75 -0.09 3.83 0.09 3.73 -0.07 0.02 Seattle 3.82 3.58 0.34 0.24 Denver 3.80 Quebec 333 0.41 Tampa Bay New England Buffalo 3.77 -041 Hartford 332 -0.34 3.60 -a.18 3.53 3.38 Q.63 Detroit 0.04 NY Giants 3.27 -0.32 Dallas 3.15 0.23 Houston 2.88 0.38 Miami 2.80 -1.60