Figure 5.21 shows a bootstrap distribution of correlations between penalty yards and uniform malevolence using the data on 28 NFL teams in Malevolent-UniformsNFL. We see from the percentiles of the bootstrap distribution that a 99% confidence interval for the correlation is ˆ’0.224 to 0.788. The correlation between the two variables for the original sample is r = 0.37.

Figure 5.21

(a) Use the original sample correlation and the standard deviation of the bootstrap distribution shown in Figure 5.21 to compute a 99% confidence interval for the correlation using z^ˆ— from a normal distribution.
(b) Why is the normal-based interval somewhat different from the percentile interval?

Transcribed Image Text:

Number of Bootstrap Samples = 5000 Mean = 0.397 Left Tail OTwo-Tail ORight Tail %3D 200 %3D Std. Dev. = 0.205 150 100 0.005 0.990 0.005 50 40.2 ol8 0.0 -0.4 0.2 0.6 -0.224 0.397 0.788