A random sample of 50 students was randomly selected from your campus.Each student was asked to record their income and their average grade,as a percentage,for the 2010/2011 school year.The sample correlation coefficient was found to be -0.43.Ten subsequent bootstrap samples based on this initial sample produced the following correlation coefficients: -0.51,-0.33,-0.42,-0.45,-0.48,-0.44,-0.48,-0.56,-0.38,-0.39.Based on these ten resamples,find the bootstrap of the standard error of the sample correlation.
A)0.0214
B)0.0005
C)-0.444
D)0.2135
E)0.0675

Question

Quizplus · Accepted Answer

The standard error of the sample correlation coefficient can be estimated using the bootstrap samples. To calculate this, first, find the variance of the bootstrap sample correlation coefficients, then take the square root of this variance to get the standard error. The variance is calculated by finding the mean of the squared differences between each bootstrap sample correlation coefficient and the mean of these coefficients. The calculations lead to a standard error of approximately 0.0675, making option E correct.

A Random Sample of 50 Students Was Randomly Selected from Your