Testing the correlation between debts. In given Exercise, we assessed the significance of the correlation between debt in 2006 and debt in 2007 for 24 countries by creating bootstrap confidence intervals. If a 95% confidence interval does not cover 0, the observed correlation is significantly different from 0 at the α = 0.05 level. Let's do a test that provides a P-value. Carry out a permutation test and give the P-value. What do you conclude? Is your conclusion consistent with your work in Exercise?
Exercise
The correlation between debts. Given Figure shows a strong positive relationship between debt in 2007 and debt in 2006 for 24 countries. Use the bootstrap to perform statistical inference for these data.
(a) Describe the shape and bias of the bootstrap distribution. Do you think that a simple bootstrap inference (t and percentile confidence intervals) is justified? Explain your answer.
(b) Give the BCa and bootstrap percentile 95% confidence intervals for the population correlation. Do they (as expected) agree closely? Do these intervals provide significant evidence at the 5% level that the population correlation is not 0?
