Listed below are numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from The New York Times). Is there sufficient evidence to conclude that a correlation exists between enrollment and burglaries? Generate a correlation coefficient and confidence interval. Interpret both. Enrollment 32 31 53 28 27 36 42 30 34 46Burglaries 103 103 86 57 32 131 157 20 27 161

First generate the correlation coefficient by performing the regression analysis. To perform the regression analysis in Excel, select the option data analysis and then regression. This gives the following output. SUMMARY OUTPUT Regression Statistics Multiple R 0.561297 R Square 0.315054 Adjusted R Square 0.229436 Standard Error 46.1113 Observations 10 ANOVA df SS MS F Significance F Regression 1 7824.082 7824.082 3.679752 0.091359 Residual 8 17010.02 2126.252 Total 9 24834.1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -36.7669 66.50335 -0.55286 0.595467 -190.124 116.5901 E 3.467046 1.807383 1.918268 0.091359 -0.70079 7.634879The value corresponding to multiple R is the correlation coefficient which is r≈0.561. The correlation is positive and not very close to 0, thus the data in sample indicates a positive linear relation. To test about the population correlation, the hypothesis claim will be that the correlation is 0 and alternate hypothesis will claim that the correlation is not 0. H0:ρ=0H1:ρ≠0 Compute the t statistic using t=rn-21-r2, where n is the sample size which is 10. t=0.56110-21-0.5612=0.561×80.685279≈1.92The degree of freedom is defined by n-2 and the sample size is 10, so degree of freedom is 8. Find P value for two tailed using the table of t distribution corresponding to 8 degrees of freedom and t=1.92 is 0.092. The P value is larger than 0.05 significance level, so the null hypothesis can not be rejected and it is plausible that the population correlation is 0.Generate the 1000 bootstrap sample of size 10 and then find the 95% confidence interval. This gives 95% confidence interval (-0.1061,0.8798). So it can be said with 95% confidence interval that the population correlation will lie in between -0.1061 and 0.8798. In this interval 0 is captured so this also indicates that it is plausible that the correlation value can be 0.