In June 2009 an onslaught of miserable weather in New England played havoc with people's plans and psyches. However, the dreary weather brought a quiet benefit to many city neighborhoods. Police reported that the weather was a key factor in reducing fatal and nondeadly shootings (The Boston Globe, July 3, 2009). For instance, it rained in Boston on 22 days in June, when 15 shootings occurred. In 2008, the city saw rain on only eight days and 38 shootings occurred. The table below shows the n u m b e r o f rainy days and the number of shootings that occurred in June from 2005 to 2009.
a. Calculate and interpret the covariance and the correlation coefficient.
b. Specify the competing hypotheses in order to determine whether there is a negative population correlation between the number of rainy days and crime.
c. Calculate the value of the test statistic and approximate its p-value.
d. At the 5% significance level, what is the conclusion to the test? Does it appear that dreary weather and crime are negatively correlated?