In June 2 0 0 9 an onslaught o f m iserable w e a th e r in N ew England played havoc w ith people's plans and psyches.

How ever, th e dreary w e a th e r b ro u g h t a q u iet benefit to m an y city neighborhoods. Police reported th a t th e w e a th e r was a key factor in reducing fatal and no ndeadly shootings

(The Boston Globe, July 3 ,2 0 0 9 ). For instance, it rained in Boston on 22 days in June, w h en 15 shootings occurred. In 2008, th e city saw rain on only e ig h t days and 38 shootings occurred. Th e ta b le b e lo w show s th e n u m b e r o f rainy days a nd th e n u m b e r o f shootings th a t occurred in June from 2005 to 2009.

Number of Rainy Days Number of Shootings June 2005 7 31 June 2006 15 46 June 2007 10 29 June 2008 8 38 June 2009 22 15 Source: The Boston Globe, July 3 , 2009.

a. Calculate and interpret th e covariance and the correlation coefficient.

b. Specify th e com peting hypotheses in order to determ in e w h e th e r th e re is a n e g a tiv e p o p u la tio n correlation b etw een th e n u m b er o f rainy days and crime.

c. C alculate th e v alu e o f th e test statistic a n d a p p ro x im a te its p -value.

d. A t th e 5 % sign ificance level, w h a t is th e conclusion to th e test? Does it a p p ear th a t dreary w e a th e r and crime are negatively correlated? P-968