Is the Number of Games Won by a Major League $$\sum y = 1,134 , \sum x = 3.642 , \sum y ^ { 2 } = 93,110 , \sum x^ { 2 } = .948622 , \text { and } \sum x y = 295.54$$

Essay

Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: $$\sum y = 1,134 , \sum x = 3.642 , \sum y ^ { 2 } = 93,110 , \sum x^ { 2 } = .948622 , \text { and } \sum x y = 295.54$$
Assume $\hat { \beta } 1 = 455.27$ and $\hat { \sigma } = 9.18$ . Conduct a test of hypothesis to determine if a positive linear relationship exists between team batting average and number of wins. Use $\alpha = .05$ .