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

Essay

Is the number of games won by a major league baseball team in a season related to the
teamʹs batting average? Data from 14 teams were collected and the summary statistics
yield: $\sum y = 1,134 , \sum ^ { x } = 3.642 , \sum y ^ { 2 } = 93,110 , \sum ^ { x ^ { 2 } } = .948622$ , 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 $\alpha = .05$ .