During the National Football League (NFL) season, Las Vegas odds makers establish a point spread on each game for betting purposes. For example, the Carolina Panthers were established as 3.5-point favorites over the eventual champion Denver Broncos in the 2016 Super Bowl. The final scores of NFL games were compared against the final point spreads established by the odds makers in Chance (Fall 1998). The difference between the game outcome and point spread (called a point-spread error) was calculated for 240 NFL games. The mean and standard deviation of the point-spread errors are 1.6 and 13.3, respectively.
Use this information to test the hypothesis that the true mean point-spread error for all NFL games is positive. Conduct the test at α = .10 and interpret the result.
Can you please show:
- The null and alternative hypotheses
- Test statistic
- Rejection, please show on the distribution curve (the bell curve)
- P-value: if z distribution is used
- Decision: whether to reject or not to reject the null
- Conclusion: what you do find in term of the specific situation described in the question