The management of a professional baseball team is in the process of determining the budget for next year.

The model is of the form: Y = 0 + 1X1 + 2X2 + 3X3 + where:

Y = attendance at a home game

X1 = current power rating of the team on a scale from 0 to 100 before the game.

X2 and X3 are dummy variables, and they are defined below.

- X2 = 1, if weekend

- X2 = 0, otherwise

- X3 = 1, if weather is favourable

- X3 = 0, otherwise

After collecting the data based on 30 games from last year and implementing the above stated multiple regression model, the team statistician obtained the following least squares multiple regression equation: y = 1050 + 250x1 + 2200x2 + 5400x3

The multiple regression compute output also indicated the following: sb1 = 800, sb2 = 1000, sb3 = 1850

QUESTION:

Assume that the overall model is useful in predicting the game attendance and the team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays. State the appropriate null and alternative hypotheses.