Question

In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week.

In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent.

Round your responses to at least two decimal places.

Bet placed the following week
Result of picking the Crush		Picked Crush to win	Picked Crush to lose	Total
	Crush won	44	11	55
	Crush lost	27	18	45
	Total	71	29	100

Answer 1

Observed Frequencies:

	Picked Crush to win	Picked Crush to lose	Total
Crush won	44	11	55
Crush lost	27	18	45
Total	71	29	100

Expected Frequencies

	Picked Crush to win	Picked Crush to lose	Total
Crush won	71 X 55/100 = 39.05	29 X 55/100 = 15.95	55
Crush lost	71 X 45/100 = 31.95	29 X 45/100 =13.05	45
Total	71	29	100

So,

Anaswer is:

Expected Frequencies

	Picked Crush to win	Picked Crush to lose	Total
Crush won	39.05	15.95	55
Crush lost	31.95	13.05	45
Total	71	29	100