Question

2. Are the teams that play in the World Series evenly matched? To win a World Series, a team must win four games. If the teams are evenly matched, we would expect the number of games played in the World Series to follow the distribution shown in the first two columns of the following table. The third column represents the actual number of games played in each World Series from 1930 to 2014. Do the data support the distribution that would exist if the teams are evenly matched and the outcome of each game is independent? Use the a = 0.05 level of significance. Number of Games Probability Observed Frequency | 4 | 0.125 | 16 5 0.25 17 6 0.3125 19 0.3125 32

Answer 1

Null hypothesis: Ho: Sampling data is similar to the distribution that would exist if the teams are evenly matched

Alternate hypothesis: Ha: Sampling data is not similar to the distribution that would exist if the teams are evenly matched

degree of freedom =categories-1=			3
for 0.05 level and 3 df :crtiical value X2 =				7.8147
Decision rule: reject Ho if value of test statistic X2>7.815

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
4	0.13	16	10.50		2.881
5	0.25	17	21.00		0.762
6	0.31	19	26.25		2.002
7	0.31	32	26.25		1.260
total	1.000	84	84		6.9048
test statistic X2 =		6.905

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that data support the   distribution that would exist if the teams are evenly matched