Question

The table below lists the number of games played in a yearly​ best-of-seven baseball championship​ series, along with the expected proportions for the number of games played with teams of equal abilities. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

Games Played	4	5	6	7
Actual contests	19	19	21	38
Expected proportion	two sixteenths	four sixteenths	five sixteenths	five sixteenths

Determine the null and alternative hypotheses.

Calculate the test​ statistic, chi squaredχ2.

Answer 1

null hypothesis:Ho: actual numbers of games fit the distribution indicated by the expected proportions.

Alternate hypothesis:Ha: actual numbers of games does not fit the distribution indicated by the expected proportions.

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
4	1/8	19	12.13	1.97	3.898
5	1/4	19	24.25	-1.07	1.137
6	5/16	21	30.31	-1.69	2.861
7	5/16	38	30.31	1.40	1.950
total	1.000	97	97		9.845

test​ statistic X² =9.845