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 7 Actual contests Expected proportion 4 16 2 16 5 20 4 16 6 23 5 16 37 5 16 Calculate the test statistic, x? x2 = 5.267' (Round to three decimal places as needed.) Calculate the P-value. P-value = 0.1533 (Round to four decimal places as needed.) What is the conclusion for this hypothesis test? Question is complete. Tap on the red Indicators to see incorrect answers.

Answer 1

From the given information: 7 Total N=96 37 Games Played 4 5 6 Actual Contests (0) 16 20 23 2 4 5 Expected Proportion (p) 16 16 16 2 4 5 Expected value (E = Np) 96x6 =12 96% = 24 96x = 30 96 x 5 16 5 30 16 16 16 16 Null hypothesis, H, : the actual numbers of games fit the distribution indicated by the expected proportions. Alternative hypothesis, H,: the actual numbers of games does not fit the distribution indicated by the expected proportions.

Calculate the chi-square table. Observed (O) Expected(E) (0-E) 12 16 20 4 -4 (O-E E 1.333 0.667 1.633 1.633 23 24 30 30 -7 37 7 Calculate the chi-square test statistic value. χ = Σ. -(0-E) E =1.333+0.667 +1.633+1.633 = 5.267 Calculate the degrees of freedom. df =n-1 =4-1 =3

Calculate the P-value. P-value =(=CHIDIST(5.267,3)) = 0.1533 (Use MS Excel) Decision: Fail to reject H,, because, the P-value is greater than the 0.05 level of significance. Conclusion: The claim that the actual numbers of games fit the distribution indicated by the expected proportions is true.