Question

Q4: 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   Actual_contests   Expected_proportion
4   20   0.125
5   18   0.25
6   23   0.3125
7   35   0.3125

A) Ho:     A. The observed frequencies agree with two of the expected proportions.

B. At least one of the observed frequencies do not agree with the expected proportions.

C. The observed frequencies agree with the expected proportions.

D. The observed frequencies agree with three of the expected proportions.

Answer Ho: ________

H1:   A. The observed frequencies agree with two of the expected proportions.

          B. At least one of the observed frequencies do not agree with the expected proportions.

         C. The observed frequencies agree with the expected proportions.

          D. The observed frequencies agree with three of the expected proportions.

B) What is the Test Statistic-_______

C) What is the Critical Value and P value________

D) What is the Null Hypothesis:-________

What is the Research Hypothesis_________

Reject or fail to reject null hypothesis________

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
4	20	0.125	96 * 0.125 = 12	(20 - 12)²/12 = 5.3333
5	18	0.25	96 * 0.25 = 24	(18 - 24)²/24 = 1.5
6	23	0.3125	96 * 0.3125 = 30	(23 - 30)²/30 = 1.6333
7	35	0.3125	96 * 0.3125 = 30	(35 - 30)²/30 = 0.8333
Total	96	1.00	96	9.3000

Null hypothesis:

C. The observed frequencies agree with the expected proportions.

Alternative hypothesis:

B. At least one of the observed frequencies do not agree with the expected proportions.

Test statistic:

χ² = ∑ ((O-E)²/E) = 9.30

df = n-1 = 3

Critical value:

χ²α = CHISQ.INV.RT(0.05, 3) = 7.8147

p-value:

p-value = CHISQ.DIST.RT(9.3, 3) = 0.0256

Decision:

p-value < α, Reject the null hypothesis

There is enough evidence to conclude that at least one of the observed frequencies do not agree with the expected proportions.