The table below lists the number of games played in a yearly best-of-seven baseb

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.

1. Determine the null and alternative hypotheses.

H0: 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 three of the expected proportions.

d. The observed frequencies agree the expected proportions

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 three of the expected proportions.

d. The observed frequencies agree the expected proportions

2. Calculate the test statistic, 2.

2 = ___ (Round to three decimal places as needed.)

3. Calculate the P-value.

P-value = ___ (Round to four decimal places as needed.)

4. What is the conclusion for this hypothesis test?

A. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

C.Reject H0. There is insufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions..

D. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

Games played 4 5 6 7 Actual contests 20 20 23 37 Expected proportions 2/16 4/16 5/16 5/16

Explanation / Answer

1) d. The observed frequencies agree the expected proportions

H1:  b. At least one of the observed frequencies do not agree with the expected proportions.

2) applying chi square goodness of fit test:

2)from above test statistic 2 =8.736

3)p value =0.0330

4)

as p value is less then 0.05 level

B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

observed Expected Chi square games played Probability O E=total*p =(O-E)^2/E 4 1/8 20.000 12.50 4.50 5 1/4 20.000 25.00 1.00 6 5/16 23.000 31.25 2.18 7 5/16 37.000 31.25 1.06 1 100 100 8.7360

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