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Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III
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World Series Are the teams that play in the World Series

Chapter 5, Problem 2RE

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QUESTION:

Problem 2RE

World Series Are the teams that play in the World Series evenly matched? To win a World Series, a team must win 4 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 2010. 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 α = 0.05 level of significance

Number of Games

Probability

Observed Frequency

4

0.125

15

5

0.25

17

6

0.3125

18

7

0.3125

30

Source: Major League Baseball

Questions & Answers

QUESTION:

Problem 2RE

World Series Are the teams that play in the World Series evenly matched? To win a World Series, a team must win 4 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 2010. 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 α = 0.05 level of significance

Number of Games

Probability

Observed Frequency

4

0.125

15

5

0.25

17

6

0.3125

18

7

0.3125

30

Source: Major League Baseball

ANSWER:

Answer:

Step 1

Use the α = 0.05 level of significance

The Hypotheses can be expressed as

H0 : The teams are evenly matched

H1 : The teams are not evenly matched

Formulate an analysis plan: For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data: Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

    Degrees of freedom = k - 1 = 4 - 1 = 3

           

Number of Games

Probability

Observed Frequency

(

Expected Frequency

()

4

0.125

15

10

5

0.25

17

20

6

0.3125

18

25

7

0.3125

30

25

80

 

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