Concept explainers
To test: The given claim.
Answer to Problem 1RE
Solution: There is enough sign at the level of significance
Explanation of Solution
Given: The necessary information is provided.
Explanation: To test the randomness of the data, the requirements for randomness should be satisfied by the data.
The provided sample is an arrangement of observations in the order of existence and the outcomes consist of mutually exclusive classes.
A hypothesis test is conducted through the following steps.
Step 1: The hypotheses are defined as
Step 2: The significance level alpha is provided as
Step 3: The count of runs r is used to calculate the test statistic. As the
The total number of winningsbeingsampled be represented by n. Consider that
There are 25 winnings out of which 14 winnings are from Western Division (W) and 11 winnings are from Eastern Division (E).
In the provided sequence, the first one winning from Western Division forms a run of length1 as they are of the same type. The next five winnings from Eastern Division form a run of length5 as it is of another type. The next run consists of fourwinnings from Western Division. In this way, the number of runs is 11.
Hence, the values are
The number of runs is obtained as 11. Therefore, the test statistic is
Step 4: Use the critical values table for the number of runs to determine the intersection of the row that corresponds to
The test statistic
Conclusion: There isadequateindication to determine that the winning divisionoccurs randomly.
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Chapter 15 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
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