The Pittsburgh Police department claims that the standard deviation of the number of tickets they issue is 15 tickets. A police officer does not agree, and randomly selects the records of 14 officers. He finds the sample standard deviation to be 13.43 tickets. Assuming that the data is normally distributed, test the department’s claim using a = 0.01. Use the Chi-square test.

Solution:

STEP 1: The hypotheses are

STEP 2: This test corresponds to a two-tailed test. We’ll use a Chi-Square test.

STEP 4: The significance is, and therefore, the critical values are

and

,

for 13 degrees of freedom. The rejection region is

.

STEP 5: The Chi Square-statistics is computed as

STEP 6: We fail to reject the null hypothesis. That means that we have don’t have enough evidence to reject the claim, at the 0.01 significance level.

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