Question

The average age for licensed drivers in a county is 42.6, with a standard deviation of 12, and the distribution is approximately normal. A county police officer was interested in whether the average age of those receiving speeding tickets is less that the average age of the population who has a license. She obtained a sample of 16 drivers with speeding tickets. The average age for this sample was 34.4. Do all the steps of hypothesis testing using the 0.01 significance level.

***Write out all steps of hypothesis testing including populations, hypotheses, cutoff scores, and all relevant calculations.

Answer 1

Given: = 42.6, = 34.4, = 12, n = 16, = 0.01, df = n - 1 = 15

The population are all the drivers in the county who have a driving license.

The Hypothesis:

H0: = 42.6

Ha: < 42.6

This is a Left Tailed Test.

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The Rejection Region:

The Critical Value:   The critical value (Left Tail) at = 0.01, for df = 15, tcritical = -2.602

Therefore reject H0 if t observed < -2.602

Also Reject H0 if p value is < (0.01)

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The Test Statistic: Although the population standard deviation is known, we use the students t test as n < 30.

The test statistic is given by the equation:

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The p Value:    The p value (Left Tail) for t = -2.74, for df = 15 , is; p value = 0.0076

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The Decision:   Since tobserved (-2.74) is < -2.6, We Reject H0.

Also since P value (0.0076) is < (0.01) , We Reject H0.

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The Conclusion: There is sufficient evidence at the 99% significance level to conclude that the average age of those receiving speeding tickets in the county is less than the average age of the population.

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