Question

# For each problem students will write out all steps of hypothesis testing including populations, hypotheses, cutoff...

For each problem students will write out all steps of hypothesis testing including populations, hypotheses, cutoff scores, and all relevant calculations.

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.

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 42.6
Alternative Hypothesis, Ha: μ < 42.6

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (34.4 - 42.6)/(12/sqrt(16))
z = -2.73

P-value Approach
P-value = 0.0032
As P-value < 0.01, reject the null hypothesis.

Rejection Region Approach
As the value of test statistic, z is outside critical value range, reject the null hypothesis

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