Question

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.

Answer 1

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