Question

The average age of licensed drivers in a county is μ = 42.6, σ = 12, and the distribution is approximately normal. A county police officer was interested in whether the average age of drivers receiving speeding tickets differed from the average age of the driving population. She obtained a sample of N = 16 drivers receiving speeding tickets. The average age for this sample was M = 34.4. Perform the steps 2-5 of the hypothesis testing necessary to determine whether this group differs from the population of drivers in the county.

Answer 1

Here as we defined the hypothesis for two tailed test

H₀ : = 42.6

H_a : 42.6

Here standard deviation = σ = 12

Sample size n = 16

standard error of sample mean = σ/sqrt(n) = 12/sqrt(16) = 3

Average age of sample = M = 34.4

Step 2 :

Define the confidence level = 0.05

Step 3 :

Critical region for the two tailed test and alpha = 0.05

Z_critical = 196

Step 4 :

Z = (34.4 - 42.6)/3 = -2.7333

Step 4

Here as Z > Z_critical so we will reject the null hypothesis and we will conclude that this group differes from the population of drivers in the county.