Question

store manager claims that the average age of his customers is less than 40 years old, while the industry average is 40 years old. He asks you to test his thinking. You collect a sample of 50 customers and found that the average age is 38.7. Assuming that the population standard deviation is 12.5 years and using α = 0.05, test your manager's hypothesis. What is your conclusion?
H0
μ = 40
H1
μ < 40

Answer 1

Null and alternative hypotheses:

$$H _ {0}: \mu = 4 0$$ $$H _ {1}: \mu < 4 0$$

Test statistics:

$$z = \frac {\bar {x} - \mu_ {0}}{\sigma / \sqrt {n}} = \frac {3 8 . 7 - 4 0}{1 2 . 5 / \sqrt {5 0}} = - 0. 7 4$$

Critical value:

$$z _ {0. 0 5} = - 1. 6 4 5$$

Since $z > z_{0.05}$ we fail to reject $H_0$ . There is no enough evidence at $\alpha = 0.05$ to conclude that $\mu < 40$ .