Answer to Question #321027 in Statistics and Probability for Cha

Question

A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The o if the population is 2.3 years. At a = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?

Answer 1

$\mu=9, \sigma=2.3,n=40,\bar{x}=8.2,\alpha=0.05.$

Null and alternative hypotheses:

$H_0:\mu\geq9;\\ H_1:\mu<9.$

Because $\sigma$ is known and $n=40>30,$ we can use the z-test.

$z=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\cfrac{8.2-9}{2.3/\sqrt{40}}=-2.20.$

In z-table, the area corresponding to $z=-2.20$ is 0.0139. Because the test is a left-tailed test, the P-value is equal to the area to the left of $z=-2.20,$ so, $P=0.0139.$

Because the P-value is less than $\alpha$ =0.05, we reject the null hypothesis, there is enough evidence at the 5% level of significance to support the claim that the average age of the taxis in this company is less than the national average.