Answer to Question #321027 in Statistics and Probability for Cha

Question #321027

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?


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Expert's answer
2022-03-31T07:42:55-0400

μ=9,σ=2.3,n=40,xˉ=8.2,α=0.05.\mu=9, \sigma=2.3,n=40,\bar{x}=8.2,\alpha=0.05.

Null and alternative hypotheses:

H0:μ9;H1:μ<9.H_0:\mu\geq9;\\ H_1:\mu<9.


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

z=xˉμσ/n=8.292.3/40=2.20.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=2.20z=-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,z=-2.20, so, P=0.0139.P=0.0139.


Because the P-value is less than α\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.


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