Answer to Question #197825 in Statistics and Probability for Lovelyn Grace Ferr

Question

A report in LTO stated that the average age of taxis in the Philippines is 12 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 11.2 years. The standard deviation of the population is 2.3 years. At level of significance of 0.05, can it be concluded that the average age of the taxis in his company is less than the national average? In a clean white sheet of paper, State the hypotheses, the level of significance and critical region, compute for the value of one sample z test, write your decision rule and conclusion. 

Answer 1

Sample mean $\bar{x}=11.2 years$

Population mean $\mu=12 years$

Sample standard deviation (s)=2.3 years

Sample size n=40

Null Hypothesis $H_o:\mu=12$

Alternate hypothesis $H_a:\mu<12$

This is a left tail test.

We should use significance level $\alpha=0.05$

we used a z-test statistics-

$z=\dfrac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$

  $=\dfrac{11.2-12}{\frac{2.3}{\sqrt{40}}}$

  $=-2.20$

P-value approach-

$p-value=P(z<-2.20)=0.0139$

Conclusion: As p-value $<\alpha .$ We reject Null Hypothesis and conclude that the average age of the taxi in his company is less than the national average.