Answer to Question #280474 in Statistics and Probability for Ella

Question

For the year 2013 (E.C), the average fuel consumption of HU vehicles was 200 liters per

day and the standard deviation is 90 liters per day. The manager of the system claims that

the average fuel consumption has increased this year. Assume that – to test the claim, the

manager sampled 40 vehicles of HU, and the mean of selected vehicles’ fuel

consumption is 160 liters per day. Formulate hypothesis testing with 1% α; assume the

distribution is normally distributed

Answer 1

We test the following hypotheses;

$H_0:\mu=200\space vs \space H_1: \mu\lt200$

$n=40, \space \bar{x}=160,\space \sigma=90,\space \alpha=0.01$

The test statistic is given by,

$Z={(\bar{x}-\mu)\over ({\sigma\over\sqrt{n}})}={(160-200)\over({90\over\sqrt{40}})}=-2.811$

$Z$ is compared with the standard normal distribution table value at $\alpha=0.01$ given as,

$Z_{0.01}= -2.326348$

The null hypothesis is rejected if, $Z\lt Z_{0.01}$

Since $Z=-2.811\lt Z_{0.01}=-2.326348,$ we reject the null hypothesis and conclude that there is enough evidence to show that the average fuel consumption is less than 200 liters per day at 1% level of significance.