## Related questions with answers

The data that accompanies this exercise show miles per gallon (MPG) for a sample of 25 cars.

a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not MPG follow the normal distribution.

b. Calculate the value of the Jarque-Bera test statistic. Use Excel to calculate the $p$-value.

c. At $\alpha=0.05$, can you conclude that MPG are not normally distributed?

Solution

Verified**(a)** First let us state the two competing hypotheses for the problem.

First we have the null hypotheses $H_0$

$H_0:S=0 \text{ and } K=0.$

where $S$ is the skewness coefficient and $K$ is the kurtosis coefficient. The null hypotheses states that the MPG Data follows the normal distribution.

Next we have the alternative hypotheses $H_A$

$H_A:S\ne0 \text{ or } K\ne0.$

The alternative hypotheses states that the MPG Data does not follow the normal distribution.

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