Question

an auditor for a local court system is tasked with comparing the rulings of two judges. the auditor needs to determine if judge hughes issues shorter sentences than judge wilson. the data below are the sentence lengths, in months, issued by each judge in their last twelve cases that dealt with operating a motor vehicle without a license. test the claim that judge hughes issues shorter sentences than judge wilson for this particular type of case at the 0.10 level of significance. let judge hughes sentences be population 1 and let judge wilsons sentences be population 2. assume that both populations are approximately normal and that the population variances are equal.

judge hughes	30	18	18	30	24	24	18	24	18	18	18	12
judge wilson	18	18	18	36	30	36	36	24	30	24	36	30

copy data

step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below.

$h_0:mu_1=mu_2$
$h_a:mu_1$ ____ $mu_2$

answer

<

$
eq$

Explanation:

Step1: Identify the claim

The claim is that judge Hughes issues shorter sentences than judge Wilson. So the alternative hypothesis should reflect this one - sided relationship.

Step2: Determine the alternative hypothesis symbol

Since we want to test if the mean of judge Hughes' sentences ($\mu_1$) is less than the mean of judge Wilson's sentences ($\mu_2$), the symbol in the alternative hypothesis $H_a$ is '<'.

Answer:

<