The following data shows the total rainfall fo Michigan and

The following data shows the total rainfall fo Michigan and Ohio

We want to test if rainfall in Michigan is greater than Ohio.

At a level of significance alpha=.05, preform the required test. (Hint this is a matched pairs design)

Solution

Let mu_d be the mean difference between Michigan and Ohio

The test hypothesis:

Ho: mu_d= 0 (i.e. null hypothesis)

Ha: mu_d >0 (i.e. alternative hypothesis)

The test statistic is

t= mean difference/(s/vn)

=-1.2308/(22.1088/sqrt(13))

=-0.20

It is a right-tailed test.

The degree of freedom =n-1=13-1=12

Given a=0.05, the critical value is t(0.05, df=12) =1.78 (from student t table)

The rejection region is if t>1.78, we reject the null hypothesis.

Since t=-0.20 is less than 1.78, we do not reject the null hypothesis.

So we can not conclude that rainfall in Michigan is greater than Ohio