Researchers wanted to compare the effectiveness of a water softener used with a filtering process with a water softener used without filtering. Ninety locations were randomly divided into two groups of equal size. Group A locations used a water softener and the filtering process, while group B used only the water softener. At the end of three months, a water sample was tested at each location for its level of softness. (Water softness was measured on a scale of 1 to 5, with 5 being the softest water.)
The results were as follows:
x1-bar= 2.1
s1 = 0.7
x2-bar = 1.7
s2 = 0.4
This data will be used to test the claim that there is a difference between the two types of treatments.
What are the hypotheses for this test?