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: Group A (water softener and filtering) x1=2.1 s1=0.7 Group B (water softener only) x2=1.7 s2=0.4 Determine, at the 90% confidence level, whether there is a difference between the two types of treatments.

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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: Group A (water softener and filtering) x1=2.1  s1=0.7 Group B (water softener only) x2=1.7   s2=0.4 Determine, at the 90% confidence level, whether there is a difference between the two types of treatments.

stuth1 · Accepted Answer

Group A x1=2.1 s1=0.7 n1=45 Group B x2=1.7 s2=0.4 n2=45 S.E.=(0.7)245+(0.4)245=0.120 d=x1−x2=2.1−1.7=0.4 tcnc(at 0.10losand90−2df)=1.65 ∴C.I.=d±tcncS.E. =0.4±1.65(0.120) =0.4±0.198 ∴C.I.=(0.202,0.598)

Researchers wanted to compare the effectiveness of a water softener used with a filtering process with a water softener used without filtering. Ninety

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