The national society of acupuncturists asked a random sample of 450 adults their opinion about acupuncture being a reasonable form of medicine or not a reasonable form of medicine. The table below shows the responses, along with the highest level of education achieved for each person sel ected. High School Graduate or Below Some College Bachelor’s Degree or Higher Total
Acupuncture is a reasonable form of medicine 100 80 60 240
Acupuncture is not a reasonable form of medicine 60 70 80 210
Total 160 150 140 450
Assuming that all conditions for inference have been met, which of the following represents the correct chi-square test statistic and number of degrees of freedom to test whether there is an association between level of education and opinion about acupuncture?
A. χ2=(100−85.33)2100+(80−80)280+(60−7 4.67)260+(60−74.67)260+(70−70)270+( 80−65.33)280χ2=(100−85.33)2100+(80− 80)280+(60−74.67)260+(60−74.67)260+ (70−70)270+(80−65.33)280 with 2 degrees of freedom
B. χ2=(100−85.33)285.33+(80−80)280+(60 −74.67)274.67+(60−74.67)274.67+(70− 70)270+(80−65.33)265.33χ2=(100−85.3 3)285.33+(80−80)280+(60−74.67)274.6 7+(60−74.67)274.67+(70−70)270+(80−6 5.33)265.33 with 2 degrees of freedom
C. χ2=(100−75)275+(80−75)275+(60−75)27 5+(60−75)275+(70−75)275+(80−75)275χ 2=(100−75)275+(80−75)275+(60−75)275 +(60−75)275+(70−75)275+(80−75)275 with 6 degrees of freedom
D. χ2=(100−85.33)2450+(80−80)2450+(60− 74.67)2450+(60−74.67)2450+(70−70)24 50+(80−65.33)2450χ2=(100−85.33)2450 +(80−80)2450+(60−74.67)2450+(60−74. 67)2450+(70−70)2450+(80−65.33)2450 with 6 degrees of freedom
E. χ2=(100−85.33)285.33+(80−80)280+(60 −74.67)274.67+(60−74.67)274.67+(70− 70)270+(80−65.33)265.33χ2=(100−85.3 3)285.33+(80−80)280+(60−74.67)274.6 7+(60−74.67)274.67+(70−70)270+(80−6 5.33)265.33 with 6 degrees of freedom