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 selected. 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? (100-85.33) (80-80) ² (60-74.67) (60-74.67) (70-70)? (80-65.33)" A with 2 degrees of freedom 100 80 60 60 70 80 B) x? (100–85.33) (80-80) (60–74.67) (60-74.67) (70-70) (80-65.33) with 2 degrees of freedom 85.33 80 74.67 74.67 70 65.33 c) x? (100-75) (80–75) (60-75) (60-75)? (70–75)² (80-75) with 6 degrees of freedom 75 75 75 75 75 75 (100-85.33) (80-80) (60-74.67) (60-74.67) (70-70) (80-65.33) D x² = with 6 degrees of freedom 450 450 450 450 450 450 (100-85.33) (80-80) (60-74.67) (60-74.67) + (70-70) E) x (80-65.33) with 6 degrees of freedom 85.33 80 74.67 74.67 70 65.33

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?

• χ2=(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

  chi square equals the fraction with numerator open parenthesis, 100 minus 85.33, close parenthesis, squared and denominator 100, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 80, close parenthesis, squared and denominator 80, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 74.67, close parenthesis, squared and denominator 60, end fraction, plus the fraction with numerator open parenthesis, 60 minus 74.67, close parenthesis squared and denominator 60, end fraction, plus the fraction with the numerator, open parenthesis, 70 minus 70, close parenthesis, squared and denominator 70, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 65.33, close parenthesis, squared and denominator 80 with 2 degrees of freedom
  A

• 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)265.33 with 2 degrees of freedom

  chi square equals the fraction with numerator, open parenthesis, 100 minus 85.33, close parenthesis, squared and denominator 85.33, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 80, close parenthesis, squared and denominator 80, end fraction, plus the fraction with numerator open parenthesis, 60 minus 74.67, close parenthesis, squared and denominator 74.67, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 74.67, close parenthesis, squared and denominator 74.76, end fraction, plus the fraction with the numerator, open parenthesis, 70 minus 70, close parenthesis, squared and denominator 70, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 65.33, close parenthesis, squared and denominator 65.33 with 2 degrees of freedom
  B

• χ2=(100−75)275+(80−75)275+(60−75)275+(60−75)275+(70−75)275+(80−75)275 with 6 degrees of freedom

  chi square equals the fraction with numerator, open parenthesis, 100 minus 75, close parenthesis, squared and denominator 75, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 75, close parenthesis, squared and denominator 75, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 75, close parenthesis, squared and denominator 75, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 75, close parenthesis, squared and denominator 75, end fraction, plus the fraction with numerator, open parenthesis, 70 minus 75, close parenthesis, squared and denominator 75, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 75, close parenthesis, squared and denominator 75 with 6 degrees of freedom
  C

• χ2=(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

  chi square equals the fraction with numerator, open parenthesis, 100 minus 85.33, close parenthesis, squared and denominator 450, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 80, close parenthesis, squared and denominator 450, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 74.67, close parenthesis, squared and denominator 450, end fraction, plus the fraction with numerator, open parenthesis, 60 minus 74.67, close parenthesis, squared and denominator 450, end fraction, plus the fraction with the numerator, open parenthesis, 70 minus 70, close parenthesis, squared and denominator 450, end fraction, plus the fraction with numerator, open parenthesis, 80 minus 65.33, close parenthesis, squared and denominator 450 with 6 degrees of freedom
  D

• 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)265.33 with 6 degrees of freedom