Question

PRESIDENT Reagan Taft Truman Harding Eisenhower Hoover G. W. Bush Garfield Pierce T. Roosevelt Harrison Lincoln J. Kennedy J. Adams McKinley Johnson G. H. W. Bush Cleveland Hayes Taylor HEIGHT 185 182 175 183 179 182 183 183 178 178 168 193 183 170 170 192 188 180 173 173 HEIGHT OPP 177 178 173 178 178 180 185 187 196 175 180 188 182 189 178 180 173 180 178 174

Answer 1

n = 20, x = 11

p̂ = x/n = 0.55

95% Confidence interval :

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̂ - z_c*√(p̂ *(1- p̂)/n) = 0.55 - 1.96 *√(0.55*0.45/20) = 0.332

Upper Bound = p̂ + z_c*√(p̂ *(1- p̂)/n) = 0.55 + 1.96 *√(0.55*0.45/20) = 0.768

33.2% < p < 76.8%

If greater height was an advantage, then taller candidates should have won more than 50% of the elections. In this case, greater height does not seem to be an advantage for presidential candidates because the confidence interval does include 50%.