Question

In a poll of 1000 randomly selected U.S. adults, 372 indicated that they considered themselves to be baseball fans. Of the 372 baseball fans, 283 stated that they thought the designated hitter rule should either be expanded to both baseball leagues or eliminated.

(a)Construct a 95% confidence interval for the proportion of U.S. adults who consider themselves to be baseball fans. (Round your answers to three decimal places.)

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(b)Construct a 95% confidence interval for the proportion of those who consider themselves to be baseball fans who think the designated hitter rule should be expanded to both leagues or eliminated. (Round your answers to three decimal places.)(b)

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Answer 1

a) n =   1000, x =    372

Sample proportion, p̄ = x/n = 0.372

95% confidence interval for the proportion of U.S. adults who consider themselves to be baseball fans :

At α = 0.05, two tailed critical value, z-crit = NORM.S.INV( 0.05 / 2) = 1.96

Lower Bound = p̄ - z-crit*(√( p̄ *(1- p̄ )/n)) = 0.372 - 1.96*(√( 0.372 *(1- 0.372 )/1000)) = 0.342   

Upper Bound = p̄ + z-crit*(√( p̄ *(1- p̄ )/n)) = 0.372 + 1.96*(√( 0.372 *(1- 0.372 )/1000)) =0.402

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b) n =   372
x =    283
Sample proportion, p̄ = x/n = 0.7608

95% confidence interval for the proportion baseball fans who think the designated hitter rule should be expanded to both leagues or eliminated

At α = 0.05, two tailed critical value, z-crit = NORM.S.INV( 0.05 / 2) = 1.96

Lower Bound = p̄ - z-crit*(√( p̄ *(1- p̄ )/n)) =  0.7608 - 1.96*(√( 0.7608 *(1- 0.7608 )/372)) = 0.717

Upper Bound = p̄ + z-crit*(√( p̄ *(1- p̄ )/n)) = 0.7608 + 1.96*(√( 0.7608 *(1- 0.7608 )/372)) = 0.804