Question

On September 1, 1939, Germany invaded Poland, causing Britain and France to declare war on Germany. Between September 1 and September 6 that year, Gallup conducted a poll asking whether the U.S. should send its Army and Navy abroad to fight against Germany. 84% of 926 Americans surveyed said no.

(a) Construct a 95% confidence interval for the proportion of Americans who didn’t believe that the U.S. should send its Army and Navy abroad to fight against Germany.

(b) Construct a one-side 95% confidence interval with an upper bound for the proportion of Americans who didn’t believe that the U.S. should send its Army and Navy abroad to fight against Germany.

Answer 1

a)

95% CI is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.84 - 1.96 * sqrt [ 0.84 ( 1 - 0.84) / 926 ] < p < 0.84 + 1.96 * sqrt [ 0.84 ( 1 - 0.84) / 926 ]

0.816 < p < 0.864

95% CI is ( 0.816 , 0.864 )

b)

95% Upper bound is

+ Z * sqrt [ ( 1 - ) / n ] > p

0.84 + 1.645 * sqrt [ 0.84 ( 1 - 0.84) / 926 ] > p

0.860 > P