On September 1, 1939, Germany invaded Poland, causing Britain and France to declare war on Germany....

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.

Expert Solution

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

orchestra answered 2 years ago

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