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he table to the right shows the results of a survey in which 400 adults from the

ID: 3046599 • Letter: H

Question

he table to the right shows the results of a survey in which 400 adults from the East, 400 adults from the South, 400 adults from the Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts (a) and (b). Adults who say that traffic congestion is a serious problem East 36% South 32% Midwest 26% West 53% (a) Construct a 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem. The 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem is left parenthesis nothing comma nothing right parenthesis . (Round to three decimal places as needed.) (b) Construct a 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem. Is it possible that these two proportions are equal? Explain your reasoning. The 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is left parenthesis nothing comma nothing right parenthesis . (Round to three decimal places as needed.) Is it possible that these two proportions are equal?

Explanation / Answer

a) n = 400

phat = 0.53

alpha = 0.01

z_{alpha/2} = z_{0.005} = 2.5758

z_{alpha/2}*sqrt( phat(1-phat)/n ) = (2.5758)*sqrt((0.53)(0.47)/(400)) = 0.0643

phat - 0.0642 < p < phat + 0.0642

0.476 < p < 0.524

b) n = 400

phat = 0.36

alpha = 0.01

z_{alpha/2} = z_0.005 = 2.5758

z_{alpha/2}*sqrt( phat(1-phat)/n ) = (2.5758)*sqrt((0.36)(0.64)/(400)) = 0.0618

phat - 0.0618 < p < phat + 0.0618

0.476 < p < 0.524