The table shows the results of a survey in which separate samples of 400 adults

Question

The table shows the results of a survey in which separate samples of 400 adults each from the East, South, Midwest, and West were asked Bad Traffic Congestion? if traffic congestion is a serious problem in their community. Complete parts (a) and (b). who say that traftic congestion a serious problem East South Midwwes West 3496 3296 26% 54% (a) Construct a 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem. The 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem is ( 0.491 , 0.589 ). (Round to three decimal places as needed.) b) Construct a 95% confidence interval for the proportion of adults from the Midwest who say a fic congestion is a serious problem. The 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem s (Round to three decimal places as needed.) ).

Explanation / Answer

a)

b)

                                                                                           x                    =   216 sample size n                    = 400 sample proportion     p x/n= 0.5400 std error       =Se            =(p*(1-p)/n) = 0.0249 for 95 % CI value of z= 1.9600 margin of error E=z*std error                            = 0.0488 lower confidence bound=sample proportion-margin of error 0.491 Upper confidence bound=sample proportion+margin of error 0.589

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