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 if traffic congestion is a serious problem in their community. Complete parts (a) and (b). A table consists of four rows containing the following information from top to bottom, with row listed first and information listed second; row 1, East 35%; row 2, South 32%; row 3, Midwest 25%; row 4, West 53%. East South Midwest West 35% 32% 25% 53% (a) Construct a 95% confidence interval for the proportion of adults from the MidwestMidwest who say traffic congestion is a serious problem. The 95% confidence interval for the proportion of adults from the MidwestMidwest who say traffic congestion is a serious problem is (nothing,nothing). (Round to three decimal places as needed.)

Explanation / Answer

Solution:-Given that n = 400 p = 0.25 q = 1-p = 0.75 Z0.025 = 1.96

95% confidence interval for  the proportion of adults from the Midwest = p +/- z*sqrt{ (p)*(1-p)/n}

=> 0.25 +/- 1.96*sqrt {(0.25)(0.75)/400}

= 0.25 - 0.0424 , 0.25 + 0.0424

= (0.2076 ,  0.2924)

= (0.208 , 0.292) rounded

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