multiple parts to one question.. help please 4, A mayor of a big city finds that

Question

multiple parts to one question.. help please

4, A mayor of a big city finds that 212 of 400 selected city residenns believe that the city should spend more money on road maintenance. this inference of the proportion of all city residents who believe that the city should be spendinwL a) (0.5 points) What percentage of the sample members believe the city should be spending more? 212 212 b) (1 point) Calculate the standard error of the proportion c) (1 point) Find and interpret the 95% confidence interval for the population proportion.

Explanation / Answer

(a) p = 212/400 = 0.53

(b) Standard error of the proportion = (p(1 - p)/n) = (0.53 * (1 - 0.53)/400) = 0.025

(c) z- score = 1.959963985

Width of the confidence interval = z * SE =     1.95996398454005 * 0.025 = 0.04891082

Lower Limit of the confidence interval = P - width =     0.53 - 0.048910821712452 = 0.48108918

Upper Limit of the confidence interval = P + width =     0.53 + 0.048910821712452 = 0.57891082

The 95% confidence interval is [0.4811, 0.5789]

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