There were two surveys which were given of a proportion of individuals in favor

Question

There were two surveys which were given of a proportion of individuals in favor of legislation passing

The first survey was given and 42% responses were positive out of a sample size of 1,019

The second survey (the same survey) was given five months later to a sample of 1,023 individuals, and the percentage of positive responses rose to 55%

Use normal approximation to estimate

a) 95% upper confidence bound for the first survey

b) 95% lower confidence bound for the second survey

b) 95% confidence interval of the expected increase

Please show work, especially computations. Thank you!

Explanation / Answer

a)

standard error = sqrt(0.42 * 0.58 /1019) = 0.01546

margin of error = 0.01546 * 1.96 = 0.0303

upper bound = 0.42 + 0.0303 = 45.03 %

b)

standard error = sqrt(0.55 * 0.45/1023) = 0.01555

margin of error = 1.96 * 0.01555 = 0.0305

lower bound = 0.55 - 0.0305 = 51.95%

c)

proportion = 0.55 - 0.42 = 0.13

standard error = sqrt ( 0.01546^2/1019 + 0.01555^2/1023)

= 0.000686

margin of error = 1.96 * 0.000686 = 0.001345

confidence interval is [ 0.13 - 0.001345 , 0.13 + 0.001345]

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