Question

A hot topic in the news is the possible replacement of the Brent Spence Bridge which connects northern Kentucky to Cincinnati. If the bridge is replaced, it will likely become a toll bridge. A 2013 survey of 1867 northern Kentucky AAA members was asked their opinion on instituting a toll on the Brent Spence Bridge. Of those surveyed, 1101 were opposed to tolls.

With 95% confidence, we estimate between---% and---- % of all northern Kentucky residents are opposed to tolls on the Brent Spence Bridge. (After converting to percentages, round the limits of your interval to two decimal places.)

Does the interval above provide evidence that more than 60% of northern Kentucky residents are opposed to tolls? Yes because both limits of the interval are greater than 60%.

-Yes because the upper limit of the interval is greater than 60%.

-No because the upper limit of the interval is greater than 60% while the lower limit is less than 60%.

-No because both limits of the interval are below 60%.

State legislators would like to conduct a new survey to update the estimate for 2016. They would like to increase the level of confidence to 99% with a margin of error of 2.2%. If they were to use the estimate in 2013 as a starting point, how many people should be included in the 2015 sample? n =

Answer 1

sample proportion, = 0.5897
sample size, n = 1867
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5897 * (1 - 0.5897)/1867) = 0.0114

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0114
ME = 0.0223

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5897 - 1.96 * 0.0114 , 0.5897 + 1.96 * 0.0114)
CI = (0.57 , 0.61)

With 95% confidence, we estimate between 57% and 61 % of all northern Kentucky residents are opposed to tolls on the Brent Spence Bridge.

No because the upper limit of the interval is greater than 60% while the lower limit is less than 60%.

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.022

The provided estimate of proportion p is, p = 0.5897
The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5897*(1 - 0.5897)*(2.58/0.022)^2
n = 3327.57

Therefore, the sample size needed to satisfy the condition n >= 3327.57 and it must be an integer number, we conclude that the minimum required sample size is n = 3328
Ans : Sample size, n = 3328