Question

A sample poll of 100 voters chosen at random from all voters in a given school district indicated that 53% of them were in favor of a 1% increase in property taxes in order to provide funds to hire more teachers.

          a.       Find the 95% confidence interval for the population proportion of voters supporting the property tax

                    hike?

          b.       Can we be confident that the tax hike will pass given your results in part (a)? Explain.

          c.       What is the required sample size needed to get the margin of error within ±2%?

Answer 1

Sample size=100 and sample proportion=p(hat)=0.53 and at 95 5 confidence level Z=1.96 calculated by Z table shown below

a) The confidence interval for proportion is calculated as

or can be written as 53%+/-9.78%

The confidence interval would be{43.22, 62.78}

b) Since there is a margin of error calculated as 9.78% hence we can be confident that tax hike will pass.

c) The sample size is calculated as, since E=2%