A random sample of 200 voters in a town is selected, and 114 are found to support an annexa- tion suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.
(b) What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?

b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.

Step-by-step explanation:

The proportion of the sample is

[tex]p=\frac{114}{200}=0.57[/tex]

The standard deviation of the sample proportion is

[tex]\sigma=\sqrt{\frac{p(1-p)}{n} } =\sqrt{\frac{0.57(1-0.57)}{200} } =\sqrt{\frac{0.2451}{200} } =0.035[/tex]

For a 96% CI, the z-value is z=1.751.

Then, the 96% CI can be written as:

[tex]p-z\cdot \sigma\leq\pi\leq p+z\cdot \sigma\\\\0.57-1.751*0.035\leq\pi\leq 0.57+1.751*0.035\\\\0.57-0.06\leq\pi\leq 0.57+0.06\\\\0.51\leq\pi\leq 0.63[/tex]

b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.