Arandom 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?

a) 96% CI:

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

The standard deviation of the sample proportion is

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

Then, the 96% CI can be written as:

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.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are