Question

Lets suppose that we wanted to have a very tight confidence interval, with a total width of the interval of 0.01. This means that the lower bound and upper bound are no more than 0.01 from one another. How many spins are needed in order to construct a 92% confidence interval with that margin of error?

Answer 1

The margin of error we desire is ME = 0.01, and for 92% confidence, we use Z0.04 = 1.75 (well know value using Z table). Since we have no prior knowledge about the proportion p, we use the conservative estimate of = 0.5. We have:

  

  

We need to take n = 7656 such that the total width of the confidence interval (left end to right end) will be no more than 0.01.