What is the lower limit of the confidence interval? Record your answer as a value between 0 and 1, and round to four decimal places.

Question

According to information from Gallup, a large surveying organization, 1000 respondents are randomly surveyed from the population that one of its polls is focused on. A 2022 Gallup poll estimates that 85% of the world’s adult population had access to a bank or mobile money provider.

Using this information, calculate the 80% confidence interval for the true proportion of the world’s adult population that has access to a bank or mobile money provider as of 2022.

Answer 1

This answer requires making a bit of an assumption that is not clearly stated in the problem. If Gallop surveyed 1,000 people, and their conclusion was that 85% of the world's adult population that has access to a bank or mobile money provider as of 2022, then we can assume that 85% of their sample did. So, sample proportion = 0.85

Formula for confidence intervals:

sample proportion + & - critical z times standard error,

with standard error = square root of (sample proportion times (1 minus sample proportion) divided by sample size)

standard error = square root of (.85 * .15 / 1000) = 0.011292

critical z = 1.281552 (use table or technology to find)

lower bound = 0.85 - 1.281552 * 0.011292 = 0.835529

upper bound = 0.85 + 1.281552 * 0.011292 = 0.864471

Answer (rounded): 0.8355