Question

in the newspaper article referred to in exercise 9.57, 32% of the 1600 adults polled said the u.s. space program should emphasize scientific exploration. how large a sample of adults is needed for the poll if one wishes to be 95% confident that the estimated per- centage will be within 2% of the true percentage?

Answer 1

To determine the sample size needed for the poll, we can use the formula:

n = (z^2 * p * q) / E^2

where:
n = sample size
z = z-score for the desired level of confidence (95% in this case), which is 1.96
p = estimated proportion (0.32, based on the 32% result from the previous poll)
q = 1 - p
E = margin of error (0.02, or 2%)

Substituting the values, we get:

n = (1.96^2 * 0.32 * 0.68) / 0.02^2
n = 752.65

Rounding up to the nearest whole number, we get a sample size of 753. Therefore, to be 95% confident that the estimated percentage will be within 2% of the true percentage, a sample of at least 753 adults is needed.