This is a Statistics problem based on confidence

Question

An Orlando radio station is interested in knowing the percentage of their listeners who attend their Summer Concert Series. How many listeners would the radio station need to sample to determine with a 95% confidence that they attend the summer concerts within 7%?

Answer 1

From n ≥ p(1 − p)z_c² ÷ E², construct n ≥ 0.5(1 − 0.5)(1.96)² ÷ 0.07² which gives 196 exactly. Then a sample of at least 196 listeners is required.

Note that, in the absence of information about the population proportion p, a conservative value of p = 0.5 is used. As p goes to 0.5, the required sample size increases because p(1 − p) is at a maximum when p is equal to 0.5 and setting p at 0.5 ensures a sample size large enough to give the desired margin of error.

Also, z_c = 1.96 corresponds to 0.95 or 95% in a Table Of Proportions Of Area Under The Standard Normal Curve.