The researcher needs a minimum sample size of 1093 young urban people (ages 21 to 35 years) to estimate the proportion of those who go to at least 3 concerts a year with a 95% confidence level and an accuracy of within 1%.
To find the minimum sample size necessary to estimate the proportion of young urban people who go to at least 3 concerts a year with a 95% confidence level and an accuracy of within 1%, we can use the formula:
n = (z^2 * p * q) / E^2
where:
n is the minimum sample size
z is the z-score for the confidence level (in this case, 1.96 for a 95% confidence level)
p is the estimated proportion from previous studies (42% or 0.42)
q is 1 - p (the complement of p)
E is the maximum error or accuracy (1% or 0.01)
Plugging in the values, we get:
n = (1.96^2 * 0.42 * 0.58) / 0.01^2
n = 1.96^2 * 0.42 * 0.58 * 10000
n = 1092.33
Rounding up to the nearest whole number, the minimum sample size necessary is 1093.
Therefore, the researcher needs a minimum sample size of 1093 young urban people (ages 21 to 35 years) to estimate the proportion of those who go to at least 3 concerts a year with a 95% confidence level and an accuracy of within 1%.