Question

In the wake of the Newtown Connecticut tragedy, a local school district surveyed a random sample of 250 residents and found 173 that would be in favor stationing a heavily armed police officer on the school property continuously.

a.   Estimate with 90% confidence the true proportion of all residents in favor of such a policy.

b.   How many residents would need to be sampled to estimate the desired proportion to within 2 percent, using 90% confidence?

Answer 1

Given that, n = 250 and x = 173

=> sample proportion = 173/250 = 0.692

A 90% confidence level has significance level of 0.10 and critical value is,

a) The 90% confidence interval for population proportion (p) is,

Therefore, the 90% estimate of the true proportion of all residents in favour of such a policy is (0.6440, 0.7400)

b) Given that, margin of error (E) = 0.02 (2%)

We want to find the sample size (n),

Therefore, required sample size is 1442