Statistics Homework

Question

If n = 380 and ˆpp^ (p-hat) = 0.3, construct a 90% confidence interval.

Give your answers to three decimals

Answer 1

This is a typical central limit theorem problem, i.e., "construct the confidence interval," but you need to know a couple of extra things to solve it.

1.) A proportion is a mean.

2.) The variance of a proportion is always p*(1 - p). So in this case, the variance is (.30)(.70)

3.) The standard error of the mean, SE_mean, remains, sqrt(variance/N). In this case, = sqrt((.30 * .70)/380)

4.) Your sample size is well large enough to use a Z score instead of a t score for your test-statistic.

5.) The Z-critical, two-tailed, alpha = .10. p(Z) < .05 and p(Z > .95). Z = -1.645 and 1.645. You can verify this with excel, NORM.S.DIST(.05) and NORM.S.DIST(.95)

6.) Your CI95 is: p-hat +- Z_crit*SE_mean