Question

QUESTION PART A: Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E.that corresponds to a sample of size 300 with 44% successes at a confidence level of 99.9%.

M.E. = %

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place

QUESTION PART B: We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 68 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county.

Give your answers as decimals, to three places.

_____ < p < _____

Answer 1

A)

std error se= √(p*(1-p)/n) =		0.0287
for 99.9 % CI value of z=		3.291
margin of error E=z*std error   =		0.0943 ~ 9.4 %

B)

sample success x =		68
sample size          n=		100
sample proportion p̂ =x/n=		0.6800
std error se= √(p*(1-p)/n) =		0.0466
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0914
lower bound=p̂ -E                       =		0.589
Upper bound=p̂ +E                     =		0.771

95% confidence interval for the proportion : 0.589 < p < 0.771