Question

Volunteering: The General Social Survey asked 1306 people whether they performed any volunteer work during the past year. A total of 521 people said they did. Part: 0/3 Part 1 of 3 (a) Find a point estimate for the proportion of people who performed volunteer work during the past year. Round the answer to at least three decimal places. The point estimate for the proportion of people who performed volunteer work during the past year is

B: construct a 99% confidence interval for the proportion of people who performed volunteer work during the past year, round answers to at least three decimal

C construct a 95 confidence interval for the proportion of people who performed volunteer work during the past year, round answers to at least three decimal

D A sociologist states that 43% of Americans perform volunteer work in a given year. Does the confidence interval of 99 or 95 contradict this statement

Answer 1

a)

sample success x =		521
sample size n=		1306
pt estiamte p̂ =x/n=		0.3989

b)

se= √(p*(1-p)/n) =

0.0135

for 99 % CI value of z=

2.576

from excel:normsinv((1+0.99)/2)

margin of error E=z*std error   =		0.0349
lower bound=p̂ -E                       =		0.3640
Upper bound=p̂ +E                     =		0.4338
from above 99% confidence interval for population proportion =(0.364,0.434)

c)

for 95 % CI value of z=

1.960

from excel:normsinv((1+0.95)/2)

margin of error E=z*std error   =		0.0266
lower bound=p̂ -E                       =		0.3723
Upper bound=p̂ +E                     =		0.4255
from above 95% confidence interval for population proportion =(0.372,0.425)

d)

confidence interval of 95 contradict this statement ; since 43% is not contained in that interval