A research company conducts a poll in a particular geographical
area asking adults to imagine a ladder with 10 rungs. Rung 0
represents the worst possible life and rung 10 represents the best
possible life. Respondents are asked what rung they would say they
are on. Responses are classified as "Thriving" (standing on rung 7
or higher and expecting to be on rung 8 or higher five years from
now), "Suffering" (standing on rung 4 or lower and expecting to be
on rung 4 or lower 5 years from now), or "Struggling" (not
thriving or suffering). From a sample of 1800 people, results
found 40% of respondents considered themselves to be "thriving."
Complete parts a and b below.
a) Calculate the margin of error for the proportion of adults
in this particular geographical area who were rated
as "thriving" for 90% confidence
b) Would the margin of error be larger or smaller for 85%
confidence? Choose one.
A. To be less confident, the interval needs to contain the true
proportion less often, so the margin of error would be larger.
B. To be less confident, the interval needs to contain the true
proportion more often, so the margin of error would be larger.
C. To be less confident, the interval needs to contain the true
proportion less often, so the margin of error would be
smaller.
D. To be less confident, the interval needs to contain the true
proportion more often, so the margin of error would be
smaller.