Question

Fireman's Fund commissioned an online survey of 1,000 wealthy homeowners to find out what they knew about their insurance coverage. Complete parts (a) through (c) below.

(a) When asked whether they knew the replacement value of their home, 66% replied yes. In this case, should Fireman's Fund conclude that more than half of wealthy homeowners know the value of their homes?

Find the 95% confidence interval for the parameter of interest.

The 95% confidence interval for the parameter of interest is (_____ to ______).
(Round fo six decimal places as needed.)

Should Fireman's Fund conclude that more than half of wealthy homeowners know the value of their homes?

A. The entire confidence interval is greater than 0.5, so we can conclude that more than half of wealthy homeowners know the replacement value of their home
B. The entire confidence interval is less than 0.5, so we can conclude that more than half of wealthy homeowners know the replacement value of their home.
C. The confidence interval contains 0.5, so we are unable to conclude that more than half of wealthy homeowners know the replacement value of their home.
D. The confidence interval contains 0.5, so we can conclude that more than half of wealthy homeowners know the replacement value of their home.

(b) Round the interval into a form suitable for presentation.

(c) The results of the survey were accompanied by the statement, "In theory, with probability samples of this size, one could say with 95 percent certainty that the results have a statistical precision of about plus or minus 3 percentage points. This online sample was not a probability sample." What is the point of this comment?

A. The comment is noting the fact that the margin of error for the sample will always be about​ 3% because of the large sample size.
B. The comment is noting the fact that the data set was too large to be considered a probability sample.
C. The comment is recognizing that because the sample was​ online, the respondents chose to respond to the survey and therefore were not randomly​ selected, as in a probability sample.​ Thus, the theoretical precision may not apply here.
D. The comment does not provide any useful information.

Answer 1

a)

x                    =				660
sample size		n                    =		1000
sample proportion     p̂		x/n=		0.6600
std error       =Se		=√(p*(1-p)/n) =		0.0150
for 95 % CI value of z=				1.960
margin of error E=z*std error                            =				0.0294
lower confidence bound=sample proportion-margin of error				0.630640
Upper confidence bound=sample proportion+margin of error				0.689360

therefore 95% CI = 0.630640 ; 0.689360

A. The entire confidence interval is greater than 0.5, so we can conclude that more than half of wealthy homeowners know the replacement value of their home

C. The comment is recognizing that because the sample was​ online, the respondents chose to respond to the survey and therefore were not randomly​ selected, as in a probability sample.​ Thus,the theoretical precision may not apply here.