In 2012, a survey of 83 homes in a region found that 49 had overestimated market

Question

In 2012, a survey of 83 homes in a region found that 49 had overestimated market values. Suppose you want to estimate the true proportion of homes in this region with market values that are overestimated.

a)Here the population of interest is:
proportion of home with overestimated market value
83 homes whose market values were surveyed
49 homes with overestimated market value
all homes in the region

b)Here the sample is:

all homes in the region
49 homes with overestimated market value
83 homes whose market values were surveyed
proportion of home with overestimated market value

c)What is the target parameter in this problem?

83 sampled homes
proportion of homes with overestimated market values in the sample
proportion of homes with overestimated market values in the region
no parameter is involved in this problem

d)Here, the standard error of sample proportion takes the value: [Answer to 4 decimal places]

e)Here, the margin of error for the 95% confidence interval of sample proportion is (here z* = 1.960) [Answer to 4 decimal places]

f)The 95% confidence interval of proportion of homes in the region with overestimated market values:

(0.5016, 0.6791)
(0.4999, 0.6809)
(0.4846, 0.6962)
(0.4819, 0.6988)

g)Is the sample size sufficiently large to compute the above 95% confidence interval?

Yes, because n[^(p)] ? 10 and n(1?[^(p)]) ? 10.
Yes, because n ? 30.
It is not possible to answer this question without knowing what is the number of failure here.
No, the sample size is actually not sufficiently large.

Explanation / Answer

Ans:

a)all homes in the region

b)83 homes whose market values were surveyed

c)proportion of homes with overestimated market values in the region

d)sample proportion=49/83=0.59036

standard error fro proportion=sqrt(0.59036*(1-0.59036)/83)=0.0540

e)Margin of error=1.960*0.0540=0.1058

f)95% confidence interval for p

=0.5904+/-0.1058

=(0.4846, 0.6962)

g)Yes, because n[^(p)] ? 10 and n(1?[^(p)]) ? 10.

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