Question

The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 30 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was $9008 with a standard deviation of $1909. Complete parts (a) through (c) below.

a) What assumptions and conditions must be checked before finding a confidence interval? How would one check them?

A. The data are assumed to be dependent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal. Check the independence assumption by ensuring that there are at least 10​ "successes" and 10​ "failures."

B. The data are assumed to be independent and from a Normal population. Check the independence assumption with the Nearly Normal Condition using a histogram. Check the Normal population assumption with the Randomization Condition.

C. The data are assumed to be independent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal. Check the independence assumption with the Randomization Condition. Check the sample size assumption by ensuring that there are at least 10​ "successes" and 10​ "failures."

D. The data are assumed to be independent and from a Normal population. Check the independence assumption with the Randomization Condition. Check the Normal population assumption with the Nearly Normal Condition using a histogram.

b) Find a 90% confidence interval for the mean loss in value per home.

($___, $___)

(Round to the nearest whole number as needed.)

c) Interpret this interval and explain what 90% confidence means in this context. Choose the correct answer below.

A. One is 90​% confident that the true average loss in home value is between the lower boundary of the interval and the upper boundary of the interval.

B. There is a 90​% chance that the average true loss in home value is between the lower boundary of the interval and the upper boundary of the interval.

C. There is a 90​% chance that the true average loss in home value of the homes sampled is between the lower boundary of the interval and the upper boundary of the interval.

D. One is 90​% confident that the true average loss in home value of the homes sampled is between the lower boundary of the interval and the upper boundary of the interval.

Answer 1

a) What assumptions and conditions must be checked before finding a confidence interval? How would one check them?

Here we want to calculate the confidence interval for the mean.

the main assumptions are the data from the normal population & data is independent.

Assumption of normality check by plotting the histogram.

and assumption of independence is checked by randomization condition.

Answer:-

D) The data are assumed to be independent and from a Normal population. Check the independence assumption with the Randomization Condition. Check the Normal population assumption with the Nearly Normal Condition using a histogram.

b) 90% confidence interval for the mean loss in value per home.

x: loss in value per home.

we sampled 30 bids from potential buyers to estimate the average loss in home value, so n = 30

The sample showed the average loss was $9008 with a standard deviation of $1909.

mean = $ 9008 & std deviation = $1909

for 90% of confidence interval, alpha = 0.10

z value = Zalpha /2  = Z0.10/2 = Z0.05 = 1.645

sample mean = M = 9008
standard error = = √(s2/n)

sM = √(19092/30)

= 348.53
The 90 % confidence interval for mean is

M ± Z(sM)

=008 ± 1.645*348.53
= 9008 ± 573.33

= ( 9008 - 573.33 ; 9008 + 573.33)

= ( 8434.67 , 9581.33)

The 90% confidence interval for mean is

( $8435 , $9581)

c) Interpret this interval and explain what 90% confidence means in this context.

A. One is 90​% confident that the true average loss in home value is between the lower boundary of the interval and the upper boundary of the interval.