The housing market has recovered slowly from the economic crisis of 2000. recent
ID: 3208628 • Letter: T
Question
The housing market has recovered slowly from the economic crisis of 2000. recently, in one large community, reactors randomly sampled 36 hits from potential buy on estimate the average loss in home value. The sample showed the average loss was $8417 with a standard deviation of $1411 Complete Parts (a) through (c) below. What assumptions and conditions must be checked before finding confidence Interval? How would one check them? The data are assumed to be independent and from a Normal population. Check the independence assume or with the Random condition. Check the Normal population assumption with the Nearly Normal Condition using a histogram. 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 The data are assumed to be dependent and to have a sample size large enough to have sampling contribution that is approximately Normal Check the independence assumption by ring that there are at lessthanorequalto 'successes' end 10 failures The data are assumed to an dependent and to have a sample size that is large enough have a sampling distribution that is approximately. Check the independence assumption with the Randomization Condition. Check the sample size assumption by ensuring that there are at least 10"success " and "failures" Find a 90% confide interval for the mean loss in value per home Interpret this interval and explain what 90% confidence means in context, Choose the correct answer below. One is 90% confidant 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 interwar One is confident that the true between the lower boundary of interval and the upper nondairy at the There is a 90% change that the average true los in home value is between the lower boundary of the interval art the upper boundary of the interval 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 intervalExplanation / Answer
a.
Option A
b.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=8417
Standard deviation( sd )=1411
Sample Size(n)=36
Confidence Interval = [ 8417 ± t a/2 ( 1411/ Sqrt ( 36) ) ]
= [ 8417 - 1.69 * (235.167) , 8417 + 1.69 * (235.167) ]
= [ 8019.568,8814.432 ]
= [ 8019.568,8814.432 ]
c.
Interpretations:
1) We are 90% sure that the interval [8019.568 , 8814.432 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population mean
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