Question

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled 38 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was ​$9547 with a standard deviation of $2033.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 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.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."

C.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.

D.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) Find a 95% 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 95​% confidence means in this context. Choose the correct answer below.

A.One is 95​% 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 95​% 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.One is 95​% 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.

D.There is a 95​% 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.

Answer 1