Question

In: Statistics and Probability

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​...

The housing market has recovered slowly from the economic crisis of 2008.​ Recently, in one large​ community, realtors randomly sampled 28 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was ​$8644 with a standard deviation of ​$1157.

A. Find a 99​% confidence interval for the mean loss in value per home.

​($__​,$__​ )

Solutions

Expert Solution

Solution :

Given that,

= $8644

s = $1157

n = 28

Degrees of freedom = df = n - 1 = 28 - 1 = 27

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,27= 2.771

Margin of error = E = t/2,df * (s /n)   

= 2.771 * (1157 / 28) = 605.8859

The 99% confidence interval estimate of the population mean is,

- E < < + E

8644 - 605.8859< <8644 +605.8859

28038.1141 < < 9249.8859

($28038.1141 , $ 9249.8859 )


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