You want to rent an unfurnished one-bedroom apartment in Boston next year. The m

Question

You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 13 apartments advertised in the local newspaper is $1400. Assume that the standard deviation is $260. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. (Round your answers to two decimal places.)

$  , $

Will the 95% confidence interval include approximately 95% of the rents of all unfurnished one-bedroom apartments in this area? Explain why or why not. (Pick One)

A)Yes, this range implies that it will cover 95% of all of the rents in this area.

B) No, this is a range of values for the mean rent, not for individual rents.     

C) No, this confidence interval would include 95% of all individual rents in the area.

D) Yes, this is a range where 95% of the means and individual costs will be covered by the interval.

E) It is impossible to know because we would have to find all of the rents for unfurnished one-bedroom apartments in this area.

Explanation / Answer

Confidence interval for 95% confidence level has z=1.96 and the formula

(Mean-z*Sigma/sqrt(n) , Mean+ z* Sigma/sqrt(n) ) = [1400- 1.96*260/sqrt(13) , 1400+1.96* 260/sqrt(13)] = [1258.66, 1541.33]

For the second question, the correct answer is B. This is for mean rent, not individual rents

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