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 $1100. Assume that the standard deviation is $220. 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.

Yes, this range implies that it will cover 95% of all of the rents in this area.Yes, this is a range where 95% of the means and individual costs will be covered by the interval.    It is impossible to know because we would have to find all of the rents for unfurnished one-bedroom apartments in this area.No, this is a range of values for the mean rent, not for individual rents.No, this confidence interval would include 95% of all individual rents in the area.

Explanation / Answer

Solution:

We have x = $1100, = $220, and n = 103
The 95% confidence interval gives 1400 ± (1.96) 220/10
= 1100 ± 1.96(69.57)
= 1100 ± 136.36.
The 95% confidence interval is ($1236.36, $963.64)

No, this calculation is about estimating the mean apartment rent for a one-bedroom. We do not need
to sample 95% of the apartment prices to estimate . The 95% is the measure of a probability, the
probability that the parameter ( in this case ) is in the calculated interval.

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