Question

Be sure to explain your answer:

You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $2534. Assume that the standard deviation is $670. Find the 90%, 95%, and 99% confidence intervals for the mean monthly rent for this category of apartments.

Look at the 95% confidence interval and say whether the following statement is true or false. “This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area.”

Answer 1

Answer:

a) .For 90%

Mean(X) = 2534,

Z* =1.645,
SD = 670,
N = 10
Confidence interval = 2534±1.645*(670/√10)
= 2534± 348.53

I am 90% that the true number of monthly rent between $2185.47 to $2882.53

For 95%

Mean(X) = 2534,
Z* =1.96,
SD = 670,
N = 10
Confidence interval = 2534±1.96*(670/√10)
= 2534± 415.26

I am 95% that the true number of monthly rent between $2118.74 to $2949.26

For 99%
Mean(X) = 2534,
Z* =2.576,
SD = 670,
N = 10
Confidence interval = 2534±2.576*(670/√10)
= 2534± 545.77

I am 95% that the true number of monthly rent between $1988.23 to $3079.77

b)

Yes, because mean $2534 lies in the interval between $2118.74 to $2949.26 This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area.

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