You want to rent an unfurnished one-bedroom apartment in Laguna Beach next year.

Question

You want to rent an unfurnished one-bedroom apartment in Laguna Beach next year. The mean monthly rent for a random sample of 20 apartments advertised in the local newspaper is $2872. Assume that the standard deviation of all apartments in the area is $1191. 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 this statement is true or false. Be sure to explain your answer: This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Laguna Beach area.

Thanks!

Explanation / Answer

90% interval

Margin of error = (1.645*1191)/Sqrt(20) = 438.0503

(2872-438.0503, 2872+438.0503)

= (2433.95, 3310.05)

95% interval

Margin of error = (1.960*1191)/Sqrt(20) = 521.9692

(2872-521.9692, 2872+521.9692)

(2350.031, 3393.969)

99% interval

Margin of error = (2.5758*1191)/Sqrt(20) = 685.9838

(2872-685.9838, 2872+685.9838)%

= (2186.016, 3557.984)

It is false. The 95% Interval means that we are 95% Confident that price of the rents will lies in this interval

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