To estimate the average monthly rent for 1 bedroom apartment

To estimate the average monthly rent for 1 bedroom apartments, 14 complexes were randomly selected in Orlando. The mean cost of the selected complexes is $995 with a standard devaition of $97.

1. Find and interpret a 98% confidence interval for the mean monthly rent of all 1 bedroom apartments.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    995          
t(alpha/2) = critical t for the confidence interval =    2.650308838          
s = sample standard deviation =    97          
n = sample size =    14          
df = n - 1 =    13          
Thus,              
              
Lower bound =    926.2924913          
Upper bound =    1063.707509          
              
Thus, the confidence interval is              
              
(   926.2924913   ,   1063.707509   ) [ANSWER]

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Thus, we are 98% confident that the true mean monthly rent of all 1 bedroom apartments is between $926.29 and $1063.71.