A family is relocating from St Louis Missouri to California

A family is relocating from St. Louis. Missouri. to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The ream also tells them that based on her prior experience, the population standard deviation is 72 days Use Table 1 a. What assumption regarding the population is necessary for making an interval estimate of the population mean? Assume that the population has a normal distribution. Assume that the central limit theorem applies . b. Construct a 90% confidence interval of the mean sale time for all homes in the neighborhood. (Round your intermediate calculations to 4 decimal places,z value and final answers to 2 decimal places.) Confidence interval to

Solution

A)

Assume that the central limit theorem applies. [ANSWER]

We do not need to assume that the underlying distirbution is normal, because the sampling distrbution of means will be approximately normal if the central limit theorem applies.

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    218          
z(alpha/2) = critical z for the confidence interval =    1.64          
s = sample standard deviation =    72          
n = sample size =    26          
              
Thus,              
Margin of Error E =    23.15739324          
Lower bound =    194.8426068          
Upper bound =    241.1573932          
              
Thus, the confidence interval is              
              
(   194.84   ,   241.16   ) [ANSWER]