A family is relocating from St. Louis, Missouri, to California. Due to an increa

Question

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. Her realtor friend informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The realtor 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 for the population mean? Assume that the population has a normal distribution. Assume that the central limit theorem applies. b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to 4 decimal places. Round "z value" to 3 decimal places and final answers to 2 decimal places.)

Explanation / Answer

a) Since the sample size is 26 which is less than 30, we need to assume that the original population is normally distributed.

Option A is correct.

b) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 72

90% confidence interval results:

Hence,

90% confidence interval will be:

(194.77, 241.23)

Mean n Sample Mean Std. Err. L. Limit U. Limit 26 218 14.120362 194.77407 241.22593

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