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 75 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 8 days

What assumption regarding the population is necessary for making an interval estimate for the population mean?

2) Assume that the population has a normal distribution.

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 answer to 2 decimal places.)

a.

What assumption regarding the population is necessary for making an interval estimate for the population mean?

1) Assume that the central limit theorem applies.

2) Assume that the population has a normal distribution.

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 answer to 2 decimal places.)

Explanation / Answer

assumption regarding the population  necessary are :

that 1)population follows normal distribution

2) and sample taken is random

b)

std error =std deviaiton/(n)1/2 =8/(26)1/2 =1.5689

for 90% CI ; z=1.645

hence confidence interval =sample eman -/+ z*std error =72.42 ; 77.58

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