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In: Statistics and Probability

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of...

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 21 houses that sold in their neighborhood took an average time of 120 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 25 days. What assumption regarding the population is necessary for making an interval estimate for the population mean?

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

. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood

Solutions

Expert Solution

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

.the population should be normally distributed

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

The sample mean should follow a normal distribution

Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood

The provided sample mean is 120 and the population standard deviation is 25. The size of the sample is n = 21 and the required confidence level is 99%.

Based on the provided information, the critical z-value for α=0.01 is z_c = 2.576

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

CI= (120 - 14.052, 120 + 14.052)

CI = (105.948, 134.052)

orchestra answered 1 year ago
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