Prices of Dwellings. C. P. Barros et al. studied prices of new, resale and unoccupied dwellings in Beijing in the 2011 article “Housing Sale in Urban Beijing” (School of Economics and Management, Technical University of Lisbon). According to the article, the mean price of a newly constructed dwelling space in Beijing (yuan per square meter) is 13993.0 yuan with a standard deviation of 412 yuan. The variable “dwelling price” is known to have a right-skewed distribution.

a. Using units of yuan, determine the sampling distribution of the sample mean for samples of size 200. Interpret your result.

b. Repeat part

(a) for samples of size 600.

c. Why can you still answer parts

(a) and

(b) when the distribution of the prices of dwellings is not normal, but rather right skewed?

d. What is the probability that the sampling error made in estimating the population mean dwelling price by the mean dwelling price of a simple random sample of 200 dwellings will be at most 50 yuan?

e. Repeat part

(d) for samples of size 600.