Suppose we have a large population of houses in a community. The average annual

Question

Suppose we have a large population of houses in a community. The average annual heating expense for each house is $400 with a population standard deviation of $25. A random sample of 25 houses had a sample mean of $380 and a sample standard deviation of $35. a. What is the mean of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses? b. What is the standard deviation of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses? c. Is it safe to assume that the sampling distribution of the sample mean for samples of size 25 is normally distributed? Why or why not?

Explanation / Answer

18)a) sample mean will remain equal to population mean =400

b)as std deviation of sample mean =population std deviation/(n)1/2 =25/(25)1/2 =5

c) No as we do not know if population distribution is normal and sample size is less then 30 we can not asume that sampling distribution is normal.

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