Question

3.11. A random sample of 10 different unfurnished 1-bedroom apartments off-campus yield an average monthly rent of $500 with standard deviation $100. A second sample of 10 2-bedroom apartments yield an average rent of $650 with standard deviation $100 a. Suppose that WMU students get a $20 discount on the monthly rent for all 1-bedroom apartments. The discounted monthly rent for the sample of 1-bedroom apartments should yield an average o with standard deviation b. Instead of a $20 discount, suppose that WMU students get a 5% discount on the monthly rent for all 1-bedroom apartments. The discounted monthly rent for the sample of 1-bedroom apartments should yield an average ofih standard deviation c. If you took the 1-bedroom and 2-bedroom samples together, would you guess that the standard deviation of the combined sample is around $100, smaller than $100, or larger than $100

Answer 1

a)

avergae=Σx/n = $550

if $20 is discounted for all 1-bedroom apartment

then average will be= Σ(x-20)/n=Σx/n - 20n/n = $500-20=$480(answer)

std dev before discount= √(Σ(x-xbar)²/(n-1)) = $100

std dev after discount = √(Σ((x - 20)-(xbar-20))²/(n-1)) = √(Σ(x-xbar)²/(n-1))

so, std dev will remain =$100(answer)

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b)

5% discount = $500*5% = $25

so, average will be = $500-25 =$475(answer)

std dev will remain same = $100(answer)

c)

since,the average of both samples vary each other by large value and std dev of both samples are equal

so, we can guess that std dev of combined samples will be greater than 100