13. (17 pts) You want to rent an unfurnished one-bedroom apartment for next seme

Question

13. (17 pts) You want to rent an unfurnished one-bedroom apartment for next semester. mean monthly rent for a random sample of 10 apartments advertised in $550. Assume that the standard deviation for all apartments is $100 The the local newspaper is a) How many one-bedroom apartments would you need to sample if you wanted the standard deviation of x-bar to be $21? b) Find a 90% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community c) How large a sample of one-bedroom apartments would be needed to estimate the mean within ±$20 with 90% confidence?

Explanation / Answer

a)

for std deviaiton of sampling mean =std deviation of population/(n)1/2

n =(100/21)2 =~23

b)

here std error of mean =std deviaiton/(n)1/2 =100/(10)1/2 =31.62

for 90% CI ; critical value of z =1.645

therefore 90% confidence interval =sample mean -/+ z*Std error =550 -/+1.645*31.62 =497.99 ; 602.01

c)

for margin of error E =20

for 90% CI ; critical value of z =1.645

therefore required sample size n=(z*std deviation/E)2 =(1.645*100/20)2 ~ 68

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