2 You want to rent an unfurnished onebedroom apartment for n

2. You want to rent an unfurnished one-bedroom apartment for next semester. You take a random sample of 10 apartments advertised in the local newspaper and record the monthly rent. Here are the sample data: 500, 650, 600, 505, 450, 550, 515, 495, 650, 395 a. Find the sample mean b. Find the sample median c. Find the standard deviation d. Find the variance e. Find the range f. Construct a 95% confidence interval estimate of the population mean. (You may assume that the original population is normally distributed.) g. Use a 0.05 significance level to test the claim that the mean rent of all advertised apartments is greater than $500 per month.

I only need part G done. Thanks

Solution

a)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    5310      
As n =    10      
Thus,          
X =    531   [ANSWER]

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b)  

Ordering the data,

395
450
495
500
505
515
550
600
650
650

Thus, the median is the average of the 5th and 6th entries,

median = (505+515)/2 = 510 [ANSWER]

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c)
          
Setting up tables,          
x   x - X   (x - X)^2  
500   -31   961  
650   119   14161  
600   69   4761  
505   -26   676  
450   -81   6561  
550   19   361  
515   -16   256  
495   -36   1296  
650   119   14161  
395   -136   18496  

Thus, Sum(x - X)^2 =    61690      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    10      
          
s^2 =    6854.444444      
          
Thus,          
          
s =    82.7915723   [ANSWER, STANDARD DEVIATION]

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d)  

s^2 =    6854.444444   [ANSWER, VARIANCE]

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e)
          
Also, we have          
          
Maximum =    650      
Minimum =    395      
Range = max - min =    255   [ANSWER, RANGE]  

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