A random sample of 10 houses heated with natural gas in a particular area is sel

Question

A random sample of 10 houses heated with natural gas in a particular area is selected, and the amount of gas (in therms) used during the month of January is determined for each house. The resulting observations are as follows:

154  107  127  98  117  147  129  112  164  133

(a) Let J denote the average gas usage during January by all houses in this area. Compute a point estimate of J.
therms

(b) Suppose that 10,000 houses in this area use natural gas for heating. Let denote the total amount of gas used by all of these houses during January. Estimate using the given data.
therms

What statistic did you use in computing your estimate?

sample variance

sample range    

sample means

ample standard deviation

(c) Use the given data to estimate p, the proportion of all houses that used at least 100 therms.


(d) Give a point estimate of the population median usage based on the given sample.
therms

Which statistic did you use?

population variance

sample median    

population mean

sample standard deviation

Explanation / Answer

Solution:-

a) Mean = (Sum of terms/Number of terms)
  
= (154 + 107 + 127 + 98 + 117 + 147 + 129 + 112 + 164 + 133)/10

= 1288/10
  
= 128.8

b) 10000 * 128.8 = 1288000

c) p = 9/10 = 0.9

d) median = (127+129)/2
= 256/2
= 128

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