A random sample of 10 houses in a particular area, each of which is heated with

Question

A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the am cunt of gas (therms) used during the month of January is determined for each no use. The resulting observations are 122, 99, 142, 116, 125, 146, 138, 90, 109, 103. Let mu denote the average gas usage during January by all houses in this area. Compute a point estimate of mu. ___________ therms Suppose there are 17,000 houses in this area that use natural gas for heating. Let tau denote the total amount of gas used by all of these houses curing January. Estimate tau using the data of part (a). ___________ therms What estimate did you use in computing your estimate? nx bar s/x bar s x bar p cap Use the data in part (a) to estimate rho, the proportion of all houses that used at least 100 therms. Give e point estimate of the population median usage (the middle value in the population of all houses) based on the sample of part (a) _________ therms What estimator did you use? X bar s p cap x bar s/x bar

Explanation / Answer

Given,

10 houses with average gas usage as 122,99,142,118,125,148,138,90,109,103

A.a)point estimate(X)=122+99+142+118+125+148+138+90+109+103/10

point estimate(X)=119.4

A.b) total amount of gas=119.4*17000=2029800

estimator used is nx

A.c) proportion of all houses used atleast 100 therms is

p=8/10 or 0.8

A.d) arrange the data values in ascending order

90,99,103,109,118,122,125,138,142,148

median=118+122/2=120

point estimate of median is 120

estimator used is x~

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