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 amount of gas (therms) used during the month of January is determined for each house. The resulting observations are 103, 156, 118, 89, 125, 147, 122, 109, 138, 99 a) Let mu denote the average gas usage during January by all houses in this area. Compute a point estimate of mu and the estimated standard error. (b) Let theta denote the proportion of all houses that used at least 100 therms. Compute a point estimate of theta and the estimated standard error.

Explanation / Answer

a)

b) as there are 8 house which uses at least 100 therms out of 10,

point estimate =8/10=0.8

std error =(p(1-p)/n)1/2 =0.1265

X 103 156 118 89 125 147 122 109 138 99 mean(X) 120.600 std deviation(S) 21.578 std error =S/(n)1/2 6.823

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