Question

(a)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 138, 145, 99, 125, 144, 103, 109, 89, 122, 118. Let μ denote the average gas usage during January by all houses in this area. Compute a point estimate of μ.

(b) Suppose there are 25,000 houses in this area that use natural gas for heating. Let τ denote the total amount of gas used by all of these houses during January. Estimate τ using the data of part (a).
therms

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

(d) Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample of part (a).

Answer 1

Explanation:

From the given sample of 10 entries we find

Mean =119.2

Median =120

Point estimate of μ.=
`19.2`

b) Suppose there are 25,000 houses in this area that use natural gas for heating. Let τ denote the total amount of gas used by all of these houses during January.

τ =
`25000(119.2)\\= 2980000`

c) Proportion would be sample proportion =
`(8)/(10) =0.8`

d) Population median usage = sample median usage = 120