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.

140  148  112  101  130  79  117  91  96  110

(a)

Let μ_J denote the average gas usage during January by all houses in this area. Calculate a point estimate of μ_J.

therms

(b)

Suppose that 10,000 houses in this area 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 given data.

therms

What statistic did you use to calculate your estimate?

sample standard deviation sample variance     sample range sample mean

(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?

sample median population variance     sample standard deviation population mean

Answer 1

a)

point estimate of μ =x̅ = Σxi/n =

112.4

b)

total amount of gas used by all of these houses during January =number of house*average consumption per house =n*x̅=

1124000

sample mean

c)

proportion of all houses that used at least 100 therms=7/10=

0.7

d)

point estimate of the population median usage =

111

sample median