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:
103 156 118 89 12 147 122 109 138 99
a. Let µJ denote the average gas usage during January by all houses in this area. Compute a point estimate of µJ.
b. Suppose that 10,000 houses in this area use natural gas for heating. Let t denote the total amount of gas used by all of these houses during January. Estimate t using the given data. What statistic did you use in computing your estimate?
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 based on the sample of Part (a). Which statistic did you use?