Question

ta) A random sample ot 10 houses in a particular area, each of which is heated with natural gas, s selected and the amount of gas (therms) used during the month of lanuary is determined tor each house. The resuing observations are 103, 138, 109, 122, 125, 148, iso, su, 9, 118. Let ? denote the average gas usage during January by all houses in this area. Compute a port estimate of c. therms o Bao o ) suppose there are 29,000 houses in this area that use natural qas ror heating. Let ? denote the total amount or gas used by all or these houses durinQ January. Estirnate ? usinq the deta of part ( What estimator did you use in computing your estimate? 02 c) use the data in part (a) to estimate , the proportian of ail houses that used at laast 100 therms. d) Cia a point estimate of the population median unaga (tha middle valua in tha population of all hausas) based on the samale of part (a) therm What estimator did you use:

Answer 1

a)
point estimate of mu = 119.2

b)
n = 29000
total amount = 29000 * 119.2 = 3456800

nxbar estimator used

c)
The proportion of all houses that used at least 100 therms, you could examine the above data and count the number. Then divide it by the total for the sample, which was 10.
It would be all houses using greater than or equal to 100:
Pi = 8/10 = 4/5

d)

80, 99 , 103 , 109 , 118 , 122 , 125, 138 , 148 , 150

Median is the middle number of data

Median = (118 + 122)/2 = 120