Primary Heating Fuel. According to Current Housing Reports, published by the U.S. Census Bureau, the primary heating fuel for all occupied housing units is distributed as follows.

Primary heating fuel Percentage Utility gas 50.8 Fuel oil, kerosene 7.9 Electricity 33.9 Bottled, tank, or LPG 5.2 Wood and other fuel 1.9 None 0.3 Suppose that you want to determine whether the distribution of primary heating fuel for occupied housing units built after 2010 differs from that of all occupied housing units. To decide, you take a random sample of housing units built after 2010 and obtain a frequency distribution of their primary heating fuel.

a. Identify the population and variable under consideration here.

b. For each of the following sample sizes, determine whether conducting a chi-square goodness-of-fit test is appropriate and explain your answers: 200; 300; 400.

c. Strictly speaking, what is the smallest sample size for which conducting a chi-square goodness-of-fit test is appropriate?