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# Working with the Chi-Square Procedure.

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Suppose that you want to decide whether the distribution of primary heating fuel of occupied housing units built after 1974 differs from that of all occupied housing units. To help you decide, you take a random sample of n housing units built after 1974 and obtain a frequency distribution of their primary heating fuel.

The primary heating fuel for all occupied housing units is distributed as follows.

Primary heating fuel Percentage
Natural gas 51.3
Fuel oil, kerosene 10.9
Electricity 29.4
Liquid propane gas 5.4
Wood 2.2
Other 0.8

a. Identify the population and variable under
consideration.

b. For each of the following sample sizes (values of n),
decide whether conducting a chi-square goodness-of-fit
test is reasonable and explain your answer.: 100, 150;
200; 250

##### Solution Summary

Suppose that you want to decide whether the distribution of primary heating fuel of occupied housing units built after 1974 differs from that of all occupied housing units. To help you decide, you take a random sample of n housing units built after 1974 and obtain a frequency distribution of their primary heating fuel.

The primary heating fuel for all occupied housing units is distributed as follows.

Primary heating fuel Percentage
Natural gas 51.3
Fuel oil, kerosene 10.9
Electricity 29.4
Liquid propane gas 5.4
Wood 2.2
Other 0.8

a. Identify the population and variable under
consideration.

b. For each of the following sample sizes (values of n),
decide whether conducting a chi-square goodness-of-fit
test is reasonable and explain your answer.: 100, 150;
200; 250

##### Solution Preview

a. The population is the distribution of primary heating fuel of occupied housing units built (after 1974) and the variable is the different primary heating fuels, like Natural gas, Fuel oil, kerosene etc.

<br>b. The formula of chi-square goodness-of-fit test is:
<br> X2=SUM(Observed-Expected)^2/Expected
<br>However, two assumptions are to ...

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