Discussion
A frequency data is classified in 10 classes and normal \(N(\mu, \sigma^{2})\) distribution is fitted to data after estimating the parameters. To use \(\chi^{2}\) goodness of fit test, two classes are combined into one class. Hence the degrees of freedom associated with \(\chi^{2}\) test are :
Answer: D
The degrees of freedom are 6.
For a chi-square goodness of fit test, df = (number of classes used) - 1 - (number of parameters estimated). Combining two classes leaves 9 classes, and fitting a normal distribution estimates two parameters, \(\mu\) and \(\sigma^{2}\):
\[ \text{df} = 9 - 1 - 2 = 6 \]
9 is the number of classes, 8 forgets the estimated parameters, and 7 subtracts only one of them.
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