Question

Which of the given is not a requirement for the validity of the chi‑square goodness‑of‑fit test?

1) independent observations

2) all observations falling into one of k outcome classes

3) a fixed number of observations

4) normally distributed data

Answer 1

Chi-squre goodness of fit test is a non parametric test which is very useful to find find out how the observed value of a given sample is significantly different from the expected value or not. Chi-Square goodness of fit test determines how well theoretical distribution fits the empirical distribution.

Assumption required for chi-squre test:-

1) For chi-squre test you should have independent observation. And collection process of sample data is simple random sampling.

2) The variable under study is categorical variable.

3) The groups of the categorical variable must be mutually exclusive.

4)  At least 5 expected frequencies in each group.

We see that there is no assumption on the population or parent distribution of the sample data. And we also know that chi-squre goodness of fit test is a non parametric test i.e assumption on population distribution or parent distribution is not required. So from the above discussion we see that independent observation, categorical variable, and fixed number of observations required for chi-squre goodness of fit test and normally distributed data not required for chi-squre goodness of fit test.

Ans:- Correct answer is,

Option 4) normally distributed data.