To determine which option is not a condition required for a chi-square goodness-of-fit test, let's review the conditions needed for such a test:
1. Data should be collected using a random sample or randomized experiment: This ensures that the sample accurately represents the population.
2. When sampling without replacement, the sample size cannot be greater than 10 percent of the population size: This condition helps to maintain the independence of observations, which is crucial for the validity of the test.
3. All expected counts should be greater than 5: This condition ensures that the chi-square approximation to the true distribution of test statistics is valid. If expected counts are too small, the approximation is not accurate.
4. The distribution of the sample should be approximately normal: This is not a requirement for the chi-square goodness-of-fit test. The chi-square test does not assume normality of the data but rather that the data are categorical and fit a certain expected distribution.
5. During the sampling process, each individual chosen should be independent of the next: This condition is essential for the statistical validity of the chi-square test. Independence of observations ensures that the results are not biased or correlated.
Given these conditions, it is clear that the statement "The distribution of the sample should be approximately normal" is not a condition required for a chi-square goodness-of-fit test.
Therefore, the correct answer is:
D) The distribution of the sample should be approximately normal.
