Step 1: Define the chi-square test.
The chi-square test is a statistical method for determining if there is a significant association between observed and expected frequencies. It is classified as a non-parametric test because it does not necessitate a normal distribution of the data.
Step 2: Evaluate each option.
- (A) It is a non-parametric test: Accurate. The chi-square test does not assume any underlying data distribution, qualifying it as non-parametric.
- (B) It is based on frequencies, not on parameters like mean and standard deviation: Accurate. The chi-square test operates with frequency data (observed versus expected counts) and does not involve parameters such as mean and standard deviation.
- (C) It can be used when individual observations of the sample are dependent: Inaccurate. The chi-square test presumes independent observations and is unsuitable for dependent data.
- (D) It can be used for testing hypotheses but is not useful for estimation: Accurate. The chi-square test is primarily employed for hypothesis testing, particularly with categorical data, but it does not provide parameter estimates.
Step 3: Conclusion.
The correct statements are (A), (B), and (D). The chi-square test is non-parametric, frequency-based, and utilized for hypothesis testing.