# The Chi-Square Test and the Related Issues

## Testing Hypotheses

The process of determining correlations between specific data sets or locating a tendency within one of them is a crucial part of assuring quality in the context of any organization (Groebner, Shannon, & Fry, 2014b).

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Therefore, it is imperative to make sure that proper statistical tests are applied to test a certain hypothesis or to identify a trend in the corresponding data set. Seeing that the test involving the measurement of the standard deviation alone is not a possibility, the chi-square test is typically used as the tool for identifying whether the null hypothesis should be accepted or rejected. However, when considering the phenomenon, one must admit that the definitions typically provided for the subject matter and its elements raise several questions among the people who are only exploring the theory.

### Can the chi-square distribution be completely symmetrical, and if it can, under what circumstances?

Groebner, Shannon, and Fry (2014a) make it quite clear that the graphical representation of the chi-square distribution is typically arranged as a curve. However, the authors also note that, with the increase of the degree of freedom, the curve becomes closer to being symmetrical (Groebner et al., 2014). Therefore, one may wonder whether the degree of freedom will have to stretch to the infinity, or whether there is a point at which the image of the chi-square distribution can become completely symmetrical (Inferential statistics, 2016).

### Why is the sample size of at least 30 items typically viewed as sufficient?

The concept of sample size is admittedly vague. Despite the evident significance of the subject matter for carrying out statistical tests, the identification of the items number that is usually viewed as sufficient for conducting a test needs further commentary. For instance, the process of locating the number 30, which is considered to be enough for carrying out a statistical test, could be explained in a more detailed fashion (Chi-square goodness of fit test, 2016). At present, the statement concerning the sufficiency of 30 elements is viewed as an axiom, which is barely passable for the realm of statistics. In other words, a further review of the issue in question is required (HyperStat online: Ch. 16, chi-square, 2016).

### Can the Goodness of Fit be viewed as the expected outcome of the chi-squared test?

Last but not least, the issue regarding the Goodness-of-Fit test needs to be brought up. An admittedly peculiar concept, the phenomenon of the Goodness of Fit is rendered as the degree, to which the outcomes meet the expected results. Therefore, it begs the question of whether the phenomenon of the Goodness of Fit can be equal to the proof of the research hypothesis. In other words, it could be assumed that the value of the Goodness of Fit allows determining whether the null hypothesis should be rejected or confirmed. If there is a correlation between the two concepts, the level of the Goodness of Fit should be in an inverse proportion to the veracity of the null hypothesis (Statistics and probability dictionary, 2016).

Carrying out a statistical analysis is a challenging task. However, the application of the chi-square test will help one make an essential business decision even in the environment that involves an array of variables. Once learning the essential details about the subject matter, one is likely to apply the tests successfully to measure the potential of each decision available.

## Reference List

Chi-square goodness of fit test. (2016). Web.

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Groebner, D. F., Shannon, P. W., & Fry, P. C. (2014a). Chapter 11. Hypothesis tests and estimation for population variance. In Business statistics (9th ed.) (pp. 448-474). Upper Saddle River, NJ: Pearson.

Groebner, D. F., Shannon, P. W., & Fry, P. C. (2014b). Chapter 13. Goodness-of-fit tests and contingency analysis. In Business statistics (9th ed.) (pp. 547-578). Upper Saddle River, NJ: Pearson.

HyperStat online: Ch. 16, chi square. (2016). Web.

Inferential statistics. (2016). Web.

Statistics and probability dictionary. (2016). Web.

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