When evaluating a chi-square test, describe the importance of the goodness of fit test. Provide an example and explain how the test is used to evaluate data. In replies to peers, provide additional examples not already discussed. 150 word minimum per response.
Respond to peers R1 to R4. Original question is above on the word document all are to be answered with 150 word minimum.
R1.
The Goodness of Fit test is a hypothesis test based on the Chi-squared distribution. The Chi-squared test statistic is used to determine if an observed sampling of data “fits” within a hypothesized distribution. The hypothesized distribution could be based on historical data such as the example in the book of market shares or it could be used to determine if a dataset has varied from random chance, in other words statistically significant. The Goodness of Fit test answers the question has the data we are observing varied enough to cast doubt on the existing knowledge of the distribution.
An example would be if the hypothesized distribution was 75% of GCU Online students are right handed and 25% are left handed and we compared that to observed data in our class. Of course I am making these numbers up! We could perform a hypothesis test with the chi-squared test statistic to determine if we should accept that this claim is true using the data we observe from within our class.
I highly recommend this video if you are interested in a little deeper mathmatical understanding of the Goodness of Fit test.
R2.
When evaluating a chi-square test, the important of the goodness of fit test is to determine whether a random variable has a specific probability distribution (Anderson, et al. 2018). This type of test is used to evaluate data and works by comparing the distribution that you observe to the distribution that was expected if there is no relationship between the categorical variables.
An example of the test would be to take 5 different recruiting stations located in the malls for a week. Collect how many future recruits came into the station for more details about the military. After reviewing the data, it can be determined what are the busiest times to adjust for more or less personnel.
Anderson, D.R., Camm, J.D., Cochran, J.J., Sweeney, D.J., Williams, T.A. (2018). Essentials of Modern Business Statistics with Microsoft Office Excel. Retrieved from https://ng.cengage.com/static/nb/ui/evo/index.html?snapshotId=2473323&id=1222215187&deploymentId=5935181885004794112086336559&eISBN=9780357110584
R3.
A chi-squared test can be described as a statistical test used to compare observed results with expected results. The data used must be random and exclusive from independent variables. This data must also be drawn from a large enough sample. The chi-square test also tests the null hypothesis about the relationship between two variables. The goodness of fit test a statistical hypothesis test used to see how closely observed data mirrors expected data. An example of the chi-square goodness of fit test is a bag of skittles. There are 5 primary flavors, strawberry, green-apple, grape, cherry, and orange. Suppose one was curious about the distribution of flavors and wondered if each flavor is distributed equally. The chi-square goodness of fit test can also these concerns.
R4.
The Chi-square goodness of fit test is a statistic hypothesis to determine whether or not a variable is likely to come from a specified distribution. It is usually used to determine whether sample data represent the full population (SKP, 2021). An example of this would be the colors of candy in a bag like Skittles. Say there are five different colors in a bag of Skittles. The five colors are the variable of the population. The null hypothesis would be all the colors are equally distributed. But when counting the sample, we find the numbers of each color are not equal. Based on the size of our p-value, we can determine if it was large enough to reject the null hypothesis.
