The Students Calculate A Chi-Squared Value Of 92.86 And Compare It With A Critical Value Of 7.82. Which Of The Following Best Completes The Chi-Square Goodness-Of-Fit Test?

General
1

The Students Calculate A Chi-Squared Value Of 92.86 And Compare It With A Critical Value Of 7.82. Which Of The Following Best Completes The Chi-Square Goodness-Of-Fit Test?

2

What is the Chi-Square Goodness-Of-Fit Test and how is it completed?

Answer:
The Chi-Square Goodness-Of-Fit Test is a statistical test used to determine whether there is a significant difference between the observed frequency distribution and the expected frequency distribution in a categorical data set. This test is often used to assess how well the observed data fits a theoretical or expected distribution.

In the context of the information provided, it seems that the students have calculated a Chi-Squared value of 92.86 and compared it with a critical value of 7.82. The Chi-Squared value obtained is significantly higher than the critical value, indicating that there is a significant difference between the observed and expected frequencies.

To complete the Chi-Square Goodness-Of-Fit Test:

  1. Formulate Hypotheses: Begin by stating the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis typically states that there is no significant difference between the observed and expected frequencies.

  2. Calculate the Chi-Squared Value: This involves summing up the squared differences between the observed and expected frequencies divided by the expected frequency for each category.

  3. Determine Degrees of Freedom: Degrees of freedom in the Chi-Square test are calculated as the number of categories minus 1.

  4. Compare Calculated Chi-Squared Value with Critical Value: The critical value is obtained from the Chi-Square distribution table based on the chosen level of significance and the degrees of freedom. If the calculated Chi-Squared value is greater than the critical value, the null hypothesis is rejected, indicating a significant difference.

In this scenario, with a Chi-Squared value of 92.86 and a critical value of 7.82, the Chi-Square test strongly supports rejecting the null hypothesis. This suggests that there is a significant difference between the observed and expected frequencies in the data set being analyzed.