Chi Squared Goodness of Fit Test Calculator TI 83 Plus

Chi-Square Formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Chi-Square Statistic (χ²):

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1. What is Chi-Square Goodness of Fit Test?

The Chi-Square Goodness of Fit Test determines whether observed categorical data matches an expected distribution. It's commonly used to test hypotheses about distributions and proportions.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Where:

\( O \) — Observed counts
\( E \) — Expected counts under null hypothesis
\( \sum \) — Sum over all categories

Explanation: The test compares observed frequencies with expected frequencies, with larger discrepancies resulting in higher chi-square values.

3. Importance of Chi-Square Test

Details: This test is fundamental in statistics for testing categorical data distributions, used in genetics, marketing research, quality control, and more.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. Expected counts should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of this test?
A: The test assumes random sampling, categorical data, and expected counts ≥5 in each category.

Q2: How do I interpret the chi-square value?
A: Compare your result to critical values from chi-square distribution tables with appropriate degrees of freedom.

Q3: What are degrees of freedom in this test?
A: For goodness-of-fit, df = number of categories - 1 - number of estimated parameters.

Q4: Can I use this for 2x2 contingency tables?
A: No, this is for goodness-of-fit. For contingency tables, use the chi-square test of independence.

Q5: How does this relate to TI-83 Plus calculations?
A: This replicates the χ²GOF-Test function on TI-83 Plus calculators, which performs goodness-of-fit tests.