If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,
In what interval range does the P value fall?

Verified step by step guidance

1. Step 1: Understand the problem. The chi-square test is used to determine whether there is a significant difference between the observed and expected data. Here, the chi-square value is 7.83, and the degrees of freedom (df) are 4. We need to determine the range of the P-value.
2. Step 2: Recall the relationship between the chi-square value, degrees of freedom, and the P-value. The P-value is determined by comparing the chi-square value to a chi-square distribution table for the given degrees of freedom.
3. Step 3: Locate the row in the chi-square distribution table corresponding to 4 degrees of freedom. Identify the chi-square values in this row that are closest to 7.83. These values will help determine the range of the P-value.
4. Step 4: Find the P-value intervals associated with the chi-square values identified in Step 3. The P-value decreases as the chi-square value increases, so the range will correspond to the interval between the two closest chi-square values.
5. Step 5: Conclude that the P-value falls within the interval determined in Step 4. This interval provides an estimate of the probability that the observed data could occur under the null hypothesis.

Key Concepts

Chi-Square Test

The chi-square test is a statistical method used to determine if there is a significant association between categorical variables. It compares the observed frequencies in each category to the expected frequencies, which are calculated under the assumption of no association. A higher chi-square value indicates a greater discrepancy between observed and expected values.

Degrees of Freedom

Degrees of freedom (df) in a chi-square test refer to the number of independent values that can vary in the analysis. For a chi-square test of independence, the degrees of freedom are calculated as (number of rows - 1) × (number of columns - 1). In this case, with 4 degrees of freedom, it indicates the complexity of the data being analyzed.

P-Value

The P-value is a measure that helps determine the significance of the results from a statistical test. It represents the probability of observing the test results, or something more extreme, under the null hypothesis. A lower P-value (typically less than 0.05) suggests that the observed data is unlikely under the null hypothesis, leading to its rejection.