For a chi-squared distribution, find the following quantities. (Refer to table A.5 in your book.) (a) X3.95 when v = 14. (b) x.10 when v = 10. (c) X3.90 when v = 1. (d) Determine the value of a such that x² = 18.137 when ✓ = 23.
For a chi-squared distribution, find the following quantities. (Refer to table A.5 in your book.) (a) X3.95 when v = 14. (b) x.10 when v = 10. (c) X3.90 when v = 1. (d) Determine the value of a such that x² = 18.137 when ✓ = 23.
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Transcribed Image Text:This table is a section of the critical values for the Chi-Squared Distribution, essential for statistical analysis. It is used to determine the significance of hypothesis tests, particularly in variance analysis or goodness-of-fit tests.
### Table Structure:
- **Columns:**
- The top row represents the significance level (α) which are the common alpha levels used (0.30, 0.25, 0.20, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.001).
- **Rows:**
- The first column (v) denotes the degrees of freedom, ranging from 1 to 50 in this section.
### Explanation:
For each combination of degrees of freedom and alpha level, the table provides the critical value of the chi-squared statistic. These values indicate the cutoff point beyond which the observed test statistic would be considered significant or lead to rejecting the null hypothesis.
### Example Usage:
- If you have a test with 5 degrees of freedom and a significance level of 0.05, you would find:
- Look for the row where the degrees of freedom (v) is 5.
- Move across to the column under 0.05.
- The critical value would be 11.070.
These critical values are key in determining the rejection region for hypothesis testing, providing a threshold to compare against the chi-squared statistic from your data analysis.
Transcribed Image Text:For a chi-squared distribution, find the following quantities. (Refer to table A.5 in your book.)
(a) \(\chi^2_{0.95}\) when \(\nu = 14\).
(b) \(\chi^2_{0.10}\) when \(\nu = 10\).
(c) \(\chi^2_{0.90}\) when \(\nu = 1\).
(d) Determine the value of \(\alpha\) such that \(\chi^2_{\alpha} = 18.137\) when \(\nu = 23\).
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We have given the Chi-squared distribution.
We have to find the given quantities based on degree of freedom and significance level.
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