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Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to  decimals)

Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to  decimals)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to  decimals)

**Table 11.1: Selected Values from the Chi-Square Distribution Table** **Overview:** This table provides critical values from the Chi-Square distribution for various degrees of freedom and significance levels, represented by the area in the upper tail. It is commonly used in hypothesis testing, particularly in tests of independence and goodness-of-fit. **Explanation of Diagram:** The diagram at the top of the table represents a typical Chi-Square distribution curve, which is positively skewed. The curve shows the probability or area in the upper tail beyond a particular value of \(\chi^2\), which is critical in determining whether to reject a null hypothesis. **Chi-Square Distribution Values:** - **Degrees of Freedom (df):** The first column lists values from 1 to 100, representing the degrees of freedom associated with each test. - **Areas in Upper Tail:** The subsequent columns provide critical values for various significance levels: - .99 - .975 - .95 - .90 - .10 - .05 - .025 - .01 These values indicate the threshold beyond which the cumulative probability of observing a test statistic falls into the upper tail, signaling statistical significance. **Notes:** - *These values are crucial for statistical hypothesis testing in determining whether observed data significantly deviate from expected results. - **Note:** A more extensive table is available as Table 3 of Appendix B (available online).
Transcribed Image Text:**Table 11.1: Selected Values from the Chi-Square Distribution Table** **Overview:** This table provides critical values from the Chi-Square distribution for various degrees of freedom and significance levels, represented by the area in the upper tail. It is commonly used in hypothesis testing, particularly in tests of independence and goodness-of-fit. **Explanation of Diagram:** The diagram at the top of the table represents a typical Chi-Square distribution curve, which is positively skewed. The curve shows the probability or area in the upper tail beyond a particular value of \(\chi^2\), which is critical in determining whether to reject a null hypothesis. **Chi-Square Distribution Values:** - **Degrees of Freedom (df):** The first column lists values from 1 to 100, representing the degrees of freedom associated with each test. - **Areas in Upper Tail:** The subsequent columns provide critical values for various significance levels: - .99 - .975 - .95 - .90 - .10 - .05 - .025 - .01 These values indicate the threshold beyond which the cumulative probability of observing a test statistic falls into the upper tail, signaling statistical significance. **Notes:** - *These values are crucial for statistical hypothesis testing in determining whether observed data significantly deviate from expected results. - **Note:** A more extensive table is available as Table 3 of Appendix B (available online).
Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to 3 decimals) a. \( \chi^2_{0.05} \) with \( df = 5 \) b. \( \chi^2_{0.025} \) with \( df = 15 \) c. \( \chi^2_{0.975} \) with \( df = 20 \) d. \( \chi^2_{0.01} \) with \( df = 10 \) e. \( \chi^2_{0.95} \) with \( df = 18 \)
Transcribed Image Text:Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to 3 decimals) a. \( \chi^2_{0.05} \) with \( df = 5 \) b. \( \chi^2_{0.025} \) with \( df = 15 \) c. \( \chi^2_{0.975} \) with \( df = 20 \) d. \( \chi^2_{0.01} \) with \( df = 10 \) e. \( \chi^2_{0.95} \) with \( df = 18 \)
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