A sample of 20 items provides a sample standard deviation of 4. a. Compute the 90% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1. b. Compute the 95% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1. c. Compute the 95% confidence interval estimate of the population standard deviation (to 1 decimal). Use Table 11.1. sos

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A sample of 20 items provides a sample standard deviation of 4.

**TABLE 11.1: Selected Values from the Chi-Square Distribution Table**

This table provides selected values from the Chi-Square Distribution for various degrees of freedom and areas in the upper tail. The Chi-Square distribution is commonly used in statistical tests to assess the variance of a sample. 

**Graph Explanation:**
- The graph at the top illustrates the Chi-Square distribution curve with the area in the upper tail highlighted. The horizontal axis is marked with \(\chi^2_\alpha\), representing the critical value for the specified area or probability.

**Table Details:**

- **Degrees of Freedom:** Listed in the first column, ranging from 1 to 100.
- **Area in Upper Tail:** This section corresponds to \( \alpha \) levels of 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, and 0.01.

Each cell in the table represents the Chi-Square value for a specific degrees of freedom and tail area. 

**Sample Entries:**
- For 1 degree of freedom and an area of 0.05, the Chi-square value is 3.841.
- For 10 degrees of freedom and an area of 0.01, the Chi-square value is 19.675.
- For 40 degrees of freedom and an area of 0.05, the Chi-square value is 55.758.

*Note: A more extensive table is provided as Table 3 of Appendix B (available online). This provides additional Chi-Square values for further degrees of freedom and tail areas.* 

This table is a valuable tool for statistical tests, allowing users to find critical values needed for hypothesis testing.
Transcribed Image Text:**TABLE 11.1: Selected Values from the Chi-Square Distribution Table** This table provides selected values from the Chi-Square Distribution for various degrees of freedom and areas in the upper tail. The Chi-Square distribution is commonly used in statistical tests to assess the variance of a sample. **Graph Explanation:** - The graph at the top illustrates the Chi-Square distribution curve with the area in the upper tail highlighted. The horizontal axis is marked with \(\chi^2_\alpha\), representing the critical value for the specified area or probability. **Table Details:** - **Degrees of Freedom:** Listed in the first column, ranging from 1 to 100. - **Area in Upper Tail:** This section corresponds to \( \alpha \) levels of 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, and 0.01. Each cell in the table represents the Chi-Square value for a specific degrees of freedom and tail area. **Sample Entries:** - For 1 degree of freedom and an area of 0.05, the Chi-square value is 3.841. - For 10 degrees of freedom and an area of 0.01, the Chi-square value is 19.675. - For 40 degrees of freedom and an area of 0.05, the Chi-square value is 55.758. *Note: A more extensive table is provided as Table 3 of Appendix B (available online). This provides additional Chi-Square values for further degrees of freedom and tail areas.* This table is a valuable tool for statistical tests, allowing users to find critical values needed for hypothesis testing.
A sample of 20 items provides a sample standard deviation of 4.

a. Compute the 90% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1.

[_____] ≤ σ² ≤ [_____]

b. Compute the 95% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1.

[_____] ≤ σ² ≤ [_____]

c. Compute the 95% confidence interval estimate of the population standard deviation (to 1 decimal). Use Table 11.1.

[_____] ≤ σ ≤ [_____]

(Note: There are no graphs or diagrams in the image.)
Transcribed Image Text:A sample of 20 items provides a sample standard deviation of 4. a. Compute the 90% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1. [_____] ≤ σ² ≤ [_____] b. Compute the 95% confidence interval estimate of the population variance (to 2 decimals). Use Table 11.1. [_____] ≤ σ² ≤ [_____] c. Compute the 95% confidence interval estimate of the population standard deviation (to 1 decimal). Use Table 11.1. [_____] ≤ σ ≤ [_____] (Note: There are no graphs or diagrams in the image.)
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