Use the given information to find the number of degrees of freedom, the critical values X and XR, and the assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 90% confidence; n = 40, s = 65.9. Click the icon to view the table of Chi-Square critical values. df=(Type a whole number.) x²-0 (Round to three decimal places as needed.). x² = 0 (Round to three decimal places as needed.) is << The confidence interval estimate of a is ***

MATLAB: An Introduction with Applications
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**Chi-Square Distribution Analysis for Platelet Counts**

To determine the confidence interval for a population standard deviation based on a sample, the following steps and information are essential:

1. **Sample Information**:
   - **Confidence Level**: 90%
   - **Sample Size (n)**: 40
   - **Sample Standard Deviation (s)**: 65.9

2. **Objective**:
   - Calculate the degrees of freedom.
   - Identify the critical values for the Chi-Square distribution.
   - Estimate the confidence interval for the population standard deviation (σ).

3. **Calculations**:
   - **Degrees of Freedom (df)**:
     \[
     \text{df} = n - 1
     \]
     - Input a whole number for degrees of freedom.

   - **Chi-Square Critical Values**:
     - \( \chi^2_L \) (Lower critical value)
     - \( \chi^2_R \) (Upper critical value)
     - Round these values to three decimal places.

4. **Confidence Interval for σ**:
   - The interval is represented as:
     \[
     \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_R}} \right) < \sigma < \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_L}} \right)
     \]
   - Ensure accurate rounding for your final calculation.

Use the Chi-Square critical value table to find the necessary values and complete the analysis. This method assumes the sample originates from a normally distributed population.
Transcribed Image Text:**Chi-Square Distribution Analysis for Platelet Counts** To determine the confidence interval for a population standard deviation based on a sample, the following steps and information are essential: 1. **Sample Information**: - **Confidence Level**: 90% - **Sample Size (n)**: 40 - **Sample Standard Deviation (s)**: 65.9 2. **Objective**: - Calculate the degrees of freedom. - Identify the critical values for the Chi-Square distribution. - Estimate the confidence interval for the population standard deviation (σ). 3. **Calculations**: - **Degrees of Freedom (df)**: \[ \text{df} = n - 1 \] - Input a whole number for degrees of freedom. - **Chi-Square Critical Values**: - \( \chi^2_L \) (Lower critical value) - \( \chi^2_R \) (Upper critical value) - Round these values to three decimal places. 4. **Confidence Interval for σ**: - The interval is represented as: \[ \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_R}} \right) < \sigma < \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_L}} \right) \] - Ensure accurate rounding for your final calculation. Use the Chi-Square critical value table to find the necessary values and complete the analysis. This method assumes the sample originates from a normally distributed population.
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given data n = 40s = 65.990% ci for standard deviation. 

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