The commute distances (in kilometers) at a huge corporation vary from employee to employee. It is known that the population of all these employee commute distances is approximately normally distributed. You are a carpool organizer who wants to estimate the standard deviation for this population with a random sample of 47 employee commute distances. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all the employee commute distances. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from the random sample. (b) Take Sample Point estimate of the population variance: 0 Sample size: 0 Left critical value: 0 Right critical value: Compute 0.00 0.00 Number of employees 47 To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your 99% confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute". 2.00 99% confidence interval for the population variance: 99% confidence interval for the population standard deviation: Sample mean 23.41 4.00 X Confidence level 99% 95% 90% S 99% confidence interval for the population standard deviation: 6.00 Sample standard deviation Critical values Left critical value X0.995 =25.041 Xx0.975 =29.160 X0.95 = 31.439 Based on your sample, enter the values for the lower and upper limits to graph the 99% confidence interval for the population standard deviation of all the employee commute distances. Round the values to two decimal places. 4.79 8.00 Right critical value 0.005=74.437 0.025 = 66.617 0.05 = 62.830 Sample variance 10.00 22.9441 10.00
The commute distances (in kilometers) at a huge corporation vary from employee to employee. It is known that the population of all these employee commute distances is approximately normally distributed. You are a carpool organizer who wants to estimate the standard deviation for this population with a random sample of 47 employee commute distances. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all the employee commute distances. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from the random sample. (b) Take Sample Point estimate of the population variance: 0 Sample size: 0 Left critical value: 0 Right critical value: Compute 0.00 0.00 Number of employees 47 To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your 99% confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute". 2.00 99% confidence interval for the population variance: 99% confidence interval for the population standard deviation: Sample mean 23.41 4.00 X Confidence level 99% 95% 90% S 99% confidence interval for the population standard deviation: 6.00 Sample standard deviation Critical values Left critical value X0.995 =25.041 Xx0.975 =29.160 X0.95 = 31.439 Based on your sample, enter the values for the lower and upper limits to graph the 99% confidence interval for the population standard deviation of all the employee commute distances. Round the values to two decimal places. 4.79 8.00 Right critical value 0.005=74.437 0.025 = 66.617 0.05 = 62.830 Sample variance 10.00 22.9441 10.00
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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Transcribed Image Text:The text describes a procedure to estimate the 99% confidence interval for the population standard deviation of employee commute distances at a corporation. This involves using a sample to make statistical inferences about the population.
### Steps to Estimate the Confidence Interval:
**1. Sample Information:**
- **Number of Employees:** 47
- **Sample Mean:** 23.41 km
- **Sample Standard Deviation:** 4.79 km
- **Sample Variance:** 22.9441 km²
**2. Calculating the Confidence Interval:**
- Click "Take Sample" to get the sample results.
- Enter values to calculate the confidence interval for the population variance by using the point estimate of the population variance, the sample size, and critical values from the provided table.
**3. Critical Values Table:**
- For a 99% confidence level:
- **Left Critical Value (χ²₀.₉₉₅):** 25.041
- **Right Critical Value (χ²₀.₀₀₅):** 74.437
**4. Visual Representation:**
- A graphical depiction shows the range for the 99% confidence interval for the population standard deviation. The graph is aligned along an axis from 0.00 to 10.00, indicating where to place the values found.
### Additional Notes:
- To find the lower and upper limits for the graph:
- Calculate the confidence interval for the population standard deviation.
- Round these values to two decimal places for accurate representation.
This information is crucial for understanding variability in commute distances among employees and informs managerial decisions regarding transportation policies.
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