Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 22 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work s that almost all cans have volumes between 11.98 oz and 12.70 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts (a) through (d) below. b. Compute the test statistic. x2²=0 (Round to three decimal places as needed.)
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 22 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work s that almost all cans have volumes between 11.98 oz and 12.70 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts (a) through (d) below. b. Compute the test statistic. x2²=0 (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Statistical Analysis of Soda Can Volumes
**Scenario:**
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 22 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.98 oz and 12.70 oz, a range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts (a) through (d) below.
**Procedure:**
b. **Compute the test statistic:**
\[ \chi^2 = \boxed{\hspace{30px}} \]
(Round to three decimal places as needed.)
c. **Find the P-value:**
\[ \text{P-value} = \boxed{\hspace{30px}} \]
(Round to four decimal places as needed.)
d. **State the conclusion:**
\[
\text{Reject } H_0, \text{ because the P-value is} \boxed{\hspace{50px}} \text{ the level of significance. There is} \boxed{\hspace{50px}} \text{ evidence to conclude that the population standard deviation of can volumes is less than 0.18 oz.}
\]
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- **Help me solve this**
- **View an example**
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**Note:**
The values enclosed in boxes (\(\boxed{\hspace{30px}}\)) are to be filled in with the appropriate numerical calculations based on the steps provided in the scenario. The procedure involves determining the chi-square test statistic and the associated P-value to make a decision concerning the null hypothesis (\( H_0 \)).
Make sure to follow each step correctly, and refer to your course materials for detailed explanations and examples of computing chi-square test statistics and P-values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59852601-3264-4bf5-90c5-01c3b03ce4fe%2Fed0932e9-295a-429b-89f2-3733c2d92b83%2Ff32h02f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Soda Can Volumes
**Scenario:**
Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 22 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.98 oz and 12.70 oz, a range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts (a) through (d) below.
**Procedure:**
b. **Compute the test statistic:**
\[ \chi^2 = \boxed{\hspace{30px}} \]
(Round to three decimal places as needed.)
c. **Find the P-value:**
\[ \text{P-value} = \boxed{\hspace{30px}} \]
(Round to four decimal places as needed.)
d. **State the conclusion:**
\[
\text{Reject } H_0, \text{ because the P-value is} \boxed{\hspace{50px}} \text{ the level of significance. There is} \boxed{\hspace{50px}} \text{ evidence to conclude that the population standard deviation of can volumes is less than 0.18 oz.}
\]
**Options to assist:**
- **Help me solve this**
- **View an example**
- **Get more help**
- **Next**
**Note:**
The values enclosed in boxes (\(\boxed{\hspace{30px}}\)) are to be filled in with the appropriate numerical calculations based on the steps provided in the scenario. The procedure involves determining the chi-square test statistic and the associated P-value to make a decision concerning the null hypothesis (\( H_0 \)).
Make sure to follow each step correctly, and refer to your course materials for detailed explanations and examples of computing chi-square test statistics and P-values.
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