You are the owner of three local sandwich shops. Recently you've received compI customers that their "footlong" sub sandwiches were less than 12 inches long. As a measure of quality assurance, data was collected on all footlong sub sandwiches made over the period of an hour at each store. Determined which, if any, of your stores are making sub sandwiches that are significantly shorter than 12 inches. You will conduct three t-tests, one for each store. You want to be 95% confident in your results. (Note. This case is inspired by reality. Search the internet for 'claims over footlong sub' for a historical perspective and how a company used statistics to insure consistent quality.) Statistics Sandwich Measurements Store 1 Store 2 Store 3 Store 1 Store 2 Store 3 Sample Size Mean (length) Variance Standard Deviation 8.8 9.1 9.0 11.4 11.6 12.5 13.4 13.4 15.1 11.3 11.4 14.3 10.1 10.3 10.8 Hypothesized Mean (M) Difference in Means (X - M) 12.4 12.4 13.8 10.4 10.6 11.2 Standard Error T-Statistic 8.9 9.2 9.1 10.4 11.1 11.8 14.0 Degrees of Freedom 12.8 14.3 9.3 8.7 P-value P(T=t) two-tail* 12.6 13.7 *Remember that the T.DIST 2T() function requires the t-statistic argument to be an absolute value, not a negative value, or an error will occur. 11.7 12.9 11.8 13.0 9.7 10.2 12.6 14.1 Interpret the Results 8.6 1. What is the null hypothesis for these tests? 2. What is the alternative hypothesis for these tests? 3. Given the desired confidence level, what alpha should be used? 4. Can you say with 95% confidence that Store 1 is producing sub sandwiches with an average length that is less than 12 inches? 5. Can you say with 95% confidence that Store 2 is producing sub sandwiches with an average length that is less than 12 inches? 6. Can you say with 95% confidence that Store 3 is producing sub sandwiches with an average length that is less than 12 inches? 8.6 [select] [select] [select] 14.6 11.0 [select] [select] [select]
You are the owner of three local sandwich shops. Recently you've received compI customers that their "footlong" sub sandwiches were less than 12 inches long. As a measure of quality assurance, data was collected on all footlong sub sandwiches made over the period of an hour at each store. Determined which, if any, of your stores are making sub sandwiches that are significantly shorter than 12 inches. You will conduct three t-tests, one for each store. You want to be 95% confident in your results. (Note. This case is inspired by reality. Search the internet for 'claims over footlong sub' for a historical perspective and how a company used statistics to insure consistent quality.) Statistics Sandwich Measurements Store 1 Store 2 Store 3 Store 1 Store 2 Store 3 Sample Size Mean (length) Variance Standard Deviation 8.8 9.1 9.0 11.4 11.6 12.5 13.4 13.4 15.1 11.3 11.4 14.3 10.1 10.3 10.8 Hypothesized Mean (M) Difference in Means (X - M) 12.4 12.4 13.8 10.4 10.6 11.2 Standard Error T-Statistic 8.9 9.2 9.1 10.4 11.1 11.8 14.0 Degrees of Freedom 12.8 14.3 9.3 8.7 P-value P(T=t) two-tail* 12.6 13.7 *Remember that the T.DIST 2T() function requires the t-statistic argument to be an absolute value, not a negative value, or an error will occur. 11.7 12.9 11.8 13.0 9.7 10.2 12.6 14.1 Interpret the Results 8.6 1. What is the null hypothesis for these tests? 2. What is the alternative hypothesis for these tests? 3. Given the desired confidence level, what alpha should be used? 4. Can you say with 95% confidence that Store 1 is producing sub sandwiches with an average length that is less than 12 inches? 5. Can you say with 95% confidence that Store 2 is producing sub sandwiches with an average length that is less than 12 inches? 6. Can you say with 95% confidence that Store 3 is producing sub sandwiches with an average length that is less than 12 inches? 8.6 [select] [select] [select] 14.6 11.0 [select] [select] [select]
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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Problem: customers are complaining about the sandwich length

Interpret the results of the statistics:
Transcribed Image Text:### Overview of the Analysis
You are the owner of three local sandwich shops. Recently, you’ve received complaints from customers that their “footlong” sub sandwiches were less than 12 inches long. As a measure of quality assurance, data was collected on all footlong sub sandwiches made over a period of an hour at each store. You will conduct three t-tests, one for each store. The goal is to determine if any of your stores are making sub sandwiches that are significantly shorter than 12 inches. You want to be 95% confident in your results.
### Sandwich Measurements
- Store 1:
- Measurements: 8.8, 11.4, 12.4, 12.1, 12.5, 12.9, 12.6, 12.0, 12.8, 11.7, 12.6
- Store 2:
- Measurements: 9.1, 13.2, 11.2, 12.3, 12.7, 12.4, 12.3, 12.5, 10.6, 11.4, 12.3, 11.9, 11.8
- Store 3:
- Measurements: 9.0, 12.1, 15.2, 12.5, 11.0, 12.8, 13.3, 12.0, 12.4, 14.8, 11.1, 13.2, 12.9, 13.6
### Statistics
**For each store:**
- **Sample Size**: Number of measurements taken.
- **Mean (length)**: The average length of the sub sandwiches.
- **Variance**: A measure of how much the lengths vary from the mean.
- **Standard Deviation**: The square root of the variance, indicating the average distance from the mean.
- **Hypothesized Mean (M)**: 12 inches.
- **Difference in Means (x̄ - M)**: The difference between the sample mean and the hypothesized mean.
- **Standard Error**: An estimate of the standard deviation of the sample mean.
- **T-Statistic**: A value used to determine the p-value.
- **Degrees of Freedom**: The number of independent values in the calculation
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