**Calculate Statistics for Store one, two, and three**Difference in means:Standard error:T-statistic:Degrees of freedom: P-value P(T=t) two tail*: **Problem: Customers are complaining about sandwich length**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 the period of an hour at each store. Determine 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 ensure consistent quality.)**Sandwich Measurements**| | Store 1 | Store 2 | Store 3 ||--------|---------|---------|---------|| Sample | 8.8 | 9.1 | 9.0 || 1 | 11.4 | 11.6 | 12.5 || 2 | 11.3 | 11.4 | 14.5 || 3 | 11.3 | 11.5 | 10.3 || 4 | 10.1 | 10.3 | 10.8 || ... | ... | ... | ... || n | 12.6 | 14.6 | 8.4 || n+1 | 11.8 | 14.0 | 11.0 |**Statistics**- **Sample Size**- **Mean (length)**- **Variance**- **Standard Deviation**- **Hypothesized Mean (M)**- **Difference in Means (x̄ - M)**- **Standard Error**- **T-Statistic**- **Degrees of Freedom**- **P-value P(T=t) two-tail***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.***Note**: The provided datasets for each store show the measurements (in inches) of different sandwiches sampled for quality testing. The goal is to compare the average length of sandwiches

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Answered: **Calculate Statistics for Store one,…

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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**Calculate Statistics for Store one, two, and three** Difference in means: Standard error: T-statistic: Degrees of freedom: P-value P(T=t) two tail*:

**Problem: Customers are complaining about sandwich length**

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 the period of an hour at each store. Determine 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 ensure consistent quality.)

**Sandwich Measurements**

| | Store 1 | Store 2 | Store 3 |
|--------|---------|---------|---------|
| Sample | 8.8 | 9.1 | 9.0 |
| 1 | 11.4 | 11.6 | 12.5 |
| 2 | 11.3 | 11.4 | 14.5 |
| 3 | 11.3 | 11.5 | 10.3 |
| 4 | 10.1 | 10.3 | 10.8 |
| ... | ... | ... | ... |
| n | 12.6 | 14.6 | 8.4 |
| n+1 | 11.8 | 14.0 | 11.0 |

**Statistics**

- **Sample Size**
- **Mean (length)**
- **Variance**
- **Standard Deviation**
- **Hypothesized Mean (M)**
- **Difference in Means (x̄ - M)**
- **Standard Error**
- **T-Statistic**
- **Degrees of Freedom**
- **P-value P(T=t) two-tail**

*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.*

**Note**: The provided datasets for each store show the measurements (in inches) of different sandwiches sampled for quality testing. The goal is to compare the average length of sandwiches

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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