Twenty-four fast-food restaurant hourly employees were surveyed to see how many hours they worked per week, on average. The following data was obtained: 34, 45, 43, 41, 49, 48, 29, 36, 50, 40, 40, 49, 36, 54, 31, 41, 42, 37, 47, 29, 47, 36, 47, 48 Assuming the population standard deviation is a = 6, construct a 87% confidence interval for the mean number of hours per week that the population of fast-food restaurant employees work.
Twenty-four fast-food restaurant hourly employees were surveyed to see how many hours they worked per week, on average. The following data was obtained: 34, 45, 43, 41, 49, 48, 29, 36, 50, 40, 40, 49, 36, 54, 31, 41, 42, 37, 47, 29, 47, 36, 47, 48 Assuming the population standard deviation is a = 6, construct a 87% confidence interval for the mean number of hours per week that the population of fast-food restaurant employees work.
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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![**Survey of Fast-Food Restaurant Hourly Employees**
A survey was conducted involving 24 hourly employees at fast-food restaurants to determine their average weekly working hours. The collected data are as follows:
34, 45, 43, 41, 49, 48, 29, 36, 50, 40, 40, 49, 36, 54, 31, 41, 42, 37, 47, 29, 47, 36, 47, 48
**Aim**: Construct an 87% confidence interval for the mean number of hours fast-food restaurant employees work each week, using a population standard deviation (σ) of 6.
**Steps and Formulas**:
- Calculate the sample mean (\(\bar{x}\))
- Determine the critical value (\(z_{\alpha/2}\)) for an 87% confidence level
- Calculate the Margin of Error (E)
**Formulas**:
\[
\bar{x} = \text{Sample Mean}
\]
\[
\frac{\alpha}{2} = \text{Significance Level}
\]
\[
z_{\frac{\alpha}{2}} = \text{Critical Value}
\]
\[
E = \text{Margin of Error}
\]
**Confidence Interval**: We are 87% confident that fast-food restaurant hourly employees, on average, work between *[lower bound]* and *[upper bound]* hours per week.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91ece92e-6289-4e6c-97fc-a58155338153%2F9ba2ca56-fca1-4bab-946d-58bd581ea491%2Ftwb6lak_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Survey of Fast-Food Restaurant Hourly Employees**
A survey was conducted involving 24 hourly employees at fast-food restaurants to determine their average weekly working hours. The collected data are as follows:
34, 45, 43, 41, 49, 48, 29, 36, 50, 40, 40, 49, 36, 54, 31, 41, 42, 37, 47, 29, 47, 36, 47, 48
**Aim**: Construct an 87% confidence interval for the mean number of hours fast-food restaurant employees work each week, using a population standard deviation (σ) of 6.
**Steps and Formulas**:
- Calculate the sample mean (\(\bar{x}\))
- Determine the critical value (\(z_{\alpha/2}\)) for an 87% confidence level
- Calculate the Margin of Error (E)
**Formulas**:
\[
\bar{x} = \text{Sample Mean}
\]
\[
\frac{\alpha}{2} = \text{Significance Level}
\]
\[
z_{\frac{\alpha}{2}} = \text{Critical Value}
\]
\[
E = \text{Margin of Error}
\]
**Confidence Interval**: We are 87% confident that fast-food restaurant hourly employees, on average, work between *[lower bound]* and *[upper bound]* hours per week.
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