The contents of 37 cans of Coke have a mean of x = 12.15. Assume the contents of cans of Coke have a normal distributio ndard deviation of o=0.11. Find the value of the test statistic z for the claim that the population mean is μ = 12.
The contents of 37 cans of Coke have a mean of x = 12.15. Assume the contents of cans of Coke have a normal distributio ndard deviation of o=0.11. Find the value of the test statistic z for the claim that the population mean is μ = 12.
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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![Given a standard deviation of \( \sigma = 0.11 \), find the value of the test statistic \( z \) for the claim that the population mean is \( \mu = 12 \).
The test statistic is: [input box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b7ca6d8-5f13-4c7d-9445-c8deb1476275%2Fdf6db2b9-504f-4791-a4e0-24c1bf0a6b10%2Ferlfltl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a standard deviation of \( \sigma = 0.11 \), find the value of the test statistic \( z \) for the claim that the population mean is \( \mu = 12 \).
The test statistic is: [input box]
![The contents of 37 cans of Coke have a mean of \(\bar{x} = 12.15\). Assume the contents of cans of Coke have a normal distribution with a standard deviation of \(\sigma = 0.11\). Find the value of the test statistic \(z\) for the claim that the population mean is \(\mu = 12\).
The test statistic is [ ].
---
### Explanation:
This problem involves hypothesis testing, where you are given the sample mean, population standard deviation, and the hypothesized population mean. You are tasked with finding the \(z\)-score, which is the test statistic used in this hypothesis test. This score helps determine how many standard deviations the sample mean (\(\bar{x}\)) is from the hypothesized population mean (\(\mu\)).
#### Calculation:
To find the \(z\)-score, use the formula:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
- \(\bar{x} = 12.15\) is the sample mean.
- \(\mu = 12\) is the hypothesized population mean.
- \(\sigma = 0.11\) is the standard deviation.
- \(n = 37\) is the sample size.
Calculate the \(z\)-score to analyze the hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b7ca6d8-5f13-4c7d-9445-c8deb1476275%2Fdf6db2b9-504f-4791-a4e0-24c1bf0a6b10%2Fbjsgxrr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The contents of 37 cans of Coke have a mean of \(\bar{x} = 12.15\). Assume the contents of cans of Coke have a normal distribution with a standard deviation of \(\sigma = 0.11\). Find the value of the test statistic \(z\) for the claim that the population mean is \(\mu = 12\).
The test statistic is [ ].
---
### Explanation:
This problem involves hypothesis testing, where you are given the sample mean, population standard deviation, and the hypothesized population mean. You are tasked with finding the \(z\)-score, which is the test statistic used in this hypothesis test. This score helps determine how many standard deviations the sample mean (\(\bar{x}\)) is from the hypothesized population mean (\(\mu\)).
#### Calculation:
To find the \(z\)-score, use the formula:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
- \(\bar{x} = 12.15\) is the sample mean.
- \(\mu = 12\) is the hypothesized population mean.
- \(\sigma = 0.11\) is the standard deviation.
- \(n = 37\) is the sample size.
Calculate the \(z\)-score to analyze the hypothesis.
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