
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Tuna Consumption Hypothesis Test
**Scenario**:
A nutritionist claims that the mean tuna consumption by a person is 3.5 pounds per year. A sample of 80 people shows that the mean tuna consumption by a person is 3.1 pounds per year. Assume the population standard deviation is 1.17 pounds. At \(\alpha = 0.05\), can you reject the claim?
---
**Hypothesis Identification**:
(a) Identify the null hypothesis and alternative hypothesis.
- **Option A**:
- \( H_0 \): \(\mu > 3.5\)
- \( H_a \): \(\mu \leq 3.5\)
- **Option B**:
- \( H_0 \): \(\mu \leq 3.5\)
- \( H_a \): \(\mu > 3.5\)
- **Option C**:
- \( H_0 \): \(\mu > 3.1\)
- \( H_a \): \(\mu \leq 3.1\)
- **Option D**:
- \( H_0 \): \(\mu \leq 3.1\)
- \( H_a \): \(\mu > 3.1\)
- **Option E**:
- \( H_0 \): \(\mu = 3.5\)
- \( H_a \): \(\mu \ne 3.5\)
- **Option F**:
- \( H_0 \): \(\mu = 3.1\)
- \( H_a \): \(\mu \ne 3.1\)
---
**Standardized Test Statistic**:
(b) Identify the standardized test statistic.
\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \]
**Note**: Round to two decimal places as needed.
---
**P-Value Calculation**:
(c) Find the P-value.
**Note**: Round to three decimal places as needed.
---
**Hypothesis Decision**:
(d) Decide whether to reject or fail to reject the null hypothesis.
- **Option A**:
- Fail to reject \( H_0 \). There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.5 pounds.
- **Option](https://content.bartleby.com/qna-images/question/e06fe914-1239-47ca-9a69-106db7b604fb/49a3178b-832c-4be5-bdb9-0fda8b515439/sv51594_thumbnail.jpeg)
Transcribed Image Text:### Tuna Consumption Hypothesis Test
**Scenario**:
A nutritionist claims that the mean tuna consumption by a person is 3.5 pounds per year. A sample of 80 people shows that the mean tuna consumption by a person is 3.1 pounds per year. Assume the population standard deviation is 1.17 pounds. At \(\alpha = 0.05\), can you reject the claim?
---
**Hypothesis Identification**:
(a) Identify the null hypothesis and alternative hypothesis.
- **Option A**:
- \( H_0 \): \(\mu > 3.5\)
- \( H_a \): \(\mu \leq 3.5\)
- **Option B**:
- \( H_0 \): \(\mu \leq 3.5\)
- \( H_a \): \(\mu > 3.5\)
- **Option C**:
- \( H_0 \): \(\mu > 3.1\)
- \( H_a \): \(\mu \leq 3.1\)
- **Option D**:
- \( H_0 \): \(\mu \leq 3.1\)
- \( H_a \): \(\mu > 3.1\)
- **Option E**:
- \( H_0 \): \(\mu = 3.5\)
- \( H_a \): \(\mu \ne 3.5\)
- **Option F**:
- \( H_0 \): \(\mu = 3.1\)
- \( H_a \): \(\mu \ne 3.1\)
---
**Standardized Test Statistic**:
(b) Identify the standardized test statistic.
\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \]
**Note**: Round to two decimal places as needed.
---
**P-Value Calculation**:
(c) Find the P-value.
**Note**: Round to three decimal places as needed.
---
**Hypothesis Decision**:
(d) Decide whether to reject or fail to reject the null hypothesis.
- **Option A**:
- Fail to reject \( H_0 \). There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.5 pounds.
- **Option
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