State the null and alternative hypotheses. H₂₁:0² = 1 H₂:0² #1 H₂₁:0² > 1 H₂:0² $1 H₁:0² <1 H₂:0² 21 OH₁: 0² 51 H₂:0² > 1 H₂:0² 21 H₂:0² <1 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject H. We can conclude that o² > 1. O Reject H. We cannot conclude that ² > 1. O Do not reject H. We cannot conclude that o² > 2 > 1. O Reject H. We can conclude that 2² > 1.
State the null and alternative hypotheses. H₂₁:0² = 1 H₂:0² #1 H₂₁:0² > 1 H₂:0² $1 H₁:0² <1 H₂:0² 21 OH₁: 0² 51 H₂:0² > 1 H₂:0² 21 H₂:0² <1 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject H. We can conclude that o² > 1. O Reject H. We cannot conclude that ² > 1. O Do not reject H. We cannot conclude that o² > 2 > 1. O Reject H. We can conclude that 2² > 1.
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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![City Trucking, Inc., claims consistent delivery times for its routine customer deliveries. A sample of 23 truck deliveries shows a sample variance of 1.6. Test to determine whether \( H_0: \sigma^2 \leq 1 \) can be rejected. Use \( \alpha = 0.10 \).
---
**State the null and alternative hypotheses:**
\( H_0: \sigma^2 \leq 1 \)
\( H_1: \sigma^2 > 1 \)
---
**Find the value of the test statistic.**
[Input box for test statistic value]
---
**Find the p-value. (Round your answer to four decimal places.)**
\[ \text{p-value} = [Input box for p-value] \]
---
**State your conclusion.**
- \(\bigcirc\) Do not reject \( H_0 \). We can conclude that \( \sigma^2 \leq 1 \).
- \(\bigcirc\) Reject \( H_0 \). We cannot conclude that \( \sigma^2 > 1 \).
- \(\bigcirc\) Do not reject \( H_0 \). We cannot conclude that \( \sigma^2 > 1 \).
- \(\bigcirc\) Reject \( H_0 \). We can conclude that \( \sigma^2 > 1 \).
---
**Explanation:**
Given:
- Sample size, \( n = 23 \)
- Sample variance, \( s^2 = 1.6 \)
- Significance level, \( \alpha = 0.10 \)
We need to determine if the sample variance is significantly greater than 1. This involves using a chi-square test for variance.
1. **Formulate the Hypotheses:**
\[ H_0: \sigma^2 \leq 1 \]
\[ H_1: \sigma^2 > 1 \]
2. **Test Statistic:**
The test statistic for the chi-square test is calculated using:
\[ \chi^2 = \frac{(n-1)s^2}{\sigma_0^2} \]
Where:
- \( n \) is the sample size,
- \( s^2 \) is the sample variance,
- \( \sigma_0^2 \) is the hypothesized population variance.
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4959d4f7-c515-4b84-8a14-00389cef5562%2F6622a4df-e237-49c7-a7a0-7b0026e8c52b%2F9f2fwv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:City Trucking, Inc., claims consistent delivery times for its routine customer deliveries. A sample of 23 truck deliveries shows a sample variance of 1.6. Test to determine whether \( H_0: \sigma^2 \leq 1 \) can be rejected. Use \( \alpha = 0.10 \).
---
**State the null and alternative hypotheses:**
\( H_0: \sigma^2 \leq 1 \)
\( H_1: \sigma^2 > 1 \)
---
**Find the value of the test statistic.**
[Input box for test statistic value]
---
**Find the p-value. (Round your answer to four decimal places.)**
\[ \text{p-value} = [Input box for p-value] \]
---
**State your conclusion.**
- \(\bigcirc\) Do not reject \( H_0 \). We can conclude that \( \sigma^2 \leq 1 \).
- \(\bigcirc\) Reject \( H_0 \). We cannot conclude that \( \sigma^2 > 1 \).
- \(\bigcirc\) Do not reject \( H_0 \). We cannot conclude that \( \sigma^2 > 1 \).
- \(\bigcirc\) Reject \( H_0 \). We can conclude that \( \sigma^2 > 1 \).
---
**Explanation:**
Given:
- Sample size, \( n = 23 \)
- Sample variance, \( s^2 = 1.6 \)
- Significance level, \( \alpha = 0.10 \)
We need to determine if the sample variance is significantly greater than 1. This involves using a chi-square test for variance.
1. **Formulate the Hypotheses:**
\[ H_0: \sigma^2 \leq 1 \]
\[ H_1: \sigma^2 > 1 \]
2. **Test Statistic:**
The test statistic for the chi-square test is calculated using:
\[ \chi^2 = \frac{(n-1)s^2}{\sigma_0^2} \]
Where:
- \( n \) is the sample size,
- \( s^2 \) is the sample variance,
- \( \sigma_0^2 \) is the hypothesized population variance.
3
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