MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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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