The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let u denote the true average reflectometer reading for a new type of paint under consideration. A test of H: 20 versus H₂: > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) USE SALT (a) n11, t-3.1, 0.05 P-value State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (b) n=9, t= 1.6, a = 0.01 P-value= State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (c) n-30, t -0.4 P-value= State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. O Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Q7

## Effectiveness of Paint Reflector for Road Lines

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let \(\mu\) denote the true average reflectometer reading for a new type of paint under consideration. A test of \(H_0: \mu = 20\) versus \(H_1: \mu > 20\) will be based on a random sample of size \(n\) from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)

### Experiment Details:

1. **Sample Size (n)**
2. **Sample Mean (\(\bar{x}\))**
3. **Alpha (α) Level**
4. **P-value**

### Cases:

#### (a) 
- **n = 11, \(\bar{x} = 3.1\), \(\alpha = 0.05\)**
- P-value = ___________

#### Steps:
1. **State the conclusion in the problem context:**
    - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
    - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

#### (b) 
- **n = 9, \(\bar{x} = 1.6\), \(\alpha = 0.01\)**
- P-value = ___________

#### Steps:
1. **State the conclusion in the problem context:**
    - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
    - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

#### (c) 
- **n = 30, \(\bar{x} = -0.4\)**
- P-value = ___________

#### Steps:
1. **State the conclusion in the problem context:**
    - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
    - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

### Interactive Feature:

Clicking the "
Transcribed Image Text:## Effectiveness of Paint Reflector for Road Lines The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let \(\mu\) denote the true average reflectometer reading for a new type of paint under consideration. A test of \(H_0: \mu = 20\) versus \(H_1: \mu > 20\) will be based on a random sample of size \(n\) from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) ### Experiment Details: 1. **Sample Size (n)** 2. **Sample Mean (\(\bar{x}\))** 3. **Alpha (α) Level** 4. **P-value** ### Cases: #### (a) - **n = 11, \(\bar{x} = 3.1\), \(\alpha = 0.05\)** - P-value = ___________ #### Steps: 1. **State the conclusion in the problem context:** - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. #### (b) - **n = 9, \(\bar{x} = 1.6\), \(\alpha = 0.01\)** - P-value = ___________ #### Steps: 1. **State the conclusion in the problem context:** - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. #### (c) - **n = 30, \(\bar{x} = -0.4\)** - P-value = ___________ #### Steps: 1. **State the conclusion in the problem context:** - Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. - Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. ### Interactive Feature: Clicking the "
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