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 Ho: μ = 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.) LUSE SALT (a) n = 13, t = 3.1, a = 0.05 P-value = 0.687 State the conclusion in the problem context. O 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. Do not 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 that 20. (b) n = 9, t = 1.6, a = 0.01 P-value = 0.539 State the conclusion in the problem context. O 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 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 that 20. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. (c) n = 26, t = -0.4 P-value = 0.346 State the conclusion in the problem context. 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 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 that 20.

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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 \( H_a: \mu > 20 \) 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.)

### (a)
- **Sample size (\( n \))**: 13
- **Test statistic (\( t \))**: 3.1
- **Significance level (\( \alpha \))**: 0.05
- **\( P \)-value**: 0.687

**Conclusion Options:**
1. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
2. **Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.**
3. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
4. 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)
- **Sample size (\( n \))**: 9
- **Test statistic (\( t \))**: 1.6
- **Significance level (\( \alpha \))**: 0.01
- **\( P \)-value**: 0.539

**Conclusion Options:**
1. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
2. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
3. **Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.**
4. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

### (c)
- **Sample size (\( n \))**:
Transcribed Image Text: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 \( H_a: \mu > 20 \) 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.) ### (a) - **Sample size (\( n \))**: 13 - **Test statistic (\( t \))**: 3.1 - **Significance level (\( \alpha \))**: 0.05 - **\( P \)-value**: 0.687 **Conclusion Options:** 1. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. 2. **Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.** 3. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. 4. 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) - **Sample size (\( n \))**: 9 - **Test statistic (\( t \))**: 1.6 - **Significance level (\( \alpha \))**: 0.01 - **\( P \)-value**: 0.539 **Conclusion Options:** 1. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. 2. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. 3. **Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.** 4. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. ### (c) - **Sample size (\( n \))**:
Expert Solution
Step 1: Explain the basic information.

The question is about hypothesis testing.

Given :

H subscript 0 space colon space mu space equals space 20

H subscript a space colon space mu space greater than thin space 20


To find :

Conclusion for given situation.

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