Test (1031) and the Rotating Bomb Uxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3625 RBOT 370 335 TOST 4870 4475 RBOT 400 375 3750 3675 4050 2795 375 315 350 205 3450 285 (a) Calculate.the.value of the sample correlation coefficient. (Round your answer to four decimal places.) re 2700 3750 3275 220 345 280 Enter a number. Interpret the value of the sample correlation coefficient. O The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT. The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT. The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT. The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT. (b) How would the value of r be affected if we had let x = RBOT time and y TOST time? The value of r would increase. o The value of r would remain the same. The value of r would decrease. The value of r would be multiplied by -1. ✓ (c) How would the value of r be affected if RBOT time were expressed in hours? The value of r would be multiplied by -1. o The value of r would remain the same. The value of r would increase. The value of r would decrease.

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Please calculate r, t, and the p-value
The image is a screenshot from an educational website concerning statistical data analysis through correlation. Here is the transcription and the explanation of its contents:

---

**Title: Analysis of Oxidation Tests for Steam Turbine Oils**

The image presents data from two different procedures for evaluating the oxidation stability of steam turbine oils: the Thiobarbituric Acid Test (TOST) and the Rotating Bomb Oxidation Test (RBOT). An article reported the accompanying observations on six oil specimens.

**Data Table:**
- **Row Headers:** Specimen numbers (1 to 6).
- **Columns:**
  - **RBOT:** Values are 4080, 4870, 3730, 4450, 3450, 2870.
  - **TOST:** Values are 4200, 370, 3925, 3750, 3750, 3500.

**Tasks and Questions:**

1. **(a) Calculate the value of the sample correlation coefficient.**  
   (Round your answer to four decimal places.)

2. **(b) Interpret the value of the sample correlation coefficient.**  
   - Possible answers:
     - The value of r indicates that there is a strong positive linear relationship between TOST and RBOT.
     - The value of r indicates that there is a weak positive linear relationship between TOST and RBOT.
     - The value of r indicates that there is a weak negative linear relationship between TOST and RBOT.
     - The value of r indicates that there is a strong negative linear relationship between TOST and RBOT.

3. **(c) How would the value of r be affected if RBOT time were expressed in hours?**  
   - Possible answers:
     - The value of r would increase.
     - The value of r would remain the same.
     - The value of r would decrease.

4. **(d) How would the value of r be affected if we had let x = RBOT time, and y = TOST time?**  
   - Possible answers:
     - The value of r would increase.
     - The value of r would remain the same.
     - The value of r would be multiplied by -1.

---

**Explanation:**

This educational scenario guides students through the concepts of correlation analysis using sample data from experimental tests. Students are asked to calculate the correlation coefficient (r), which measures the strength and direction of a linear
Transcribed Image Text:The image is a screenshot from an educational website concerning statistical data analysis through correlation. Here is the transcription and the explanation of its contents: --- **Title: Analysis of Oxidation Tests for Steam Turbine Oils** The image presents data from two different procedures for evaluating the oxidation stability of steam turbine oils: the Thiobarbituric Acid Test (TOST) and the Rotating Bomb Oxidation Test (RBOT). An article reported the accompanying observations on six oil specimens. **Data Table:** - **Row Headers:** Specimen numbers (1 to 6). - **Columns:** - **RBOT:** Values are 4080, 4870, 3730, 4450, 3450, 2870. - **TOST:** Values are 4200, 370, 3925, 3750, 3750, 3500. **Tasks and Questions:** 1. **(a) Calculate the value of the sample correlation coefficient.** (Round your answer to four decimal places.) 2. **(b) Interpret the value of the sample correlation coefficient.** - Possible answers: - The value of r indicates that there is a strong positive linear relationship between TOST and RBOT. - The value of r indicates that there is a weak positive linear relationship between TOST and RBOT. - The value of r indicates that there is a weak negative linear relationship between TOST and RBOT. - The value of r indicates that there is a strong negative linear relationship between TOST and RBOT. 3. **(c) How would the value of r be affected if RBOT time were expressed in hours?** - Possible answers: - The value of r would increase. - The value of r would remain the same. - The value of r would decrease. 4. **(d) How would the value of r be affected if we had let x = RBOT time, and y = TOST time?** - Possible answers: - The value of r would increase. - The value of r would remain the same. - The value of r would be multiplied by -1. --- **Explanation:** This educational scenario guides students through the concepts of correlation analysis using sample data from experimental tests. Students are asked to calculate the correlation coefficient (r), which measures the strength and direction of a linear
The image is a screenshot of a statistical analysis interface. Here's a transcription of the content:

---

**Text:**

Calculate the test statistic and determine the P-value (Round your test statistic to two decimal places and your P-value to three decimal places).

**Inputs:**

P-value =  
t =

**Conclusion Options:**

- Fail to reject H₀. The model is useful.
- Fail to reject H₀. The model is not useful.
- Reject H₀. The model is useful.
- Reject H₀. The model is not useful.

State the conclusion in the problem context.

---

The interface is likely part of a statistical software tool for hypothesis testing, providing options to conclude on the usefulness of a model based on statistical test results.
Transcribed Image Text:The image is a screenshot of a statistical analysis interface. Here's a transcription of the content: --- **Text:** Calculate the test statistic and determine the P-value (Round your test statistic to two decimal places and your P-value to three decimal places). **Inputs:** P-value = t = **Conclusion Options:** - Fail to reject H₀. The model is useful. - Fail to reject H₀. The model is not useful. - Reject H₀. The model is useful. - Reject H₀. The model is not useful. State the conclusion in the problem context. --- The interface is likely part of a statistical software tool for hypothesis testing, providing options to conclude on the usefulness of a model based on statistical test results.
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