Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. An article gives the accompanying data on x = content and y = gas porosity for one particular measurement technique. 0.18 0.20 0.21 0.21 0.21 0.22 0.23 0.23 0.24 0.24 0.25 0.28 0.30 0.37 y 0.48 0.71 0.42 0.44 0.55 0.44 0.24 0.48 0.22 0.82 0.86 0.72 0.70 0.74 Minitab gives the following output in a response to a Correlation command: Correlation of Hydrcon and Porosity = 0.425 (a) Test at level 0.05 to see whether the population correlation coefficient differs from 0. State the appropriate null and alternative hypotheses. O Ho: p = 0 Hip<0 O Ho: p = 0 H:p > 0 O Hoi p = 0 H,ip #0 O Ho: p+0 Hip = 0 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.) P-value - State the conclusion in the problem context. O Fail to reject H. The data does not suggest that the population correlation coefficient differs significantly from 0. O Reject H,. The data suggests that the population correlation coefficient differs significantly from 0. O Fail to reject H. The data suggests that the population correlation coefficient differs significantly from 0. O Reject Hg. The data does not suggest that the population correlation coefficient differs significantly from 0. (b) If a simple linear regression analysis had been carried out, what percentage of observed variation in porosity could be attributed to the model relationship? (Round your answer to one decimal place.) %
Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. An article gives the accompanying data on x = content and y = gas porosity for one particular measurement technique. 0.18 0.20 0.21 0.21 0.21 0.22 0.23 0.23 0.24 0.24 0.25 0.28 0.30 0.37 y 0.48 0.71 0.42 0.44 0.55 0.44 0.24 0.48 0.22 0.82 0.86 0.72 0.70 0.74 Minitab gives the following output in a response to a Correlation command: Correlation of Hydrcon and Porosity = 0.425 (a) Test at level 0.05 to see whether the population correlation coefficient differs from 0. State the appropriate null and alternative hypotheses. O Ho: p = 0 Hip<0 O Ho: p = 0 H:p > 0 O Hoi p = 0 H,ip #0 O Ho: p+0 Hip = 0 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.) P-value - State the conclusion in the problem context. O Fail to reject H. The data does not suggest that the population correlation coefficient differs significantly from 0. O Reject H,. The data suggests that the population correlation coefficient differs significantly from 0. O Fail to reject H. The data suggests that the population correlation coefficient differs significantly from 0. O Reject Hg. The data does not suggest that the population correlation coefficient differs significantly from 0. (b) If a simple linear regression analysis had been carried out, what percentage of observed variation in porosity could be attributed to the model relationship? (Round your answer to one decimal place.) %
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![**Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. An article gives the accompanying data on x = content and y = gas porosity for one particular measurement technique.**
| x | 0.18 | 0.20 | 0.21 | 0.21 | 0.22 | 0.23 | 0.24 | 0.24 | 0.25 | 0.28 | 0.30 | 0.37 |
|------|------|------|------|------|------|------|------|------|------|------|------|------|
| y | 0.48 | 0.71 | 0.42 | 0.44 | 0.45 | 0.44 | 0.44 | 0.48 | 0.22 | 0.82 | 0.86 | 0.72 | 0.70 | 0.74 |
**Minitab gives the following output in a response to a Correlation command:**
**Correlation of Hydrcon and Porosity = 0.425**
(a) Test at a level of 0.05 to see whether the population correlation coefficient differs from 0.
State the appropriate null and alternative hypotheses.
- \( H_0: \rho = 0 \)
\( H_a: \rho < 0 \)
- \( H_0: \rho = 0 \)
\( H_a: \rho > 0 \)
- \( H_0: \rho = 0 \)
\( H_a: \rho \neq 0 \)
- \( H_0: \rho \neq 0 \)
\( H_a: \rho = 0 \)
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.)
\[ t = \_\_\_ \]
\[ \text{P-value} = \_\_\_ \]
State the conclusion in the problem context.
- Fail to reject \( H_0 \). The data does not suggest that the population correlation coefficient differs significantly from 0.
- Reject \( H_0 \). The data suggests that the population correlation coefficient differs significantly from 0.
- Fail to reject \( H_0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4e23d50-b6e1-4880-9ad9-a789799b751b%2F8d03ad5b-b8a3-426d-8780-a208c9285842%2Fqgn4uc2h_processed.png&w=3840&q=75)
Transcribed Image Text:**Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. An article gives the accompanying data on x = content and y = gas porosity for one particular measurement technique.**
| x | 0.18 | 0.20 | 0.21 | 0.21 | 0.22 | 0.23 | 0.24 | 0.24 | 0.25 | 0.28 | 0.30 | 0.37 |
|------|------|------|------|------|------|------|------|------|------|------|------|------|
| y | 0.48 | 0.71 | 0.42 | 0.44 | 0.45 | 0.44 | 0.44 | 0.48 | 0.22 | 0.82 | 0.86 | 0.72 | 0.70 | 0.74 |
**Minitab gives the following output in a response to a Correlation command:**
**Correlation of Hydrcon and Porosity = 0.425**
(a) Test at a level of 0.05 to see whether the population correlation coefficient differs from 0.
State the appropriate null and alternative hypotheses.
- \( H_0: \rho = 0 \)
\( H_a: \rho < 0 \)
- \( H_0: \rho = 0 \)
\( H_a: \rho > 0 \)
- \( H_0: \rho = 0 \)
\( H_a: \rho \neq 0 \)
- \( H_0: \rho \neq 0 \)
\( H_a: \rho = 0 \)
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.)
\[ t = \_\_\_ \]
\[ \text{P-value} = \_\_\_ \]
State the conclusion in the problem context.
- Fail to reject \( H_0 \). The data does not suggest that the population correlation coefficient differs significantly from 0.
- Reject \( H_0 \). The data suggests that the population correlation coefficient differs significantly from 0.
- Fail to reject \( H_0
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