Leel, bying compare the = 36 specimens of commercial steel y = 58.5. Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both oughness distributions are normal. (a) Assuming that ₁1.4 and ₂ = 1.0, test the relevant hypotheses using a = 0.001. (Use ₁-₂, where is the average toughness for high-purity steel and ₂ is the average toughness for commercial steel.) State the relevant hypotheses. H₂H₁ H₂ = 5 H₂H₂-H₂ <5 Ho: M₁ M₂=5 Hg: H₂-H₂>5 ⒸH₂²H₁-H₂ = 5 H₂H₁-H₂ 55 o Hỏi My k = 5 Ha: H1 -H2 +5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value= State the conclusion in the problem context. O Reject Ho. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. Fail to reject Ho. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. O Fail to reject Ho. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. O Reject Ho. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. (b) Compute for the test conducted in part (a) when #₁ - #₂ = 6. (Round your answer to four decimal places.)
Leel, bying compare the = 36 specimens of commercial steel y = 58.5. Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both oughness distributions are normal. (a) Assuming that ₁1.4 and ₂ = 1.0, test the relevant hypotheses using a = 0.001. (Use ₁-₂, where is the average toughness for high-purity steel and ₂ is the average toughness for commercial steel.) State the relevant hypotheses. H₂H₁ H₂ = 5 H₂H₂-H₂ <5 Ho: M₁ M₂=5 Hg: H₂-H₂>5 ⒸH₂²H₁-H₂ = 5 H₂H₁-H₂ 55 o Hỏi My k = 5 Ha: H1 -H2 +5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value= State the conclusion in the problem context. O Reject Ho. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. Fail to reject Ho. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. O Fail to reject Ho. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. O Reject Ho. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. (b) Compute for the test conducted in part (a) when #₁ - #₂ = 6. (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For \( n = 34 \) specimens, the sample average toughness was \( \bar{x} = 64.3 \) for the high-purity steel, whereas for \( n = 36 \) specimens of commercial steel \( \bar{y} = 58.5 \). Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both toughness distributions are normal.
**(a)** Assuming that \( \sigma_1 = 1.4 \) and \( \sigma_2 = 1.0 \), test the relevant hypotheses using \( \alpha = 0.001 \). (Use \( \mu_1 - \mu_2 \) where \( \mu_1 \) is the average toughness for high-purity steel and \( \mu_2 \) is the average toughness for commercial steel.)
**State the relevant hypotheses:**
- \( H_0: \mu_1 - \mu_2 = 5 \)
- \( H_a: \mu_1 - \mu_2 > 5 \) (selected option)
**Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)**
\[ z = \_\_\_\_ \]
\[ P\text{-value} = \_\_\_\_ \]
**State the conclusion in the problem context:**
- □ Reject \( H_0 \). The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- ☑ Fail to reject \( H_0 \). The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- □ Fail to reject \( H_0 \). The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- □ Reject \( H_0 \). The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
(Selected option: Fail to reject \( H_0 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc02cea10-2b20-4726-bfe2-8f9101f448fb%2F46cc9123-2bb1-4c66-a0e5-c262a4a0d80c%2F6k7fne_processed.png&w=3840&q=75)
Transcribed Image Text:An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For \( n = 34 \) specimens, the sample average toughness was \( \bar{x} = 64.3 \) for the high-purity steel, whereas for \( n = 36 \) specimens of commercial steel \( \bar{y} = 58.5 \). Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both toughness distributions are normal.
**(a)** Assuming that \( \sigma_1 = 1.4 \) and \( \sigma_2 = 1.0 \), test the relevant hypotheses using \( \alpha = 0.001 \). (Use \( \mu_1 - \mu_2 \) where \( \mu_1 \) is the average toughness for high-purity steel and \( \mu_2 \) is the average toughness for commercial steel.)
**State the relevant hypotheses:**
- \( H_0: \mu_1 - \mu_2 = 5 \)
- \( H_a: \mu_1 - \mu_2 > 5 \) (selected option)
**Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)**
\[ z = \_\_\_\_ \]
\[ P\text{-value} = \_\_\_\_ \]
**State the conclusion in the problem context:**
- □ Reject \( H_0 \). The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- ☑ Fail to reject \( H_0 \). The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- □ Fail to reject \( H_0 \). The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
- □ Reject \( H_0 \). The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.
(Selected option: Fail to reject \( H_0 \
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