Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Sample Mean (kg/mm²) X=104.7 s₁ = 1.1 y=124.1 5₂ = 2.2 Grade AISI 1064 AISI 1078 Sample Size m=128 n=128 (a) Does the data provide compelling evidence for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm²? Test the appropriate hypotheses using a significance level of 0.01. State the relevant hypotheses. Ho: M1064-M1078 = -10 H: 1064-10785-10 Ho: M10641078 = -10 H: #1064#1078-10 Ho: M10641078--10 Ha: M1064-M10782-10 Ho: M1064-M1078 = -10 Ha: 1064-H1078-10 Sample SD Ho: M1064-M1078--10 Ha: #1064#1078 < -10 Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z=1 P-value= State the conclusion in the problem context. O Reject Ho. The data does not suggest that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². O Fail to reject Ho. The data suggests that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². Reject Ho. The data suggests that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². O Fail to reject Ho. The data does not suggest that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². (b) Estimate the difference between true average strengths for the two grades in a way that provides information about precision and reliability. (Use a 95% confidence interval. Round your answers to two decimal places.) kg/mm²
Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Sample Mean (kg/mm²) X=104.7 s₁ = 1.1 y=124.1 5₂ = 2.2 Grade AISI 1064 AISI 1078 Sample Size m=128 n=128 (a) Does the data provide compelling evidence for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm²? Test the appropriate hypotheses using a significance level of 0.01. State the relevant hypotheses. Ho: M1064-M1078 = -10 H: 1064-10785-10 Ho: M10641078 = -10 H: #1064#1078-10 Ho: M10641078--10 Ha: M1064-M10782-10 Ho: M1064-M1078 = -10 Ha: 1064-H1078-10 Sample SD Ho: M1064-M1078--10 Ha: #1064#1078 < -10 Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z=1 P-value= State the conclusion in the problem context. O Reject Ho. The data does not suggest that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². O Fail to reject Ho. The data suggests that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². Reject Ho. The data suggests that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². O Fail to reject Ho. The data does not suggest that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². (b) Estimate the difference between true average strengths for the two grades in a way that provides information about precision and reliability. (Use a 95% confidence interval. Round your answers to two decimal places.) kg/mm²
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:### Tensile Strength Test Analysis
**Background:**
Tensile strength tests were conducted on two grades of wire rod, AISI 1064 and AISI 1078, to determine the difference in average strength. The data is as follows:
| Grade | Sample Size | Sample Mean (kg/mm²) | Sample SD |
|----------|-------------|----------------------|-----------|
| AISI 1064 | n = 128 | \( \bar{x} = 104.7 \) | \( s_1 = 1.1 \) |
| AISI 1078 | n = 128 | \( \bar{y} = 124.1 \) | \( s_2 = 2.2 \) |
#### Part (a): Hypothesis Testing
**Objective:**
To determine if there is compelling evidence that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm². A significance level of 0.01 is used.
**Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( \mu_{1064} - \mu_{1078} = -10 \)
- Alternative Hypothesis (\( H_a \)): \( \mu_{1064} - \mu_{1078} < -10 \) ✓
**Steps:**
1. Calculate the test statistic (z).
2. Determine the p-value.
3. Draw conclusions based on the p-value.
**Conclusion Options:**
- Reject \( H_0 \): The data suggests that the true average strength for the 1078 grade exceeds that of the 1064 grade by more than 10 kg/mm². ✓
#### Part (b): Confidence Interval Estimation
**Objective:**
Estimate the difference between true average strengths for the two grades with information on precision and reliability, using a 95% confidence interval.
**Interval Estimate:**
- (______, ______) kg/mm²
**Instructions:**
1. Round your test statistic to two decimal places and your p-value to four decimal places.
2. Round the confidence interval answers to two decimal places.
This analysis will help educators and students understand hypothesis testing and confidence interval concepts in a practical context.
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