### Investigation of Tensile Strength in Metal BarsAn engineer is exploring whether using a new experimental treatment instead of the established conventional treatment affects the tensile strength of metal bars. Tensile strength is the bar's capacity to resist tearing when pulled. Assume uniform population variances with random sampling. Use technology if feasible. Solve at significance level $\alpha = 0.20$.#### Data Table- **Treatment Type**: Tensile strengths (Newtons per square millimeter) - **Experimental**: 392, 355, 448, 463, 400, 425, 533 - **Conventional**: 445, 377, 428, 365, 383, 362, 409, 390, 373#### Hypotheses Formulation1. **Claim**: The new treatment **improves** tensile strength. 2. **Define Hypotheses**: - **Null Hypothesis ($H_0$)**: There is no difference in tensile strength between treatments. - **Alternative Hypothesis ($H_a$)**: There is an improvement in tensile strength with the new treatment.#### Steps for Statistical Decision1. Determine which hypothesis represents the claim: - $\boxed{\text{Alternative Hypothesis, } H_a}$2. Decision Making: - Reject or fail to reject the null hypothesis ($H_0$).3. **Conclusion in Study Context**: - At the 20% significance level, assess if there is **sufficient evidence** to support the improvement claim.By following these steps, one will conclude whether the new treatment has statistically significant effects on the tensile strength compared to the conventional method.

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Description: ### Investigation of Tensile Strength in Metal BarsAn engineer is exploring whether using a new experimental treatment instead of the established conventional treatment affects the tensile strength of metal bars. Tensile strength is the bar's capaci

Determine the claim. The claim is determined below as follows: The claim is “The new treatment is makes difference” in the tensile strength of the bars. State the hypotheses. That is, there is no difference between the mean tensile strength of the bars. That is, there is difference between the mean tensile strength of the bars. Determine which hypotheses is claim. The hypothesis that represents the claim is alternative hypotheses. Correct option: Option 2Obtain the value of test statistic. The value of test statistic is obtained below as follows: EXCEL procedure: Go to EXCEL Go to Data>Data Analysis. Choose t-test: Two Sample assuming equal variances. Enter the range for variable 1 as $A$1:$A$8. Enter the range for variable 2 as $B$1:$B$11. Enter the hypothesis mean difference as 0 Check the option Labels in First row. Enter the alpha level as 0.20. Click OK. EXCEL output: From the EXCEL output, the value of test statistic is 0.182 and the P-value is 0.8578. Determine decision. Use the level of significance is 0.20. That is, the P-value is greater than the level of significance. By rejection rule, do not reject the null hypothesis. Fail to reject the null hypothesis. Final conclusion: At the 20% level of significance there is no enough evidence to support the claim.

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An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At a=0.20, answer. Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square millimeter) Experimental 392 355 448 363 400 425 353 Conventional 445 377 428 355 363 358 382 408 390 373 Identify the claim and state Ho and Hg- The claim is "The new treatment in the tensile strength of the bars." What are Ho and H? The null hypothesis, Hg, is V. The alternative hypothesis, Hg. is Which hypothesis is the claim? O The null hypothesis, Ho O The altemative hypothesis, H. Decide whether to reject or fail to reject the null hypothesis. V he null hypothesis. Interpret the decision in the context of the original claim. At the 20% significance level, V enough evidence to support the claim.

An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At a=0.20, answer. Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square millimeter) Experimental 392 355 448 363 400 425 353 Conventional 445 377 428 355 363 358 382 408 390 373 Identify the claim and state Ho and Hg- The claim is "The new treatment in the tensile strength of the bars." What are Ho and H? The null hypothesis, Hg, is V. The alternative hypothesis, Hg. is Which hypothesis is the claim? O The null hypothesis, Ho O The altemative hypothesis, H. Decide whether to reject or fail to reject the null hypothesis. V he null hypothesis. Interpret the decision in the context of the original claim. At the 20% significance level, V enough evidence to support the claim.

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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