4. Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Tensile strength is normally distributed for both grades of wire rod. Assume the population standard deviations are unequal. $ df = 22.51 $| Grade | Sample Size | Sample Mean (kg/mm$^2$) | Sample SD ||-----------|-------------|---------------------------|-----------|| AISI 1078 | 14 | 123.6 | 2.0 || AISI 1064 | 12 | 107.6 | 1.3 |a) Does the data provide compelling evidence for concluding that the true average strength of the 1078 grade is different from the 1064 grade? Test the appropriate hypotheses using the p-value approach at the .01 level.b) Describe a Type I Error and Type II error here.

Name: 4. Tensile strength tests were carried out on two different grades of
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Description: 4. Tensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Tensile strength is normally distributed for both grades of wire rod. Assume the population standard deviations are unequal. \( df =

Solution: The data of tensile strength for two different grades of wire rod is given. It is required to test the claim that the true average strength of the 1078 grade is different from the 1064 grade. The null and alternative hypotheses are: Null hypothesis (H0): The true average strength of the 1078 grade is same as that of the 1064 grade. Alternative hypothesis (H1): The true average strength of the 1078 grade is different from the 1064 grade. The level of significance is given to be 0.01. Part a) It is assumed that the population standard deviations are unequal. Degrees of freedom = 22.51 Since the population standard deviations are unknown and unequal, we will use two independent samples t test with the following test statistic: Thus, test statistic = 24.498315 P value: It can be easily found using MS-Excel. In any empty cell of an excel sheet, type =T.DIST.RT(24.498315,22.51) and hit enter. It gives 9.23828E-18 Decision Rule: p value much smaller than the level of significance (0.01). So, null hypothesis gets rejected. Conclusion: There is sufficient evidence to support the claim that the true average strength of the 1078 grade is different from the 1064 grade. Part b) Type I and type II error needs to be described. Type I error: It is rejecting the null hypothesis (H0) when it is actually true. Here, a type I error will occur if it is concluded that the true average strength of the 1078 grade is different from the 1064 grade when the true average strength of both the grades of wire rod are actually same. Type II error: It is the non-rejection of a false null hypothesis. In this problem, a type II error can occur if we conclude that the average tensile strength of both the grades of wire rod are same when they are actually different.

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4. Tensile strength tests were carried out on two difference grades of wire rod, resulting in the accompanying data. Tensile strength is normally distributed for both grades of wire rod. Assume the population standard deviations are unequal. df= 22.51 Sample Mean (kg/mm²) 123.6 Grade Sample Size Sample SD AISI 1078 AISI 1064 14 2.0 12 107.6 1.3 a) Does the data provide compelling evidence for concluding that the true average strength of the 1078 grade is different from the 1064 grade? Test the appropriate hypotheses using the p-value approach at the .01 level. b) Describe a Type I Error and Type II error here.

4. Tensile strength tests were carried out on two difference grades of wire rod, resulting in the accompanying data. Tensile strength is normally distributed for both grades of wire rod. Assume the population standard deviations are unequal. df= 22.51 Sample Mean (kg/mm²) 123.6 Grade Sample Size Sample SD AISI 1078 AISI 1064 14 2.0 12 107.6 1.3 a) Does the data provide compelling evidence for concluding that the true average strength of the 1078 grade is different from the 1064 grade? Test the appropriate hypotheses using the p-value approach at the .01 level. b) Describe a Type I Error and Type II error here.

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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