In an inertia welding experiment, a sample of 50 welds made with a standard welding method were tested. The sample mean and sample standard deviation of the breaking strengths of these welds were found to be 94 ksi and 3 ksi, respectively. Another sample of 60 welds using an alternative welding method were also tested and the resulting sample mean and sample standard deviation were 96 ksi and 3.5 ksi, respectively.

(a) Construct a 95% confidence interval for the difference in true mean breaking strengths for the two types of welds.

(b) Is there evidence that there exists a difference in the true mean breaking strengths for the two types of welds? Use the five-step hypothesis testing procedure in answering this question. The confidence level is 95%. (Optional)

Question

Mathematics

Rosa Mendez

10 October, 07:19

In an inertia welding experiment, a sample of 50 welds made with a standard welding method were tested. The sample mean and sample standard deviation of the breaking strengths of these welds were found to be 94 ksi and 3 ksi, respectively. Another sample of 60 welds using an alternative welding method were also tested and the resulting sample mean and sample standard deviation were 96 ksi and 3.5 ksi, respectively.

(a) Construct a 95% confidence interval for the difference in true mean breaking strengths for the two types of welds.

(b) Is there evidence that there exists a difference in the true mean breaking strengths for the two types of welds? Use the five-step hypothesis testing procedure in answering this question. The confidence level is 95%. (Optional)

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Answers (1)

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Sienna Cannon · Answer 1

Yes, there is evidence that there exists a difference in the true mean breaking strengths for the two types of welds. This is because confidence interval does not contain 0

Step-by-step explanation:

Given that in an inertia welding experiment, a sample of 50 welds made with a standard welding method were tested.

Group Group One Group Two

Mean 94.000 96.000

SD 3.000 3.500

SEM 0.424 0.452

N 50 60

The mean of Group One minus Group Two equals - 2.000

standard error of difference = 0.629

t = 3.1818

df = 108

a) 95% confidence interval of this difference: From - 3.246 to - 0.754

b) Yes, there is evidence that there exists a difference in the true mean breaking strengths for the two types of welds. This is because confidence interval does not contain 0