Respuesta :
95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
What is proportional limit?
The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.
To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:
lower confidence bound = sample mean - (t-value * standard error)
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]
To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.
Substituting these values into the formula for the lower confidence bound, we get:
lower confidence bound = 8.52 - (1.725 * 0.19)
= 8.52 - 0.327
= 8.19
So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.
Hence, 95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
To know more about proportional limit visit,
https://brainly.com/question/22935390
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