The length of time a structural element can survive at temperature is a safety critical element of the system. The system requirements state the element must survive 100 C for at least 88 seconds. You collect a sample of 11 experiments measuring the time at temperature to failure of the element. Your sample has a mean of 83 seconds and a standard deviation of 3 seconds. You are constructing a 99% Confidence Interval to verify the requirement.What is the Lower Limit of the Confidence Interval?
Question
The length of time a structural element can survive at temperature is a safety critical element of the system. The system requirements state the element must survive 100 C for at least 88 seconds. You collect a sample of 11 experiments measuring the time at temperature to failure of the element. Your sample has a mean of 83 seconds and a standard deviation of 3 seconds. You are constructing a 99% Confidence Interval to verify the requirement.What is the Lower Limit of the Confidence Interval?
Solution
To calculate the lower limit of the confidence interval, we first need to find the standard error. The standard error (SE) is calculated by dividing the standard deviation (SD) by the square root of the sample size (n).
In this case, the standard deviation is 3 seconds and the sample size is 11.
SE = SD / sqrt(n) = 3 / sqrt(11) = 0.9045
Next, we need to find the z-score for a 99% confidence interval. The z-score for a 99% confidence interval is approximately 2.576.
The lower limit of the confidence interval is calculated by subtracting the product of the z-score and the standard error from the sample mean.
Lower Limit = Mean - (Z * SE) = 83 - (2.576 * 0.9045) = 80.67 seconds
So, the lower limit of the 99% confidence interval is approximately 80.67 seconds.
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