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An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is and the sample standard deviation is s = 0.22. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed.
An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is and the sample standard deviation is s = 0.22. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed.
Final answer:For a 99% lower confidence bound, we use the Z-score of -2.33 with the formula for a confidence interval. The lower bound will be: 'Sample Mean - (-2.33) * (Sample Standard Deviation/√Sample Size).'Explanation:The solution to this problem involves using concepts ofstatistics, primarily regarding normal distribution andconfidence intervals. Given that we're finding a 99% lower confidence bound, we're interested only in the lower range of the spectrum, not the upper.We need to look at the Z-score associated with a 99% confidence interval in a standard normal distribution. The Z-score for 99% is approximately 2.33 (meaning it cuts off the lowest 0.5% and highest 0.5% of the curve). However, since we're only interested in the lower bound, we will be using a Z-score of -2.33.The formula for a confidence interval is:µ = X ± Z(s/√n), where µ is the population mean, X is the sample mean, Z is the Z-score, s is the sample standard deviation, and n is the size of the sample. In our question, X is unspecified, s = 0.22, and n = 20. So, assuming 'Xbar' is your sample mean, your lower bound would be:Xbar - (-2.33) * (0.22/√20)Learn more about Confidence Interval here:brainly.com/question/34700241#SPJ12...