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To compute the 95% confidence interval, start by computing the mean and standard error: M = (2 + 3 + 5 + 6 + 9)/5 = 5. M = = 1.118. Z.95 can be found using the normal distribution calculator and specifying that the shaded area is 0.95 and indicating that you want the area to be between the cutoff points.
The 95% confidence interval defines a range of values that you can be 95% certain contains the population mean. With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.
For a population with unknown mean and known standard deviation, a confidence interval for the population mean, based on a simple random sample (SRS) of size n, is + z*, where z* is the upper (1-C)/2 critical value for the standard normal distribution.
With a 95% confidence interval, you want 95 measurement results out of 100 to be within the limits of your uncertainty estimates. At 95% confidence, you are accepting a 1 in 20 failure rate. With a 99% confidence interval, you want 99 measurement results out of 100 to be within the limits of your uncertainty estimates.
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