follow an approximately normal distribution. Suppose that our sample has a mean of = 10 and we have constructed the 90% confidence interval (5, 15) where EBM=5. To get a 90% confidence interval, we must include the central 90% of the probability of the normal distribution. If we include the central 90%, we leave out a total of = 10% in both tails, or 5% in α each tail, of the normal distribution. To capture the central 90%, we must go out 1.645 "standard deviations" on either side of the calculated sample mean. 1.645 is the z-score from a Standard Normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail.
follow an approximately normal distribution. Suppose that our sample has a mean of = 10 and we have constructed the 90% confidence interval (5, 15) where EBM=5. To get a 90% confidence interval, we must include the central 90% of the probability of the normal distribution. If we include the central 90%, we leave out a total of α = 10% in both tails, or 5% in each tail, of the normal distribution. To capture the central 90%, we must go out 1.645 "standard deviations" on either side of the calculated sample mean. 1.645 is the z-score from a Standard Normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail.
ch8_confidenceintervalsdknown.docx