tailieunhanh - Exploratory Data Analysis_7

Tham khảo tài liệu 'exploratory data analysis_7', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Confidence Limits for the Mean ENGINEERING STATISTICS HANDBOOK home TOOLS AIQỈ ISEAtCH back NEXT1 1. Exploratory Data Analysis . EDA Techniques . Quantitative Techniques . Confidence Limits for the Mean Purpose Confidence limits for the mean Snedecor and Cochran 1989 are an interval estimate Interval for the mean. Interval estimates are often desirable because the estimate of the mean Estimate for varies from sample to sample. Instead of a single estimate for the mean a confidence Mean interval generates a lower and upper limit for the mean. The interval estimate gives an indication of how much uncertainty there is in our estimate of the true mean. The narrower the interval the more precise is our estimate. Confidence limits are expressed in terms of a confidence coefficient. Although the choice of confidence coefficient is somewhat arbitrary in practice 90 95 and 99 intervals are often used with 95 being the most commonly used. As a technical note a 95 confidence interval does not mean that there is a 95 probability that the interval contains the true mean. The interval computed from a given sample either contains the true mean or it does not. Instead the level of confidence is associated with the method of calculating the interval. The confidence coefficient is simply the proportion of samples of a given size that may be expected to contain the true mean. That is for a 95 confidence interval if many samples are collected and the confidence interval computed in the long run about 95 of these intervals would contain the true mean. Definition Confidence Interval Confidence limits are defined as where V is the sample mean s is the sample standard deviation N is the sample size X is the desired significance level and 1 is the upper critical value of the t distribution with N - 1 degrees of freedom. Note that the confidence coefficient is 1 -a. From the formula it is clear that the width of the interval is controlled by two factors 1. As N .