When we calculate a statistic for example, a mean, a variance, a proportion, or a correlation coefficient, there is no reason to expect that such point estimate would be exactly equal to the true population value, even with increasing sample sizes. According to University of Glasgow Department of Statistics, Confidence Interval is defined as: A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. I appreciate your conceptual illustration of confidence intervals these illustration will be used to used to educate the medical doctors for research purpose.
This quick note serves as a supplementnote of my previous Statistical Notes (3): Confidence Intervals for Binomial Proportion Using SAS which I will extend as a SESUG 2015 paper. The farther you try to forecast into the future, the less certain you are -- how can you represent that graphically? In the above session, a binomialc option was used to compute the intervals with a continuity correction(CC). Interval estimation for the difference between independent proportions: comparison of eleven methods. Note that #1 method is the most popular one in textbook, #10 might  be the most wildly used method in industry.
Last year I dumped piece of SAS codes to compute confidence intervals for single proportion using 11 methods including 7 presented by one of Prof. If interested, a nice paper on binomial intervals with ties, the paper Confidence intervals for a binomial proportionin the presence of ties,  and the program.
This post serves as an implementation using SAS accompany with the first paper on confidence intervals for single proportion(method 1-7).
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We can now prepare a flow chart for estimating a confidence interval for ?, the population parameter. Having 11 numbered balls -0 to 10 -into a basket and have 6 spaces to be numbered with the balls selected in each 6 chances and it returned it back to the basket each time. Quota sampling Under this method enumerators shall select the respondents in place of those not available, as per the quota fixed according  to guide lines   provided to them. Chi-square analysis can be used with both Goodness-of-Fit Tests and with Tests for Independence.
Analysis of variance allows us to test whether the differences among more than two sample means are significant or not. Zinc is a trace element and it is important in wound healing, building up the immune system and DNA synthesis. To understand Confidence Intervals better, consider this example scenario: Acme Nelson, a leading market research firm conducts a survey among voters in USA asking them whom would they vote if elections were to be held today. If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter. Basically I added a new Blaker method to my file and found more CIs from SAS PROC FREQ. There are some Bayesian intervals available in SAS  procedures but since I’m not familiar with Bayes, I will leave it blank by far. I’m still trying to figure out why the exact method produces different numbers compared to what’s in Prof.
In most Six Sigma projects, there are at least some descriptive statistics calculated from sample data.

Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter. In truth, it cannot be said that such data are the same as the population’s true mean, variance, or proportion value.
In addition to Democrats and Republicans, there is this surprise independent candidate, John Doe who is expected to secure 22% of the vote. There are many situations in which it is preferable instead to express an interval in which we would expect to find the true population value. A confidence interval is an interval, calculated from the sample data, that is very likely to cover the unknown mean, variance, or proportion. For example, after a process improvement a sampling has shown that its yield has improved from 78% to 83%. If the lower end of the interval is 78% or less, you cannot say with any statistical certainty that there has been a significant improvement to the process.
There is an error of estimation, or margin of error, or standard error, between the sample statistic and the population value of that statistic. For example, if you are dealing with a sample mean and you do not know the population’s true variance (standard deviation squared) or the sample size is less than 30, than you use the t Distribution confidence interval.

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