The sample mean calculated using an estimator, used as an estimate for the population mean, is called a point estimate of the population mean. It gives us a single number as an estimate of a population parameter.
The population parameter is not likely to be equal to the point estimate because of sampling error. So, a more appropriate approach is to find a range of value that we expect for the population parameter with a specified level of probability. We use a confidence interval for describing that range.
A confidence interval is a range of which we can say with a degree of confidence that it would contain the population parameter it is intended to estimate. The degree of confidence is a probability number measured as 1 - α where α is the level of significance. It is often referred to as 100(1 - α)% confidence interval for the parameter.
A confidence interval of 95 percent for a sample mean means than 95 percent of the times the interval will contain the unknown value of the population mean.
Confidence interval = Point estimate ± Reliability factor*Standard error
where reliability factor is a number based on the assumed distribution of the point estimate and the degree of the confidence interval
A 90 percent confidence interval will not have the population mean 10 percent of the times. Those 10 percent will be distributed equally on both sides (left and right) of the distribution. The middle 90 percent will be the confidence interval, and 5 percent will be left out on each side of the distribution. So, we need to look at the probability cumulative distribution table for a z or t value of 0.05 (5 percent).
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