Chapter 10 Confidence interval estimation
We estimate population parameter using either point estimates or interval
A point estimate is the value of a single sample statistic.
A confidence interval estimate is a range of numbers, called an interval,
constructed around the point estimate.
The confidence interval is constructed such that the probability that the population
parameter is located somewhere within the interval is known.
Sample mean X, is a point estimate of the population mean µ. However the
sample mean varies from sample to sample because it depends on the items
selected in the sample.
10.1 Confidence interval estimation for the mean (ơ Known)
• In order to understand the full meaning of the interval estimate, you need to
examine a hypothetical set of all possible samples of n values.
• For some samples, the interval estimate of µ is correct, but for others it is
• When a sample mean falls anywhere between 2 numbers, the population mean is
included somewhere within the interval.
• Because in practice, you select only one sample of size n and µ is unknown, you
never know for sure whether your specific interval includes the population mean.
However if you take all possible samples of n and compute their different %
confidence intervals, the % of the intervals will include the population mean, and
only the rest % of them will not be included.
• In general, the level of confidence is symbolized by ( 1- ơ) x100%
Calculator to determine Z value for % confidence
• Mean= 0 and standard deviation=1 ALWAYS
• Select STAT F5(DIST) F1 (NORM) F3(INVN) F2(VAR)
• The calculator will show 2 results X1INV and X2INV
Calculator to determine % confidence interval