Statistical Inference for the Mean Confidence Interval Confidence level: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the rejection region, which means - in the rejection region sample means are far enough away from the assumed population mean that only 5% of sample means would fall in the rejection region by chance. - Then we can have 95% confidence that a random sample mean will fall in that interval called Confidence interval. - The confidence level is 1- α. (e.g.1-5%=95%) 1.96 -1.96 f(z)

Statistical Inference for the Mean Confidence Interval Confidence interval of sample means: e.g. 5% level of significance in two tails, i.e. 95% confidence level. Φ(<z1)=0.025 Φ(>z1)=0.025 z1=1.96 z1=-1.96 f(z) z1=-1.96 z1=+1.96 2.5% 2.5% Then the 95% confidence interval is