1. 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)

2. 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