Hypothesis Testing

Hypothesis testing: using a data observed from a distribution with unknown parameters, we hypothesise that the parameters of this distribution take particular values and test the validity of this hypothesis using statistical methods

Confidence intervals: provide probabilistic level of certainty regarding parameters of a distribution

1. X_1, X_2,..., X_n
2. unknown mean value \mu
3. known \sigma

normal distribution: N(\mu, \sigma^2)
estimate of \mu: \bar X=\frac{X_1, X_2,..., X_n}{n}
distribution of \bar x: N(\mu, \frac{\sigma^2}{n})

P(\bar X\leq \mu+2)
P(\bar X-\mu\leq 2)
P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}\leq \frac{2}{\sigma/\sqrt{n}})