Test of Significance ( Hypothesis )

Level of significance

The probability lets say $\alpha$ of rejecting a true null hypothesis is called the level of significance. $p(\text{Rejecting }{H}_0|H_0)=\alpha$ .

The level of significance is the probability of rejecting a true null hypothesis. It is denoted by $\alpha$.

If we know the probability of $\alpha$ then we can calculate the $Z$ Value. The $Z$ value is the number of standard deviations a data point is from the mean.

Example

If the $\alpha =0.05$ we look closely at the Z table and find that the value of $Z_{\alpha }$ is 1.96.

Confidence Interval

The confidence interval is the range of values within which the true value of the parameter is expected to lie with a certain level of confidence. The confidence interval is denoted by $1-\alpha$ where $\alpha$ is the level of significance. $(\bar{X}-Z_{\alpha }\frac{\sigma }{\sqrt{n}},\bar{X}+Z_{\alpha }\frac{\sigma }{\sqrt{n}})$

References

Information

• date: 2025.03.26
• time: 17:35