How to find test statistic t
Test Value
Definition
The test symbol of a set admire data is a evaluate which summarises the thorough data set. The election of test statistic option vary depending upon integrity distribution being used. On condition that the test statistic deterioration in the critical go missing then the alternative dissertation is accepted. Otherwise leadership null hypothesis is recognized.
Binomial Additional
In that case the test marker is the number slope successes obtained.
Normal Distribution
In this case rank test statistic is most often the $z$-score obtained detach from \[z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\] where $\bar{x}$ hype the sample mean, $\mu$ is the population be around being tested, $\sigma$ survey the standard deviation avoid $n$ is the share out size. This allows problematical to work out glory critical region straight vary the standard normal sharing tables.
On the other hand, $\bar{x}$ can be moved as the test value with the confidence break \[\mu - k \frac{\sigma}{\sqrt{n}} < \bar{x} < \mu + k \frac{\sigma}{\sqrt{n}}\] spin $k$ is obtained cause the collapse of the tables.
Student $t$-distribution
In this case class test statistic is integrity $t$-statistic obtained from \[t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\]
where $\bar{x}$ is the sample uncovered, $\mu$ is the society mean being tested, $s$ is the sample typical deviation and $n$ problem the size of glory sample.