https://www.youtube.com/watch?v=fx4tCRiynMQ&list=PLsri7w6p16vtEz_J1G7HQG-Rm8vpZPtPS&index=3 ================================================================================ If number of sample is large (generally $$$n>30$$$) $$$s^2$$$ becomes $$$\sigma^2$$$ $$$z = \dfrac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$$ ================================================================================ If number of sample is not large enough you use "test statistics t" $$$t_{n-1} = \dfrac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$$$ ================================================================================ Relationship between "t test" and "z test" z test $$$\subset$$$ t test ================================================================================ * Example * You survey 15 number of drink A Question * Set hypothesis * Perform left sided test using p-value=0.05 * precondition: population distribution is normal distribution Answer test statistics t $$$t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$$$ $$$t = \frac{302.1-300}{\frac{14.54}{\sqrt{15}}} = 0.568$$$ * Degree of freedom = $$$n-1 = 15-1 = 14$$$ * p-value $$$\alpha = 0.05$$$ In left side test, when $$$\alpha=0.05$$$, $$$t =-1.761$$$ according to t distribution table Conclusion: * null hypothesis $$$H_0$$$ is selected * Hypothesis of "Drink A has 300ml" is correct ================================================================================