https://www.youtube.com/watch?v=VOfKIeTpxg8&list=PLsri7w6p16vtEz_J1G7HQG-Rm8vpZPtPS&index=5 ================================================================================ 4th batter in baseball to be 4th batter, he should have batting ratio over 0.3 Criterion to be 4th batter in form of ratio: 0.3 ================================================================================ Test on hypothesis about population's ratio * AS center * 100 customer received the service * How many customers got satisfied by service? * Ratio from sample: $$$\hat{p}$$$ * Ratio from population: $$$p_0$$$ $$$H_0:\hat{p}=p_0$$$ 2 sided test $$$H_1: p \ne p_0$$$ 1 sided test left $$$H_1: p \lt p_0$$$ right $$$H_1: p \gt p_0$$$ * test statistics on population's ratio $$$z = \dfrac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$$ ================================================================================ * Example * AS center * If satisfaction ratio is >80%, no retraining on service, otherwise, perform retraining. * randomly selected 100 customers * satisfied customer: 81 customers Question * Test population's ratio with p-value=0.05 Answer $$$H_1: p\lt 0.8$$$ $$$H_0:p=0.8 $$$ n=100 p=0.8 $$$\alpha=0.05$$$ $$$z \\ = \frac{\hat{p}-p_0}{\sqrt{ \frac{p_0(1-p_0)}{n}}} \\ = \frac{0.81-0.8}{\sqrt{ \frac{0.8(1-0.8)}{n}}} \\ = 0.25$$$ ================================================================================ Rejection area is located in left 0.25 is located in the right $$$H_0$$$ can't be rejected