https://www.youtube.com/watch?v=vtT5JzOIiCU&list=PLsri7w6p16vtEz_J1G7HQG-Rm8vpZPtPS&index=4 ================================================================================ Previous methods create decision from rejection or non-rejection Test using p-value can create "intensity" on the decision ================================================================================ Probability of entire p=1.0 * Rejection area (5% in this case) to the $$$H_0$$$ is located in the right * Probability of distance from $$$\alpha$$$ * Far: red intensity ================================================================================ p-value = significance level ================================================================================ * Example drink A 300ml surveyed sample n=300 sample mean $$$\mu=294.65$$$ sample std $$$\sigma=45$$$ Question * Set hypothesis * Decide rejection of null hypothesis at $$$\alpha=0.05$$$ Answer H_0: \mu=300 H_1: \mu \lt 300 n=300 \mu=294.65 \sigma=45 \alpha=0.05 test statistics $$$z \\ = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\ = \frac{294.65-300}{\frac{45}{\sqrt{300}}} =-2.059$$$ Calculate p $$$p = p(z\lt -2.059) \\ = 0.5 - (0\le z \le 2.059) \\ = 0.5 - (0\le z \le 2.06) \\ = 0.5 - 0.48 \\ = 0.020$$$ $$$\alpha=0.05, p=0.020$$$ Reject $$$H_0$$$ ================================================================================