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 $$$H_0$$$
================================================================================