https://www.youtube.com/watch?v=uzsNpYSiXjY&list=PLsri7w6p16vtEz_J1G7HQG-Rm8vpZPtPS&index=2
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* Set null hypothesis
$$$H_0:\mu=\mu_0$$$
population mean = sample mean
* Set anti-hypothesis
- two sided test
$$$H_1:\mu\ne \mu_0$$$
- Colored ends: null hypothesis is rejected
- one sided test
(1) left-one-sided test
$$$H_1:\mu \mu_0$$$
(2) right-one-sided test
$$$H_1:\mu>\mu_0$$$
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* Set p-value
$$$\alpha=0.05$$$ against null hypothesis and anti hypothesis
* If two sided,
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Left sided test
Right sided test
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* Example
Test hypothesis when you know population's variance
* Drink A says it has 300ml
* Inspected 300 samples
* Mean was 244.65 ml
* std is 20.
Question:
* Set hypothesis
* Perform left sided test with p-value=0.05
Answer:
$$$H_0: \mu=300ml$$$
$$$H_1: \mu\lt 300ml$$$
p-value $$$\alpha=0.05$$$
$$$n=300$$$
$$$\mu_0=244.65ml$$$
$$$\sigma=20$$$
left sided test:
$$$-z_{\alpha} \\
= -z_{0.05} $$$
* See the std normal distribution table
$$$= -1.64$$$
If $$$z\lt -1.64$$$, $$$H_0$$$ is rejected, $$$H_1$$$ is selected
* Test statistics z
$$$z \\
= \frac{m-\mu}{\frac{\sigma}{\sqrt{n}}} \\
= \frac{244.65-300}{\frac{20}{\sqrt{300}}} \\
= -47.935$$$
Calculated $$$z = -47.935$$$
$$$z\lt -1.64$$$ is correct
Conclusion:
$$$H_0$$$ is rejected
$$$H_1$$$ is selected
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