Hypothesis Test - Null and Alternative Hypothesis, Significance Level and Confidence Interval, P Value

Here is how I remember things

ANA
SCS
P  

When P < S, outside C,  we accept A. (i.e. reject N)
When P > S, inside C, we accept N. (i.e. fail to reject N)

Here is the full picture

Alternative     Null    Alternative
Significance Confidence Significance
P Value

What is null hypothesis?
Null hypothesis is used to denote things that are default, original, native, nothing, innocent, natural, naught. (naught means mathematical zero). It is the native, natural and default state of the object when nothing is happening. It is the main body.

What is alternative hypothesis?
Alternative hypothesis is the opposite of null hypothesis which is used to denote things that are special, changed, modified, added, affected, guilty. It is sometimes called research hypothesis. It is the state when somethings happens, making things changes. It is the tail of the body.


Note: Null hypothesis and alternative hypotheses are mathematically opposite and they all together forms all possibilities. So, ANA is all.

What is Confidence Interval?
The 99%, 95%, 99.9% are the confidence intervals. It means central, confident, normal, default, common, natural, usual, frequent, prevailing, trivial, typical, probable. The high confidence interval is the large probability of default null hypothesis.

Whats is Significance Level?
The 1%, 5%, 0.1% are the significance levels. It means tail, significant, alternative, extraordinary, extreme, exceptional, remarkable, singular, outstanding. It is the Z value at the tails. It is sometimes called alpha, level of significance. The low significance level is the low probability for changed alternative hypothesis.

Note: Confidence interval and significance level adds up to 1, always. So, SCS = 1.

What is critical values?
Critical values is the boundary, cut-off between the confidence interval and significance level on the x-axis of the distribution.

What is p value?
P value is the probability of the sample test statistics which is calculated form the samples drawn from the population. It is compared to the significance level. When p value less than significance level (i.e. outside the tail), it means we reject the null hypothesis (i.e. the body) and accept the alternative hypothesis (i.e. the tail).

Again:

ANA
SCS
P  

When P < S, outside C,  we accept A. (i.e. reject N)
When P > S, inside C, we accept N. (i.e. fail to reject N)

What is Type 1 Error?
When Null is true but rejected to believe Alternative, Type 1.
以利用驗孕棒驗孕為例，此時未懷孕為虛無假設。若用驗孕棒為一位未懷孕的女士驗孕，結果是已懷孕，這是第一型錯誤。若用驗孕棒為一位孕婦驗孕，結果是未懷孕，這是第二型錯誤。