In this article, we will learn about different types[Z Test and t Test] of commonly used Hypothesis Testing.

在本文中，我們將學習常用假設檢驗的不同類型[ Z檢驗和t檢驗 ]。

假設是什么？ (What is Hypothesis?)

This is a Statistical process which is an assumption about population parameter.

這是一個統計過程，是有關總體參數的假設。

Using the hypothesis testing we can reject / accept the assumptions made by projecting the data from Sample to Population (or) from Population to Sample.

使用假設檢驗，我們可以拒絕/接受通過從樣本到總體(或從總體到樣本)的數據投影所做的假設。

This process can also be termed as validity of projection.This operates around Null Hypothesis H0 & Alternative Hypothesis H1.

此過程也可以稱為投影的有效性。此過程圍繞零假設 H0和替代假設H1進行 。

There are few commonly used Tests which can be classified based on 2 categories:

很少有可以根據2類進行分類的常用測試：

Sampling distribution Of Means — Z Test & T Test

均值的抽樣分布-Z檢驗和T檢驗

Sampling distribution Of Variance — Chi squared Test & F Test

方差的抽樣分布-卡方檢驗和F檢驗

Z檢驗： (Z Test:)

Assumptions for Z Test:

Z測試的假設：

a. Sample size should be greater than 30

一個。 樣本數量應大于30

b. Population Standard Deviation should be known

b。 人口標準偏差應該是已知的

c. Variables in data should be continuous

C。 數據變量應該是連續的

Steps for Z Test:

Z測試步驟：

a. State H0 or H1 — [From the given problem we need to find]

一個。 狀態H0或H1-[根據給定的問題，我們需要找到]

b. Choose the level of significance — [Will be given in problem statement] If it is 0.05 ->1–0.05 = 95%

b。 選擇顯著性水平-[將在問題陳述中給出]如果為0.05-> 1–0.05 = 95％

c. Find the Critical values — Range for 95% -> Refer the Z score table → -1.96 to +1.96

C。 查找臨界值-范圍為95％->請參閱Z得分表→-1.96至+1.96

From Emperical split there are 3 most widely used values of Z we can directly take depending on the value:

從Emperical split中可以得出3個最常用的Z值，具體取決于該值：

If the Confidence Level is 99% — Z score value is 2.56, 95% — 1.96,90% — 1.64

如果置信度為99％ -Z得分值為 2.56，則95％-1.96,90％-1.64

d. Find the Test Statistics — Z value using the below formula

d。 使用以下公式找到“測試統計量”-Z值

e. Arrive at a Conclusion, to accept the hypothesis or reject the hypothesis

e。 得出結論，接受假設或拒絕假設

Where the variables are;

變量在哪里；

• X =Mean of the Sample,
  X =樣本均值，
• μ =Mean of population
  μ =人口平均值
• σ = Standard Deviation of population
  σ=總體標準差
• n = No. of observations
  n =觀察數

If the Z value falls within the Critical Value range, then we can accept the Hypothesis, else it has to be rejected

如果Z值在臨界值范圍內，則我們可以接受假設，否則就必須拒絕該假設

If the Confidence level is other than the above 3 values, then we need to use Z Score table to find the Z Scores/probability value, with which we can decide on accepting or rejecting the hypothesis.

如果置信度水平不是上述3個值，則需要使用Z分數表查找Z分數/概率值，我們可以使用該值決定接受還是拒絕該假設。

If the resultant value[Test Statistics — Z Value] is negative, then we need to verify negative Z score table. Else we need to verify positive Z score table.

如果結果值[測試統計數據-Z值]為負，則需要驗證負Z得分表 。 否則我們需要驗證正Z得分表 。

Sample 1: If Test Statistic Z value = 1.26 , then we need to use positive Z score table. Where 1.2 in Y axis and 0.06 in X axis.

樣本1：如果測試統計Z值= 1.26，那么我們需要使用正Z得分表。 其中Y軸為1.2，X軸為0.06。

Sample 2: If the Test statistic value is negative, we need to refer the negative Z score table. Finally to get the actual area / probability we need to subtract the Z score value from 1.

示例2：如果“測試”統計量值為負，則需要參考負Z得分表。 最后，要獲得實際面積/概率，我們需要從1中減去Z得分值。

T檢驗： (T Test:)

T Test is also called as Student test.

T測驗也稱為學生測驗。

Assumptions for T Test:

T檢驗的假設：

a. Sample size can be < 30

一個。 樣本大小可以<30

b. Population Standard Deviation is not known

b。 人口標準偏差未知

c. Variables should be continuous

C。 變量應該是連續的

We need to know another small concept called Degrees of Freedom (n-1) when we study about Student “t” test.

當我們研究學生“ t”測驗時，我們需要知道另一個稱為自由度(n-1)的小概念。

(n-1) — can be defined as the number of independent observations in computing mean is called degrees of freedom.

(n-1) —可以定義為計算平均值時獨立觀察的數量稱為自由度。

“ t”測試步驟： (Steps for “t ”Test:)

a. State H0 or H1

一個。 狀態H0或H1

b. Choose the level of significance — [given] If it is 0.05 ->1–0.05 = 95%

b。 選擇顯著性水平-[給定]如果為0.05-> 1–0.05 = 95％

c. Find the Critical values [Refer the steps above — same as Z Test]

C。 查找臨界值[請參考上述步驟-與Z測試相同]

d. Find the Test Statistics — t value using the above formula

d。 使用以上公式找到測試統計量-t值

e. Arrive at a Conclusion, to accept the hypothesis or reject the hypothesis

e。 得出結論，接受假設或拒絕假設

Here we need “t” table to find the probability. Y axis — for Degrees of freedom, X axis — for level of significance.

在這里，我們需要“ t”表來找到概率。 Y軸-適用于自由度，X軸-適用于重要程度。

結論： (Conclusion:)

With this we have come to an end of this article!

至此，我們結束了本文！

In this we have learnt about Tests for Sampling distribution of Means.

在此我們了解了均值抽樣分布的檢驗。

Please wait for “Learning Series II” for Tests related to ‘Sampling distribution of Variance’

請等待“學習系列II”中與“方差抽樣分布”相關的測試

Happy Learning! 🙂

學習愉快！ 🙂