Hypothesis Testing and Its Types
Learning Series I:
In this article, we will learn about different types[Z Test and t Test] of commonly used Hypothesis Testing.
What is Hypothesis?
This is a Statistical process which is an assumption about population parameter.
Using the hypothesis testing we can reject / accept the assumptions made by projecting the data from Sample to Population (or) from Population to Sample.
This process can also be termed as validity of projection.This operates around Null Hypothesis H0 & Alternative Hypothesis H1.
There are few commonly used Tests which can be classified based on 2 categories:
Sampling distribution Of Means — Z Test & T Test
Sampling distribution Of Variance — Chi squared Test & F Test
Z Test:
Assumptions for Z Test:
a. Sample size should be greater than 30
b. Population Standard Deviation should be known
c. Variables in data should be continuous
Steps for Z Test:
a. State H0 or H1 — [From the given problem we need to find]
b. Choose the level of significance — [Will be given in problem statement] If it is 0.05 ->1–0.05 = 95%
c. Find the Critical values — Range for 95% -> Refer the Z score table → -1.96 to +1.96
From Emperical split there are 3 most widely used values of Z we can directly take depending on the value:
If the Confidence Level is 99% — Z score value is 2.56, 95% — 1.96,90% — 1.64
d. Find the Test Statistics — Z value using the below formula
e. Arrive at a Conclusion, to accept the hypothesis or reject the hypothesis
Where the variables are;
- X =Mean of the Sample,
- µ =Mean of population
- σ = Standard Deviation of population
- n = No. of observations
If the Z value falls within the Critical Value range, then we can accept the Hypothesis, else it has to be rejected
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.
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.
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.
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.
T Test:
T Test is also called as Student test.
Assumptions for T Test:
a. Sample size can be < 30
b. Population Standard Deviation is not known
c. Variables should be continuous
We need to know another small concept called Degrees of Freedom (n-1) when we study about Student “t” test.
(n-1) — can be defined as the number of independent observations in computing mean is called degrees of freedom.
Steps for “t ”Test:
a. State H0 or H1
b. Choose the level of significance — [given] If it is 0.05 ->1–0.05 = 95%
c. Find the Critical values [Refer the steps above — same as Z Test]
d. Find the Test Statistics — t value using the above formula
e. Arrive at a Conclusion, to accept the hypothesis or reject the hypothesis
Here we need “t” table to find the probability. Y axis — for Degrees of freedom, X axis — for level of significance.
Conclusion:
With this we have come to an end of this article!
In this we have learnt about Tests for Sampling distribution of Means.
Please wait for “Learning Series II” for Tests related to ‘Sampling distribution of Variance’
Happy Learning! 🙂
