What is
Hypothesis testing?
1. Hypothesis is a supposition/ assumption (made on limited evidence) which
is yet to be proved and which requires more investigation
2. Hypothesis testing is used to determine outcome of the study and to test whether the hypothesis is accepted or rejected.
3. It can be used to see which advertisements work better, sales distribution
etc.
4. There is 1 tailed test and 2 tailed test.
Errors in
Hypothesis testing?
1. IF H0 is TRUE and H0 is accepted = NO ERROR
2. IF H0 is FALSE and H0 is rejected = NO ERROR
3. IF H0 is TRUE and H0 is rejected = TYPE 1 ERROR
4. IF H0 is FALSE and H0 is accepted = TYPE 2 ERROR
5 steps in
Hypothesis testing:
STEP 1 : STATE NULL AND ALTERNATIVE
HYPOTHESIS
STEP 2: CHOOSE LEVEL OF
SIGNIFICANCE (α)
STEP 3: FIND THE CRITICAL VALUES
STEP 4 : FIND TEST STATISTICS
STEP 5: DRAW CONCLUSION
EXAMPLE 1
Average weight of the population is 100 with
standard deviation 20. A researcher believes that the value has changed. A
sample population of 75 has the average of 110. Is there enough evidence that
it is changed?
STEP 1 : STATE NULL AND ALTERNATIVE HYPOTHESIS
Null Hypothesis
H0: µ =
100 [currently believed to be true]
Alternative Hypothesis
H1: µ ≠
100 [being claimed by the researcher.]
2 tailed test will be performed as
H1 (alternative hypothesis) consists of ‘≠’ sign.
STEP 2: CHOOSE LEVEL OF
SIGNIFICANCE (α)
Let us consider
α to be 0.05
The remaining
curve are will be 1-0.05 = 0.95
The 2
tails will be symmetrical and will have same area and each will be of 0.025
STEP 3: FIND THE CRITICAL VALUES
We need to calculate the
z score from the table
Z values are the critical
values which separates the tail area and middle area.
For confidence level of 95 % Critical value is 1.96 (from the table)
STEP 4 : FIND TEST STATISTICS
Z = x̅ - µ/ (σ/ √ n)
x̅= average of the sample
µ=
average of the population
σ= standard deviation of the
population
√
n= sample size
Z = x̅ - µ/ (σ/ √ n)
= 110 -100/(20/√ 75) = 4.33
Our test statistic value is 4.33
STEP 5: DRAW CONCLUSION
Critical value = 1.96 which is lower than 4.33
(falls in the rejection region)
Therefore, Null Hypothesis is rejected
Alternative hypothesis is accepted
So, from above, we can say that there is enough
evidence that the average weight is changed.
EXAMPLE 2
Average weight of the population is 100 with
standard deviation 15. A researcher believes that the value is lower. Weights
of 5 random adults are 70,75,85,99,109. Is there enough evidence that it is changed?
STEP 1 : STATE NULL AND ALTERNATIVE HYPOTHESIS
Null Hypothesis
H0: µ =
100 [currently believed to be true]
Alternative Hypothesis
H1: µ <
100 [being claimed by the researcher.]
1 tailed test will be performed as
H1 (alternative hypothesis) consists of ‘<’ sign.
STEP 2: CHOOSE LEVEL OF
SIGNIFICANCE (α)
Let us consider
α to be 0.05
The remaining
curve are will be 1-0.05 = 0.95
STEP 3: FIND THE CRITICAL VALUES
Area is
0.05
Number
of sample size = 5
Df <
sample size
So let’s
take df = 4
So, critical
value = 2.132
STEP 4 : FIND TEST STATISTICS
Z = x̅ - µ/ (σ/ √ n)
x̅= average of the sample
µ=
average of the population
σ= standard deviation of the
population
√
n= sample size
x̅ =
70+ 75+85+99+109 / 5 =87.6
Z = x̅ - µ/ (σ/ √ n)
= 87.6 – 100/ (15/ √5) = -1.843
Our test statistic value is -1.843
STEP 5: DRAW CONCLUSION
Since test statistic lies
somewhere between critical value and the middle of the curve , it is not in the rejection region
Therefore, Null Hypothesis is accepted
Alternative hypothesis is rejected
So, from above, we accept H0: µ = 100
What is
Bayesian Inference?
Bayesian Inference is a method of statistical inference.
It is used to update the probability of an
hypothesis so that more information is available
Bayes Theorem is used which is based on conditional
probability