Hypothesis Testing for Data Science

1. Hypothesis Tests - A Primer

2. Hypothesis Testing
 Hypothesis
a. An assumption that we want to verify. Generally the assumption is made
about the population parameter.
b. Testing a Hypothesis is called Hypothesis Testing.
c. Two Types – Null and Alternate.
d. Null Hypothesis is the statement of no difference and is rep by H0.
e. Contradiction to Null Hypothesis is called Alternate Hypothesis (H1)

3. Null Hypothesis Vs Alternate Hypothesis
Null Hypothesis
H0
A statement about population
parameter.
We test the likelihood of
statement being true in order to
decide whether to accept or
reject the Alternate Hypothesis.
Can include =, <= or >= sign
Alternate Hypothesis
H1
A statement that directly
contradicts the Ho.
We determine whether or not
accept the or reject this statement
based on the likelihood of Null
being true.
Can Include > or < or != sign

4. Type – I and Type- II Error

5. Type – I and Type- II Error
In the first case, the court has made an error by punishing an
innocent person. In statistics, this kind of error is called a Type I or an
(alpha) error.
In the second case, because the guilty person has been punished, the
court has made the correct decision.
In our statistics example, a Type I error will occur when H0 is actually
true, and we wrongfully reject the null hypothesis, H0.
The value of alpha, called the significance level of the test,
represents the probability of making a Type I error.
In other words, alpha is the probability of rejecting the null
hypothesis, H0, when in fact it is true.

6. Type-II Error
 Consider this situation there are again two possibilities.
 The person has not committed the crime and is declared not
guilty.
 The person has committed the crime but, because of the lack of
enough evidence, is declared not guilty.
 In the first case, the court’s decision is correct.
 In the second case, however, the court has committed an error by
setting a guilty person free. In statistics, this type of error is called a
Type II or a (the Greek letter beta) error.
 In our statistics example, a Type II error will occur when the null
hypothesis, H0, is actually false, and we wrongfully conclude do not
reject H0

7. One Tail Vs Two Tail Test
School District A states its high school have an average of 85% pass rate in the High
School Exam. A New School was recently opened in the district and its found that a
sample of 150 students had a pass percentage of 88% with a SD of 4. Does this school
have a different pass percentage rate than the School A.
Does the new school have different pass percentage rate in compared to 85%.
What type of Test it would be?

8. One Tail Vs Two Tail Test
School District A states its high school have an average of 85%
pass rate in the High School Exam. A New School was recently
opened in the district and its found that a sample of 150 students
had a pass percentage of 88% with a SD of 4. Does this school have
a different pass percentage rate than the School A.
Does the new school have different pass percentage rate in
compared to 85%.
This is a Two Tail Test, Because we are trying to see if the mean is
either below 85% or above 85%
0.95

9. One Tail Vs Two Tail Test
School District A states its high school have an average of 85% pass rate in the High School
Exam. A New School was recently opened in the district and its found that a sample of 150
students had a pass percentage of 88% with a SD of 4. Does this school have a higher pass
percentage rate than the School A.
Does the new school have greater pass percentage rate in compared to 85%.
What type of Test it would be?

10. One Tail Vs Two Tail Test
School District A states its high school have an average of 85%
pass rate in the High School Exam. A New School was recently
opened in the district and its found that a sample of 150 students
had a pass percentage of 88% with a SD of 4. Does this school have
a higher pass percentage rate than the School A.
Does the new school have greater pass percentage rate in
compared to 85%.
This is a One Tail Test, Because we are trying to see if the mean is
greater than 85%.

11. One Tail Vs Two Tail Test
School District A states its high school have an average of 85% pass rate in the High School
Exam. A New School was recently opened in the district and its found that a sample of 150
students had a pass percentage of 88% with a SD of 4. Does this school have a lower pass
percentage rate than the School A.
Does the new school have lower pass percentage rate in compared to 85%.
What type of Test it would be?

12. One Tail Vs Two Tail Test
School District A states its high school have an average of 85%
pass rate in the High School Exam. A New School was recently
opened in the district and its found that a sample of 150 students
had a pass percentage of 88% with a SD of 4. Does this school
have a lower pass percentage rate than the School A.
Does the new school have lower pass percentage rate in
compared to 85%.
This is a One Tail Test, Because we are trying to see if the mean
is less than 85%.

13. When to Accept or Reject the Hypothesis

14. Rejection Region
The rejection regions are to the left of –z =-1.96 & to the right of z =1.96 aka critical value

15. Steps for Approaching Hypothesis Testing
The Average IQ for the adult population is 100 with a standard deviation of 15. A researcher believes this value has
changed. The researcher decides to test the IQ of 75 random adults. The average IQ of the sample is 105. Is there enough
evidence to suggest the average IQ has changed.
 Step1 – Define the Null Hypothesis: H0 – Average = 100
 Step2 - Define the Alternate Hypothesis: H1 – Average is not equal to 100
Tip - if there is not equal to in Alternate Hypothesis, we use Two Tail Tests.
 Step3 – Pick your Alpha | Selected the most commonly used 5%.
 Step4 – Find Critical Values (either z or t). Since sample >30, we will use z.
Further, the Population SD is known as well
Since we know that at 95% confidence interval, the Z value is 1.96
 Step5 – Calculate the Test Statistic
0.95
Two Tail Test
c.v. = -1.96 c.v. = +1.96

16. Table for Values

17. Critical Region
 The critical or rejection region is the set of all the values of the test statistic that causes us to reject
the null hypothesis. For example at significance level of 5%, see the test images below:
 If the standardized test statistic z falls in rejection region, then reject the H0.
 If it is not in rejection region, then fail to reject the H0

18. Example of Critical Region

19. Hypothesis Testing - Examples
Hypothesis Testing - Example 01
The mayor of a large city claims that the average net worth of families living in this city is at least 300,000. A random
sample of 25 families selected from this city produced a mean net worth of 288,000. Assume that the net worth of all
families in this city have a normal distribution with the population standard deviation of 80,000.
Using the 2.5% significance level, can you conclude that the mayor’s claim is false?
Hypothesis Testing - Example 02
At Canon Food Corporation, it used to take an average of 90 minutes for new workers to learn a food processing job.
Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean
time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes.
A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on
the new machine.
It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7
minutes. Find the p-value for the test that the mean learning time for the food processing procedure on the new machine
is different from 90 minutes. What will your conclusion be if alpha=0.01?