Hypothesis Testing

Foundations for Hypothesis Testing

Steps for DataDriven Decision Making

What is hypothesis?
 A hypothesis is an idea that can be tested
 It is a supposition of proposed explanation made on the basis of limited evidence as a starting point for further investigation

Examples of hypothesis
 Apples are expensive and they cost more than 50 rs
 Example of not an hypothesis

Null and Alternative Hypothesis
 Null Hypothesis:
 This is hypothesis to be tested
 It is statusquo. Everything which was believed until now that we are contesting with our test
 Alternative Hypothesis:
 This is change or innovation that is contesting the status quo
 If null is the status quo then the act of performing a test, shows we have doubts about the truthfulness of null. More often than not the researchers opinion is contained in alternative Hypothesis
 Null Hypothesis:
Examples
 Glassdoor publishes an article trying to state average data scientist salary is 113K USD
 Your friend tries to tell you that " I think data scientists make more than $125,000 "
 You want to check if your height is above average compared to your class mates. Try to find the null and alternative hypothesis for this test from the below options
 H0: My height is higher or equal to the average height in class H1: My height is lower than the average height of the class
 H0: My height is higher to the average height in class H1: My height is lower or equal than the average height of the class
 H0: My height is lower or equal to the average height in class H1: My height is higher than the average height of the class
 H0: My height is lower to the average height in class H1: My height is higher or equal than the average height of the class
 You want to test if the Obama administration issue fewer executive orders than bush administration. State the null and alternative hypothesis
 H0: The obama adminstration issued at least as many executive orders as the bush administration. H1: The obama adminsitration issued fewer executive orders than the bush administration
Decisions you can take
 When testing there are two decisions that can be made
 to accept the null hypothesis
 to reject the null hypothesis
 To accept the null means that there isn’t enough data to support the change or innovation brought by alternative
 To reject the null means that there is enough statistical evidence that status quo is not representative of truth
Rejection Region and a Significance Level

Significance level:
 This is represented by α
 The probability of rejecting a null hypothesis, if it is true
 Typical values for alpha are 0.01, 0.05, 0.1
 The most common alpha value is 0.05

You have called your placement officer and he has said that the average percentage marks of Engineering students is 70%
 H0: Population mean percentage is 70%
 H1: Population mean percentage is not 70%

You have called your placement officer and he has said that the average percentage marks of Engineering students is lower than 70%
 H0: Population mean percentage is <= 70%
 H1: Population mean percentage is > 70%