Hypothesis Testing

• Foundations for Hypothesis Testing

• Steps for Data-Driven 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 status-quo. 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

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
  1. 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
  2. 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
  3. 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
  4. 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%