# Hypothesis testing

- A statistical hypothesis test is a method of making statistical decisions from and about experimental data
- Null-hypothesis testing answers the question:
- â€œHow well the findings fit the possibility that chance factors alone might be responsible"
- Example: Does your score of 6/10 imply that I am a good teacher???

- There are five ingredients to any statistical test:
- Null Hypothesis
- Alternate Hypothesis
- Test Statistic
- Rejection / Critical Region
- Conclusion

**Properties of point estimators**

- Linearity
- Unbiasedness
- Minimum Variance
- Efficiency
- Best Linear unbiased estimator (BLUE)
- Consistency
- Unbiased estimator: One or more values of an estimator is equal to the true value of a parameter
- Efficient estimator: Considering only the unbiased estimators of a parameter, the one which has least variance is called the efficient estimator
- Consistent estimator: The estimator which approaches the true value of its parameter as the sample size increases

**Launching a niche course for MBA students?**

- Christos, brand manager for a leading financial training center, wants to introduce a new niche finance course for MBA students. He met some industry stalwarts and found that with the skills acquired by attending such a course, the students would be very hot in job market
- He meets a random sample of 100 students and discovers the following characteristics of the market
- Mean household income to $20,000
- Interest level in students = high
- Current knowledge of students for the niche concepts = low

- Christos strongly believes the course would adequately profitable in students if they have the buying power for the course. They would be able to afford the course only if the mean household income is greater than $19,000
- Would you advice Christos to introduce the course?
- What should be the hypothesis?
- Hint: What is the point at which the decision changes (19,000 or 20,000)?
- What about the alternate hypothesis?

- What other information do you need to ensure that the right decision is arrived at?
- Hint: confidence intervals / significance levels?
- Hint: Is there any other factor apart from mean, which is important? How do I move from population parameters to standard errors?

- What is the risk still remaining, when you take this decision?
- Hint: Type-I / II errors?
- Hint: P-value

- What should be the hypothesis?