Lecture 3 - Hypothesis Testing

Question 1

Why do we need to conduct hypothesis tests?

Answer 1

To see whether a certain observed scenario is due to random variation or due to a different population mean

Question 2

Is looking at the means for the two groups/samples sufficient?

Answer 2

No, as they tell us about the samples but not about the population as a whole

Question 3

What is a hypothesis test?

Answer 3

A sample based decision rule that helps us decide whether we should reject a hypothesis

Question 4

How many different types of hypothesis tests can we have and what are they?

Answer 4

3 types of tests:
1) 2-sided - H0 : Bj = b H1 : Bj =/ b (not equal)
2) 1-sided - H0 : Bj <= b H1 : Bj > b
3) 1-sided - H0 : Bj >= b H1 : Bj < b

Note that all values of b are covered in all 3 tests (all parameters covered) therefore equal signs important to ensure b value itself is included also

Question 5

How many possible scenarios/decisions can be made following the hypothesis test?

Answer 5

There are 4 potential decisions and these are:
1) Type I error - the probability that you reject H0 given that it is true is equal to alpha
2) Type II error - the probability that you accept H0 given that it is false (or that H1 is true) is equal to beta
3) Correct decision - probability that you reject H0 given that it is false (or that H1 is true) is equal to 1 minus alpha
4) Correct decision - probability that you accept H0 given that it is true is equal to 1 minus beta

How to remember - remember gate rejecting H0 is alpha and accepting it is beta

Note that above sentences can be written in format: P(Reject H0 I H0 is True) = alpha for example (first one)

For 2 and 3 stick to H1 being true as normally written with whatever hypothesis is true rather which one is false - state both but state the one that is false in brackets when writing in sentence form otherwise just stick to P(Accept H0 I H1 True) for example example (no. 2)