Topic 7 - Decision Statistics and Data Analysis Flashcards
What is the central limit theorem?
If the sample is big enough, anything that is a stochastic process (random walk), the final distribution will converge to become a normal distribution.
What are the procedure for testing a hypothesis?
- Define the hypothesis
- Define two competing null hypotheses
- The Null Hypothesis - typically denoted as H0, is a declaration about one (or more) population parameters that are assumed to be true until there is sufficient statistical evidence to conclude otherwise.
- The alternative hypothesis - typically denoted as Ha, is a declaration of all possibilities not covered by the null hypothesis.
- Define two competing null hypotheses
- Define and calculate test statistics
- The test statistics is the sample statistics upon which the decision to reject, or fail to reject, the null hypothesis is based. We also need to know about the distribution of the test statistics. Typical distributions of test statistics include Z, t, F and ✘2 distributions.
- Define the rejection region
- Rejecting the null hypothesis or not depends on the specified rejection region, which is the range of values such that if the test statistics fall into the range, the null hypothesis is rejected.
What is the relationship between alpha and beta errors?
There is a trade off between alpha and beta, a decrease in ne type of error increases the other.
Graphically, explain why a decrease in alpha leads to an increase in the beta error?
As you can see there two distributions. One assuming H0 is true, the other if it is false.
Beta is the area to the right of the z-score line.
A decrease in alpha would lead to an increase in beta as the area to the right of the rejection region would increase.
It is important to note the opposing areas these error occupy. If alpha occupies an area moving to negative infinity, beta would occupy an area moving to the right.
If we are able to decrease alpha, can we calculate the new beta?
We cannot calculate the value of beta as we don’t know the true mean.
All we know is that beta increases with an decrease in alpha.
What is the factorial of 0?
1