Topic 8 - Hypothesis Testing Flashcards
1
Q
What is a hypothesis
A
- A claim about a population parameter
2
Q
What are the properties about the hypothesis to be tested
A
- It is called the Null Hypothesis
- Always includes an = sign
- Always about a population parameter and not a sample statistic
3
Q
What do we assume when doing a hypothesis test
A
- That the null hypothesis is true unless there is enough evidence to prove the contrary
4
Q
What terminology is used when we come to a conclusion in a hypothesis test
A
- Reject null hypothesis
- Fail to reject hypothesis
5
Q
What does the Alternative Hypothesis state
A
- That a population parameter is smaller, greater, or different than the hypothesised value in the null hypothesis
6
Q
What are the two types of Alternate Hypothesis’
A
- Two-sided (H1: μ ≠ 50)
- One-sided (H1: μ > 50 or H1: μ < 50)
7
Q
What is a Type 1 error otherwise reffered to as
A
- The significance level of the test
- Denoted by alpha
8
Q
What is a type 2 error
A
- Failure to reject a false null hypothesis
- The probability of a type 2 error is β
- The probability of rejecting a false null hypothesis is 1-β, this is the power of the test
8
Q
What is a key property of type 1 and type 2 errors
A
- They cannot happen at the same time
- Type 1 can only occur if H0 is true
- Type 2 can only occur if H0 is false
- if alpha increases, β decreases
9
Q
What is the process for a hypothesis test if σ is known
A
- Create null and alternative hypothesis
- Convert sample mean to z with z = x bar - mu / sqrt(σ) / n
- Compare with critical value
10
Q
How do we use the Z statistical table in order to find the rejection region
A
- if alpha = 0.1, find where 0.9 changes to 0.8 and use the value which starts with 0.8
11
Q
What is the p-value
A
- The smallest value of alpha for which the hull hypothesis can be rejected
12
Q
How do we calculate the p-value
A
- P(X bar >= x | mu = b)
- P(Z >= x - b / n / sqrt(sigma))
- Compare this probabilty to alpha and come to a conclusion
- Signs change depending on the tail
13
Q
What do we do to the p-value if the test is a two tailed test
A
- Multiply by 2
14
Q
What do we use if the population variance is not known
A
- Use the sample variance and use the t-distribution
