Mod 6 Flashcards
Chapter 10
How do you write null and alternative hypotheses statements?
- H0: p = particular value (p0)
- Ha: p > p0, p < p0, p ≠ p0
Can claims/hypotheses statements be about p^?
Claims are always about true proportion (p)
- never write p-hat in our claims or sample values in general (p-hat) should never go into hypothesis statement
- Only use sample values to assess these claims/hypothesis statements
Claimed value is stated in the problem (exception: “majority of”)
Interpret the results of a hypothesis test:
What does it mean to reject the null hypothesis?
Implies strong support for the alternative hypothesis
Sample data observed would be unlikely/surprising to happen if the null hypothesis were true
Interpret the results of a hypothesis test:
What does it mean to fail to reject the null hypothesis?
- does NOT imply support for the null; just means the observed data would be unsurprising (or it could have happened) if the null were true
- Never accept or prove the null hypothesis
When is it appropriate to carry out the large-sample hypothese test for a population proportion?
Check the assumptions: np0 and n(1-p0) — p0 from the null hypothesis
What is the five-step method to carry out a large-sample hypotheses test for a population proportion?
Hypotheses: use appropriate notation (no sample values)
Method: a single proportion and a difference in two proportions
Check Criteria: np0 and n(1-p0) both at least 10 and appropriate data collection
Compute: test statistic, p-value (for one and two-sided tests)
Communicate:
- compare p-value to alpha
- state conclusion
- give conclusion in context of problem
What is a p-value?
probability of observing data as extreme or more extreme than the data we observed when the null hypothesis is true
Interpretation of a small p-value (< alpha)
p-value ≤ alpha or significance level =
statistically significant and reject null hypothesis (evidence against the null hypothesis)
Interpretation of a large p-value (< alpha)
p-value > alpha or significance level =
NOT statistically significant and fail to reject null hypothesis
How do you give conclusion in context of problem?
- If rejected the null, we do have sufficient evidence to conclude the alternative hypothesis
- If fail to reject the null, we did not have sufficient evidence to conclude the alternative hypothesis
What is type I error? What is type II error?
- type I error: rejecting the null when the null is true
- Type II error: fail to reject the null when the null is false
How does significance level affect probability of a type I error?
Significance level (alpha) controls the probability of type I error
- increased alpha = higher probability of type 1 error
- decreased alpha = lower probability of type 2 error
- Significance level is when you determine the criteria for what’s surprising is
Ex: at the 0.05 level, reject the null if it is less than 0.05–this data is surprising and will only happen 5% of the time
- Meaning you can commit a type I error if you do these hypothesis tests 5% of the time
How does probability of type I error affect probability of type II error?
Decrease the probability of a type I error increases the probability of a type II error
How does significance level affect type 2 error?
as significance level DECREASES, probability of type 2 error INCREASES
How significance level affect power?
significance level directly affects power
as alpha INCREASES, power INCREASES
as alpha DECREASES, power INCREASES
What is power?
probability that we reject the null when a value in the alternative is the truth (when we should reject the null)
How does sample size (n) affect the probability of type I error?
Sample size doesn’t affect the probability of type I error
How does sample size (n) affect the probability of type II error?
As n INCREASES, the probability of type II error DECREASES
How does sample size affect power?
as n increases, power increases
- When the difference between true population value and null hypothesis value increases, power increases
What is the reasoning behind a decision in hypothesis testing – do the data agree with the null?
What is the interpretation of p-value?
We assume that the null is true, compute the test statistic and p-value, then could this data could have come from this distribution where p0 is the true mean (or p = p0)
- Small p-value = data is surprising; data does not agree with the null
- Large p-value = data is not surprising; data could have arisen from this null
What is the difference between statistical vs practical significance?
Our tests only assess statistical significance
Statistical significance: based on sample distributions, is this data surprising?
- More likely to occur with larger sample size (n)
Practical significance: Was that intervention effective? Should I take that test prep course? It depends on the costs, risks, and amount of difference
