Hypothesis Testing

Question 1

Null Hypothesis H0

Answer 1

often represents either a skeptical perspective / perspective of no difference or a claim to be tested; states the null value (represents the value of the parameter if the null hypothesis is true)

Always list null hypothesis as an equality

Question 2

Alternative Hypothesis HA

Answer 2

represents the alternative claim under consideration (research question) and is often represented by a range of possible parameter values; often represents a new perspective, such as the possibility that there has been a change

Always list the alternative hypothesis as an inequality (

Question 3

Testing Hypothesis with confidence Intervals

Answer 3

-If value falls within range of plausible values from the confidence interval, we cannot say the
null hypothesis is implausible -> we fail to reject the null hypothesis
- If the null value is not in the confidence interval, it is implausible and we reject the null
hypothesis; data provide statistically significant evidence in favor for the alternative
- „quick-and-dirty“ approach for hypothesis testing; no information about likelihood of certain
outcomes under the null hypothesis, i.e. the p-value, based on which we can make a decision on the hypotheses

Question 4

Type 1 Decision Error

Answer 4

rejecting the null hypothesis when it is actually true (Finding suspect guilty when they are innocent)

Question 5

Type 2 Decision Error

Answer 5

failing to reject the null hypothesis when the alternative is actually true (Finding suspect innocent when they are guilty)

Question 6

Chance of Type 2 Error with 95% Confidence Interval

Answer 6

Using a 95%-confidence interval to evaluate a hypothesis test where H0 is true, we will make an
error whenever the point estimate is at least 1.96 SE away from the population parameter -> happens about 5% of the time

Question 7

Formal Testing with p-Value

Answer 7

To evaluate if the observed sample mean is unusual for the hypothesized sampling distribution, determine how many standard errors away from the null it is; therefore compute the z-score, which is also called the test statistic in this case

Question 8

p-value

Answer 8

probability of observing data at least as favorable to the alternative hypothesis as our current data set, if the null hypothesis is true; we usually use a summary statistic of the data to help compute the p-value and evaluate the hypotheses

P-value is a way of quantifying the strength of the evidence against the null hypothesis in favor of the alternative; formally the p-value is a conditional probability

Question 9

One-sided hypothesis test

Answer 9

checking for a increase or decrease, but not both

Question 10

Two-sided hypothesis test

Answer 10

checking for a increase, decrease or both (general change in data; any difference from the null value)

Question 11

Using one-sided vs two-sided test

Answer 11

Always two-sided test unless it was made clear prior to data collection that the test should be one-sided

Question 12

Hypothesis testing framework

Answer 12

1. Set the hypotheses
2. Check assumptions and conditions
3. Calculate a test statistic and a p-value.
4. Make a decision, and interpret it in context of the research question