Hypothesis Testing

Question 1

what does hypothesis testing ask? (3)

Answer 1

• how unusual it is to get our data is the null hypothesis is true
• is the data is unlikely under the null hypothesis, then we reject the null
• assumes sampling is random

Question 2

what are hypothesis about?

Answer 2

• populations, but are tested with data from samples

Question 3

null hypothesis (4)

Answer 3

• symbol: Ho
• specific statement about a population parameter made for the purposes of argument
• usually the simplest statement and is specific
• never “accept the null hypothesis”

Question 4

alternate hypothesis (3))

Answer 4

• represents all possible parameter values other than the one in the null hypothesis
• usually the statement of greatest interest and is not specific
• never reject this hypothesis even if it is not statistically significant

Question 5

test statistic

Answer 5

• number calculated to represent the match between a set of data and the null hypothesis
• can be compared to general distribution to infer probability

Question 6

P-value

Answer 6

• probability of getting the data, or something as or more unusual, if the null hypothesis were true

Question 7

null distribution for a test statistic (2)

Answer 7

• probability distribution of alternative outcomes when a random sample is taken from a hypothetical population in which the null hypothesis is true
• a value at the middle would be expected, but a value on the edges would be unlikely/unexpected

Question 8

significance level

Answer 8

• symbol (alpha)
• probability used as a criterion for rejecting the null hypothesis: if the P-value is less than or equal to alpha, then the null hypothesis is rejected
• often set as 0.05

Question 9

type I error (3)

Answer 9

• rejecting a true null hypothesis
• if the null hypothesis is true, the probability of Type I error is alpha (the significance level)
• does NOT depend on sample size because test takes size into account

Question 10

type II error (4)

Answer 10

• not rejecting a false null hypothesis (accepting a false null hypothesis)
• if the null hypothesis is false, probability of a type II error is beta
• the smaller the beta (how false the null hypothesis is), the more power a test has
• beta is lower with larger sample size

Question 11

power

Answer 11

• ability of a test to reject a false null hypothesis

- power = 1 - beta

Question 12

advantage of larger samples

Answer 12

• tend to give an estimate with a smaller confidence interval
• give more power to reject a false null hypothesis

Question 13

critical value

Answer 13

• value of a test statistic beyond where the null hypothesis can be rejected

Question 14

“statistically significant”

Answer 14

• P < beta

- we can “reject the null hypothesis”

Question 15

“two-tailed tests” (2)

Answer 15

• deviation in either direction would reject the null hypothesis
• alpha is divided into alpha/2 on one side and alpha/2 on the other

Question 16

“one-tailed tests”

Answer 16

• only used when the other tail is nonsensical