Week 6

Question 1

What is a population?

Answer 1

all units of interest,(which can’t all be

measured)

Question 2

What are samples?

Answer 2

subsets of units taken for analysis

Question 3

What does sampling introduce?

Answer 3

sampling introduces uncertainty, because

properties of samples differ from true population values simply by chance

Question 4

What is sampling error?

Answer 4

chance deviations of sample values from true population values are called sampling error

Question 5

What is the goal of statistics?

Answer 5

Estimate the values of important parameters, including:

• means
• proportions
• variances
• effects

Question 6

What are the steps in hypothesis testing?

Answer 6

1. State the hypotheses
2. Compute the test statistic with the data
3. Determine the P-value
4. Draw the appropriate conclusions

Question 7

What is the null hypothesis(H0)?

Answer 7

is a specific statement about its value

no effect, no difference, nothing interesting going on

Question 8

What is the alternate hypothesis (HA)?

Answer 8

covers every other possibility
some effect, some difference, something
interesting going on

Question 9

if data is consistent with null hypothesis what should be done?

Answer 9

If data are consistent with the null hypothesis, we fail to reject it
we never say it’s accepted or true!

Question 10

if data is inconsistent with null hypothesis what should be done?

Answer 10

If data are inconsistent with the null hypothesis, we reject it and say that the alternate hypothesis is supported instead

Question 11

What are test statistics used for?

Answer 11

to see whether mismatch compatible with chance, or too extreme for chance to explain

Question 12

When should a t test be used?

Answer 12

when hypotheses compare
• a mean to a null value
• two means
• two paired means (e.g., before/after)
• slopes or trends to null values

Question 13

When should an F test or ANOVA be used?

Answer 13

more than two means

with numerical response and categorical explanatory variable

Question 14

When should χ2 (chi-squared) be used?

Answer 14

When hypotheses compare
• frequencies or proportions to null values
• frequencies or proportions

Question 15

What is the p-value?

Answer 15

the probability of obtaining a test statistic as extreme as we did if the null hypothesis is true

Question 16

What is the null distribution?

Answer 16

The sampling distribution of the test statistic when the null is true

Question 17

What are the characteristics of the null distribution?

Answer 17

• values of the statistic are on the x-axis
• probabilities of values are on the y-axis
• probabilities depend on sample size, but
  decline as values get more extreme

Question 18

What is the advantage and disadvantage of a one sided test?

Answer 18

A one-sided test is more likely to reject the null hypothesis
- but we fail to reject H0 if an effect occurs in the opposite direction to HA

Question 19

What is the advantage of a two-sided test?

Answer 19

A two-sided test can detect any effect of interest

Question 20

What is a type I error?

Answer 20

rejecting H0 when true (a false positive)

Question 21

What is a type II error?

Answer 21

not rejecting H0 when false (a false negative)

Question 22

What is the probability of a type I error?

Answer 22

it has a probability of α (the significance level)

Question 23

What is the probability of a type II error?

Answer 23

• it has a probability of beta(and 1 - beta equals power)

- which depends on sample size, effect size, and precision