Hypothesis tests

Question 1

Test used for finding population mean (mu)

1-variable, 1-sample, numerical…

Answer 1

1-sample z/t-test

Question 2

Assumptions for 1-sample z/t-test

Answer 2

z-test: sample mean is from normal distribution (if sample size is large enough, CLT applies)
t-test: sample is from normal distribution (or sample size is large enough to be robust)

Question 3

What is a 1-sample z/t-test used for?

Answer 3

Finding the population mean (mu)

Question 4

Test used for finding the average distance between pairs

2-variables, numerical, 1-sample (e.g. over time)…

Answer 4

Paired t-test

Question 5

Assumptions for paired t-test

Answer 5

The differences between pairs are drawn from a normal population.

Question 6

What is a paired t-test used for?

Answer 6

Finding the average distance between pairs

Question 7

Test used for hypothesising a linear relationship between 2 numerical variables

Answer 7

t-test for population slope (beta)

Question 8

Assumptions for t-test for population slope

Answer 8

1. Linear model is appropriate (scatterplot)
2. Residuals are from a normal distribution (histogram)
3. Residuals have constant standard deviation (residuals vs. fit) => an even scatter along x axis

Question 9

Test used for finding the difference between averages

2 independent samples, numerical

Answer 9

2-sample t-test for difference between 2 population means

Question 10

Assumptions for a 2-sample t-test

Answer 10

1. Both samples drawn from normal distribution

2. Both samples have same standard deviation

Question 11

What is a 2-sample t-test used for?

Answer 11

Finding the difference between that averages of 2 independent samples

Question 12

Test used for hypothesising about a single proportion

Categorical, 1-variable

Answer 12

z-test for population proportion (pi)

Question 13

Assumptions for z-test for population proportion

Answer 13

n(pi) >5

n(pi-1)>5

Question 14

Test used for hypothesising about any number of proportions

Answer 14

Chi-squared goodness-of-fit test

Question 15

Assumptions for chi-squared goodness-of-fit test

Answer 15

All expected values >/= 5

Question 16

What is a chi-squared goodness-of-fit test used for?

Answer 16

Hypothesising about any number of proportions

Question 17

Test used for hypothesising about associations between 2 categorical variables

Answer 17

Chi-squared test of independence

Question 18

Assumptions for chi-squared test of independence

Answer 18

All expected values >/= 5

Question 19

What is a chi-squared test of independence used for?

Answer 19

Hypothesising about associations between 2 categorical variables.

Question 20

Name all the hypothesis tests

Answer 20

1-sample z/t-test for population mean
Paired t-test for population mean difference
T-test for population slope (beta)
2-sample t-test for differences between population means
z-test for population proportion (pi)
Chi-squared goodness-of-fit test
Chi-squared test of independence