Decisions with Data + z-test

Question 1

Confidence interval

Answer 1

Quantifies the uncertainty of our estimates.
* A q% confidence interval includes the true parameter q% of the times, if we repeat the experiment many times (an infinite number of times).

Question 2

for a standard normal curve N(0,1), c =

Answer 2

97.5th percentile ≈ 1.96
* gives 95% between ± c

Question 3

Hypothesis Testing

Answer 3

1. Set up research question - H
2. Weigh up evidence - ATP
3. Explain conclusion - C

Question 4

“innocent until proven guilty”

Answer 4

Null hypothesis holds until you can disprove it

Question 5

what is hypothesis testing?

Answer 5

a scientific method for weighing up the evidence given in the data against a given hypothesis (model)

Question 6

null hypothesis H0

Answer 6

postulates a certain expected value

Question 7

alternative hypothesis H1

Answer 7

the underlying expected value is actually different.

Question 8

the smaller the p-value is…

Answer 8

the more evidence we have against the null hypothesis

Question 9

Assumptions (for z-test)

Answer 9

• Observations are independent of each other.
• Sample mean (sample sum) follows a normal distribution or sample size is big enough such that normality is approximately satisfied (from CLT)

Question 10

reject the null hypothesis

Answer 10

The convention is to reject the null hypothesis if p<α, where α is a predetermined significance level, often chosen as α=0.05

Question 11

The practical difference between a one- and two-sided test

Answer 11

the p-value of a two-sided test is often simply double the p-value from a one-sided test under the same model

Question 12

z-test

Answer 12

used to test a hypothesis about a proportion in a population
* in fact anywhere we have an (approximately) normal test statistic with known mean and SD under H0