Foundations for Inference

Question 1

Sampling Distribution

Answer 1

a theoretical distribution of a sample statistic after taking repeated samples

Question 2

Central Limit Theorem (for proportion)

Answer 2

allows us to make inferences about population proportions based on sample data and it helps us estimate how wrong the sample is likely to be

with a large enough sample size, the distribution of sample proportions will be approximately normally distributed.

Question 3

Confidence Interval

Answer 3

A range around a sample statistic that is likely to include the population parameter.

Question 4

Standard Error

Answer 4

The standard deviation of the sampling distribution of a given sample; a measure of how far off, on average, a given sample is likely to be from the population parameter.

Question 5

Building a Confidence Interval

Answer 5

1. decide how confident we want to be (standard is 95%)
2. determine the alpha level (the probability of being wrong) (for a 95% confidence interval, alpha is 0.05)
3. determine the Z-score value for 95% (For 95% confidence, the z score is 1.96)
4. find the se (√((𝑃(1−𝑃))/𝑛)
5. find margin of error: se x z value
6. CI will be the sample proportion + or - that value

Question 6

standard error

Answer 6

√((𝑝̂(1−𝑝̂))/𝑛)

Question 7

margin of error

Answer 7

se x z

Question 8

equation for confidence interval

Answer 8

𝑝̂ ± moe
aka: 𝑝̂ ± se x z

Question 9

explain the equations for
1. find se
2. find moe
3. find CI

Answer 9

find se: √((𝑝̂(1−𝑝̂))/𝑛)
find moe: se x z
find CI: 𝑝̂ ± moe

Question 10

When you find the two values of CI (𝑝̂ ± moe) what are you saying?

Answer 10

we are 95% confident that the true proportion is within these two values

Question 11

Parameters vs Statistics

Answer 11

parameters are the features of a population while statistics are features of a sample

Question 12

Population mean (μ)
Population standard deviation (σ)
Population proportion (p)

Answer 12

parameters: greek lettters

Question 13

Sample mean (𝑥̅, x-bar)
Sample standard deviation (s)
Sample proportion (𝑝̂, p-hat)

Answer 13

statistics: latin letters

Question 14

the parameter/statistic represents what?

Answer 14

parameter: population
statistic: sample

Question 15

Will your CI become narrower or wider if your confidence level goes from 95% to 80%?

Answer 15

narrower with 80%.: confidence is lower, but possibly more precise
wide with 95%. you are more confident with 95% but less precise