Unit 8: Central Limit Theorem

Question 1

t score

Answer 1

mean is 50, sd is 10

Question 2

z score (standard score)

Answer 2

mean is 0, sd is 1

Question 3

types of Population

Answer 3

Target population
Study population

Question 4

Target population

Answer 4

a large set of people/all the individuals in the group you are trying to draw conclusions (inferences) about

Question 5

Study population

Answer 5

sampling frame (or sample pool)

Question 6

Sample

Answer 6

• A set of individuals selected from the population

Question 7

• Descriptive statistics

Answer 7

• Tells us about a set of data
• Example: sample mean

Question 8

• Inferential statistics

Answer 8

Calculated from the sample data
and tells us about the underlying
population

Question 9

statistic

Answer 9

is a number that describes some characteristic of a sample.

The value of a statistic can be computed directly from the sample data.

We often use a statistic to estimate an unknown parameter.

Question 9

parameter

Answer 9

is a number that describes some characteristic of the
population. In statistical practice, the value of a p

Question 10

statistics come from

Answer 10

samples

Question 11

parameters come from

Answer 11

populations

Question 12

Statistical inference

Answer 12

use samples to say something about an underlying population

• How many M&Ms are in a fun size bag?
• How many red M&Ms (proportion wise) in a bag?

Question 13

Random sampling

Answer 13

the process of obtaining a random sample such that:

• All members have same probability of being chosen
• All chosen members are independent of one another

Question 14

Sampling error

Answer 14

degree to which the sample differs from the population; due to chance

• How much does my sample of M&M fun size bags differ from the population’s?
• How much does my sample of red M&Ms differ from that of the population? (by chance)

Question 15

Sampling distribution

Answer 15

Probability distribution of a given statistic (see below for examples) based on random
sampling
* Mean
* Median
* Standard deviation
* Correlation, etc.

We need to be able to describe the sampling distribution of the possible values of the
mean in order to perform statistical inference.

Question 16

The Distribution of Sample Means

Answer 16

• Draw multiple random samples from a larger population
• Draw with replacement
• For each sample, we calculate a mean value
• We plot the mean on a frequency distribution

Question 17

SRS

Answer 17

simple random sample

Question 18

sample size

Answer 18

number of observations in the sample
* n = 100 means you have 100 observations

Question 18

number of samples

Answer 18

number of observations

• 10 samples, each with sample size of 100
• How many observations are there in total?

Question 19

The concept of sampling “with replacement” suggests that a person’s selection in one sample does NOT affect their probability of being selected in another sample

TRUE OR FALSE

Answer 19

true

Question 20

Central Limit Theorem

Answer 20

Distribution of sample means will be normal, even if the underlying distribution (of the population) is not normal
* This happens because of the process of random sampling

helps us go from sample → population
* The sampling distribution of the sample statistic will be normal
* As sample size increases, the sampling error decreases (you become more precise with your estimate)
* You randomly select participants
* Theoretically, every one should have equal chance of being selected as a participant

Question 21

Law of large numbers

Answer 21

as the sample size increases the sampling
error will decrease

• A larger sample drawn from the population will better emulate the characteristics of that population, thus reducing sampling error

Question 22

Sampling Bias

Answer 22

• More systematic sampling error
• Have implications for your generalizability
  Even with random sampling, you can still have sampling error
• Sampling error → Quantified in standard error of mean

Question 23

• Population parameter:

Answer 23

what you want to estimate
* Example: mean

Question 24

Kurtosis

Answer 24

how extreme the tails are
* Often conflated with the “peak”:
* Sharper peak tend to have more outliers, heavier tails: higher degree
of kurtosis
* But kurtosis does not measure “peak

Question 25

When I plot a distribution of sample means, the Central Limit
Theorem says that my distribution of sample means will only be normal if the underlying population is also normal.
A. True
B. False

Answer 25

False (doesn’t matter what the population looks like)

Question 26

what does n=100 mean

Answer 26

you have 100 observations, but the number of samples and the number of observations is not equal

Question 27

3 main distributions

Answer 27

population probability distribution (typically unknown)
sample frequency distribution (what we observe)
sampling distribution of the statistic (theoretical concept, we typically only use one sample but it needs infinite samples to make the curve)

Question 28

can we collect enough samples to approximate the population parameter

Answer 28

no, but as n gets bigger the distribution becomes more normal and the dispersion decreases