Inferential Statistics Fundamentals

Question 1

Define Inferential Statistics

Answer 1

Inferential Statistics allows you to make predictions (“inferences”) from data.

With inferential statistics, you take data from samples and make generalizations about a population.

Question 2

Inferential statistics rely on what?

Answer 2

Refers to methods that rely on Probability Theory and Distributions to predict population values based on sample data.

Question 3

What is a Distribution?

Answer 3

A distribution is a function that shows the possible values for a variable and how often they occur.

We usually mean a Probability Distribution. Examples of distributions are:
1. Normal
2. Binomial
3. Uniform - all outcomes have an equal chance of occurring

A distribution is a function that shows the possible values for a variable and the probability of their occurrence.
Shows us the frequency at which possible values occur within an interval

Question 4

What are Point Estimates?

Answer 4

a single value given as an estimate of a parameter of a population

Question 5

What are Confidence Intervals?

Answer 5

The range within which you expect the population parameter to be.

It’s estimation is based on the data we have in our sample

A confidence interval is a much more accurate representation of reality

Question 6

Inferential Statistics are the gateway into…

Answer 6

Fundamentals of Quantitative Research and Data Driven Decision Making

Question 7

We are sure you have exhausted all possible values when what occurs?

Answer 7

When the sum of the probabilities is equal to 1 or 100%

Question 8

Is a Distribution just the graph?

Answer 8

No, a distribution is visual representation. It is defined but the underlying probabilities.

Question 9

What is the relationship of Mean, Median and Mode in a Normal Distribution

Answer 9

They are equal. mean = median = mode. It has no skew.

Question 10

What is the Origin in a graph?

Answer 10

It is the zero point. Adding it to any graph gives us persepcitve.

Question 11

Can every distribution be standardized?

Answer 11

Yes

Question 12

What is Standardization?

Answer 12

Is the process of transforming this variable to a mean of 0 and a stdev of 1

Question 13

Can a normal distribution be standardized?

Answer 13

Yes, it is called a standard normal distribution

Question 14

What letter is used to denote a Standard Normal distribution?

Answer 14

Z

Question 15

What is the standardized variable called?

Answer 15

The z-score. It is equal to the original variable - its mean / its stdev

Question 16

What are the benefits of using a Standard Normal distribution?

Answer 16

Using it makes predictions and inference much easier.

Question 17

What is a sampling distribution?

Answer 17

It is a distribution formed my many combined samples

Question 18

What is Central Limit Theorem?

Answer 18

No matter the underlying distribution, the sampling distribution approximates a normal distribution

Question 19

For Central Limit Theorem to apply, what is the minimum number of observations?

Answer 19

30

Question 20

Why is the Central Limit Theorem so important?

Answer 20

CLT allows us to perform tests, solve problems and make inferences using the Normal distribution, even when the population is not normally distributed

Question 21

What is Standard Error?

Answer 21

is the deviation of the distribution formed by the sample means

Like Stdev the standard error shows variability

Question 22

What is the formula for Standard Error?

Answer 22

sigma(stdev) / sqrt of n

Question 23

Why is Standard Error important?

Answer 23

It is used for almost all statistical tests because it shows how well you approximated the true mean

*it decreases as the sample size increases. Bigger samples give a better approximation of the population.

Question 24

What is an Estimator of a population paramater?

Answer 24

it is an approximation depending solely on sample information. A specific value is called an estimate

Question 25

What are the two types of Estimates?

Answer 25

1. Point Estimates
2. Confidence Interval Estimates

Question 26

What are the differences between Point Estimates and Confidence Intervals?

Answer 26

Point Estimates are a single number - located exactly in the middle of the confidence interval
Confidence intervals are intervals - provide much more information and are preferred when making inferences

Question 27

What are examples of Point Estimates?

Answer 27

Sample mean x-bar is a point estimate of the population mean mu

Question 28

What are the two properties of each Point Estimate?

Answer 28

1. Bias
2. Efficiency

Estimators are like judges, we are always looking for the most efficient and unbiased

An unbiased estimator = has an expected value = the population parameter (example: x-bar = mu)

The most efficient estimators are the ones with the least variability of outcomes. The most efficient estimator is the unbiased estimator with the smallest variance.

Question 29

What is the difference between Statistics and Estimators?

Answer 29

Statistics is the broader term. A point estimate is a statistic.

Question 30

You are given a dataset with a sample mean of 10. In this case, 10 is:
a point estimator
or
a point estimate

Answer 30

a point estimate

Question 31

Example of Sample Mean

Answer 31

The mean salary is $122,150. The sample mean is the estimator and the $122,150 is the estimate.