Chapter 11 statistical sampling

Question 1

Mean

Answer 1

Sum of the numbers in a data set divided by the total number of values in the data set. Average. Best used in data set with numbers that are close together.

Question 2

Median

Answer 2

Midpoint value of a data set, where the values are arranged in ascending or descending order. Better with a data set with outliers.

Question 3

Random Variable

Answer 3

A variable that describes all of the possible outcomes of a random process. For example if you have X for a coin flip, then X=1 when it is heads and X=0 when it is tails.

Question 4

Discrete

Answer 4

The total number of possible outcomes is countable. An example is heads or tails.

Question 5

Continous

Answer 5

The total number of possible outcomes is uncountable. An example is time measurements.

Question 6

Probability Density Function

Answer 6

A continuous probability distribution function. This means that for any measurement x sub 1, there exists a corresponding value for f(x sub1).

Question 7

Empirical Probabilities

Answer 7

Are probabilities generated from data.

Question 8

Expected VAlue

Answer 8

Also known as the mean or average of the probability distribution. Can be thought of as the outcome we should expect on average.

E(x)=Sum(x*P(x))

Question 9

Random Sampling

Answer 9

A method of choosing an equally distributed subset from a larger population. There is simple random samples, stratified random samples, cluster sampling, and systematic random samples

Question 10

Sampling

Answer 10

A part of a population used to describe the whole group.

Question 11

Population

Answer 11

All members of a specified group.

Question 12

Simple Random Sampling

Answer 12

A type of random sampling where the variables have an equal, and unsystematic, chance of selection. Best used when a researcher does not know a lot about the demographics in the population.

Question 13

Stratified Random Sampling

Answer 13

Divide members of a population into ‘strata’ or homogeneous subgroups. Different in that you seperate the population into groups first. Stratified random sampling cannot have crossover. Stratified random samples must include all members of a population.
Example is splitting up a high school with freshman, sophomore, junior, and senior students to then decide how many of each group is needed to take a sample. Best used when research is familiar with the demographics. No more then four to six strata is recommended but you can have as many as you want.

Question 14

Cluster Random Samples

Answer 14

The sampling method where different groups within a population are used as a sample. Cluster cannot have crossover and must include all members of a population. Unlike stratified, the cluster sampling does not have to have an equal selection from each group but must be as close to the same size as possible. Use this when the entire population is unclear or unknown.

Question 15

Systematic Random Sampling

Answer 15

Requires selecting samples based on a system of intervals in a population. For example selecting very 4th customer in a movie theater. Can only do this if the population is homogenous with a randomized list.

Question 16

Law of Large Numbers

Answer 16

Theorem that states that the larger sample sizes, the closer the sample mean will be to the mean of the population.

Question 17

Normal Distribution

Answer 17

Roughly bell shaped distribution that occurs over and over throughout populations and samples.

Question 18

Central Limit Theorem

Answer 18

If you run a random experiment enough times the results will follow a normal distribution. The data set only maintains integrity if the new students are drawn from a random sampling of students.

Question 19

Mean

Answer 19

Average value of all individuals in the sample.

Question 20

Standard Error

Answer 20

How accurate your mean is by comparing it to the mean of a value that exists.
To find the standard error
Standard error=(standard deviation)/(root(samplesize))

Question 21

Regression LIne

Answer 21

A straight line that attempts to predict the relationship between two points. Also called trend line or line of best fit.

Question 22

Simple Linear Regression

Answer 22

A prediction when a variable Y is dependent on a second variable X based on the regression equation of a given set of data.

Question 23

Scatterplot

Answer 23

A graph of ordered pairs showing a relationship between two sets of data.

Question 24

Correlation

Answer 24

The relationship between two sets of variables used to describe or predict information.

Question 25

Regression Analysis

Answer 25

Study of two variables in an attempt to find a relationship, or correlation.

Question 26

Independent Variable

Answer 26

A condition or piece of data in an experiment that can be controlled or changed.

Question 27

Dependent Variable

Answer 27

A condition or piece of data in an experiment as controlled or influenced by an outside factor, most often the independent variable.

Question 28

Positive Correlation

Answer 28

The dependent variables and the independent variables in the data set increase or decrease together.

Question 29

Negative Correlation

Answer 29

The dependent variables and independent variables in a data set either increase or decrease opposite from one another.

Question 30

Causation

Answer 30

An observed event or action appears to have caused a second event or action.

Question 31

Chi-square

Answer 31

A statistical test used to compare expected data with what we collected.

Question 32

Null hypothesis

Answer 32

The prediction that there is no interaction between variables. If there is a big enough difference between the scores, then we can say something significant happened which would be rejecting the Null hypothesis.

Question 33

Chi squared definition and formula

Answer 33

(O-e)^2/e. Where o is the observed data and e is what you expected. P value needs to be under .05 for it to be considered sucessfull. A statistical test used to compare expected data with what we collected.

Question 34

Degrees of Freedom

Answer 34

of categories-1=Degrees of freedom

Question 35

Formula for the ax+b regression line

Answer 35

a=(nsum(xy)-sum(x)sum(y))/(nsum(x^2)-sum(x)^2)

b=1/n (sum(y)-a(sumxi))