Econ 2740

Question 1

Population

Answer 1

: The group of all items of interest to a statistics practitioner(Everyone we are interested learning about). Frequently very large or can be infinitely large.

a. Examples Include: All tv viewers, Canadians, students, and all human beings
b. Typically we do not observe the population because it is too difficult

Question 2

Parameter

Answer 2

A descriptive measure of the population. In most applications of inferential statistics, the parameter represents the information we need.
a. Ex. Percent of Canadian voters who plan to vote for NDP

Question 3

Sample:

Answer 3

A set of data drawn from the studied population (Smaller number of the population)
a. Reason for using a sample is because it is cheaper and easier to collect data

Question 4

Statistic

Answer 4

A descriptive measure of a sample. Statistics are used to make inferences about parameters
a. Ex. Percent of the 1,200 voters polled who plan to vote for NDP

Question 5

Confidence Level:

Answer 5

The proportion of times than an estimating procedure will lead to correct conclusions

Question 6

Significance Level

Answer 6

Measures how frequently the conclusion will lead to false conclusions

Question 7

Descriptive statistics

Answer 7

Just describe the sample, without worrying about the population. Includes graphical and numerical methods

Question 8

Interval Data:

Answer 8

Also known as quantitative or numeric data. They are numbers that have meaning. Example, age, years of schooling, wage GDP, foul shot percentage and exchange rate.

Question 9

Ordinal Data:

Answer 9

Numbers denote ordered categories and only the order matter. Ex. Highest degree completed 1 (none), 2 (elementary), 3 (high school), 4 (university).

Question 10

Nominal Data:

Answer 10

Also known as Categorical or Qualitative. Numeric values just denote a name or category. They have no meaning as a number. Example, sex 0 (male), 1 (female) or postal code

Question 11

Frequency

Answer 11

: Number of observations falling into a group or category

Question 12

Relative Frequency

Answer 12

: Proportion of observations falling into a group or category

Question 13

Cumulative Relative Frequency:

Answer 13

: Proportion of observations falling into a group and all previous groups;
• Applies only to ordered groups
• Applies to Ordinal, but not nominal data

Question 14

Histograms

Answer 14

A graphical display of data using bars of different heights

Question 15

Reverse Causality

Answer 15

When changes in the dependent variable (Y-Variable) cause changes in the independent variable (X-Variable)
• Put another way, the causation goes in the opposite direction as expected
• You see a relationship in the scatter diagram, but the interpretation is opposite to what you would think.

Question 16

Bottom Line:

Answer 16

Due to indirect and reverse causation care is needed when interpreting relations between variables

Question 17

Direction Causation

Answer 17

When Changes in the independent variable (X-Variable) cause changes in the dependent variable (Y-Variable).

Question 18

Indirect Causation:

Answer 18

When changes in the X and Y-Variables are both caused by a third variable ( Say Z).
• You will observe a relationship in the scatter diagram even if X does not impact Y and Y does not impact X.
• Be careful interpreting such a relation ship

Question 19

Modality

Answer 19

A unimodal histogram with a single peak, while a bimodal histogram is one with two peaks:

Question 20

Measures of Variability

Answer 20

: Measures of central location fail to tell the whole story about distribution. How much are the observations spread out around the mean value.

Question 21

Sample Standard Deviation:

Answer 21

• To obtain sample variance we squared distance of each observation from the mean
• Now we undue the squaring by taking the square root
• The standard deviation is simply the square root of the variance, thus:

Question 22

Covariance (Generally Speaking):

Answer 22

• When two variables tend to move in the same direction (both increase or both decrease), the covariance will be a large positive number
• It is extremely rare that two variables always move in the same direction
• When two variables tend to move in opposite directions, the covariance is a large negative number
• When there is no particular pattern, the covariance is a small number
• However, it is often difficult to determine whether a particular covariance is large or small

Question 23

Sample of Coefficient of correlation:

Answer 23

The coefficient of correlation is defined as the covariance divided by the standard deviations of the variables

Question 24

Sampling Errors

Answer 24

Differences between population and sample that occur because of the observations that happened to be picked from our sample

Question 25

Nonsampling Errors

Answer 25

Differences between population and sample that occur due to a flaw in the sampling method

Question 26

Stratified Random Sampling

Answer 26

1. Divide the population into two (or more) mutually exclusive groups (stratas).
2. Randomly sample from each strata

Question 27

Cluster Sampling

Answer 27

Random sample of groups or clusters of observations.

• E.g. Draw townships, postal codes, or city blocks at random then survey the residents

Question 28

1. Classical Approach

Answer 28

Based on equally likely events

Question 29

2. Relative Frequency

Answer 29

Based on experimentation or historical data

Question 30

3. Subjective Approach

Answer 30

Based on (subjective) judgment

Question 31

4. Bayesian Approach

Answer 31

Based on combination of subjective assessment with relative frequency

Question 32

Marginal Probabilities

Answer 32

Computed by adding across rows and down columns; that is they are calculated in the margins of the table

Question 33

Conditional Probability

Answer 33

Used to determine how two events are related. That is, we can determine of one event given the occurrence of another related event.
Written as P(A|B)

Question 34

Independence

Answer 34

• One of the objectives of calculating conditional probability is to determine whether two events are related
• In particular, we would like to know whether they are independent, that is, if the probability of one event is not affected by the occurrence of the other event.
-There are independent if:
P(A|B)=P(A) or P(A|B)=P(B)

Question 35

Multiplication Rule

Answer 35

Used to calculate the joint probability of two events. It is based on the formula for conditional probability earlier defined

P(A|B)= [P(A and B)] / P(B)