BUAL 2600 Final Chen Yan

Probability

chance of experimental outcome occurring

Time Series Data

data collected over a time from the same subjects or entities (e.g., monthly sales, over a year)

Complement

everything outside a singular venn diagram

Multiple Choice Questions

several predefined answer options to choose from.

np.

the mean of the binomial distribution is equal to

Intersection

the possible outcomes that belong to A and B only (the middle shaded part)

Mutually exclusive

A and B are mutaully exclusive if they have no sample space outcomes in common ( Events A and B have no outcomes in common)

Variable

A characteristic or property that can vary among individuals in a data set (e.g., age, gender, income).

Data Set

A collection of related data points, often organized in tables or spreadsheets.

3

A normal population has 99.73 percent of the population measurements within .... Standard deviation(s) of the mean?

Normative (measurement/scale)

A qualitative variable for which there is NO meaningful ordering or ranking of the categories Ex: eye color, name, car color

Ordinal (measurement/scale)

A qualitative variable for which there is a meaningful ordering or ranking of the categories Difference between the values is meaningful Ex. (1st, 2nd, 3rd,) [(best)5,4,3,2,1(worst)]

Sample

A subset of the elements in a population (e.g., 100 college students from different universities).

Random Variables

A variable whose value is a numerical value that is determined by the outcome of an experiment

conditional probability

A(n) .............. is the probability that one event will occur given that we know that another event already has occurred.

Binomial Distribution

Four properties (x,n,p,q): Sample size = n, Success P(s) = p, Failure P(f) = q, x = number of successes (0,1,2,3...n) Binomial distribution is Discrete

Open-ended Questions

Most honest and complete information

Qualitative (Categorical) Data

Non-numerical data that represents categories or characteristics (e.g., gender, eye color, nationality).

Quantitative Data

Numerical data representing quantities or amounts (e.g., height, weight, income).

Ratio (measurement/scale)

Numerical data with meaningful differences and a TRUE zero point Ex: Height, weight, income

Interval (measurement/scale)

Numerical data, difference between the values is meaningful, but there is no zero point Ex: Temperature 0 degrees does not mean there is no temperature, it just means it is very cold

Interval and Ratio

Only for Quantitative Data

Discrete random variables

Only integer (whole numbers) values; possible values can be counted or listed (Ex: the number of defective units in a batch of 20)

0.8944

P(z<1.25)

Discrete probability distribution

Probabilities must sum to 1 and be greater than or equal to zero

Subjective method

Probability based on experience or intuition Ex: Tom and Judy make an offer on a house Possible outcomes: E1= offer is accepted, E2= offer rejected Judys probability estimates P(E1) = 0.8, P(E2) = 0.2 Tom's probability estimates P(E1) = 0.6, P(E2) = 0.4

Systematic Sampling

Randomly select a starting point and take every k piece of data from a listing of the population Ex: start at person number 2, then go to person number 12, 22nd, 32nd, 42nd, etc.

Data

Raw information collected through observations, measurements, or research.

Judgment Sampling

Sampling in which a person who is extremely knowledgeable about the population selects population elements he or she feels are the most representative. The quality of the sampling is completely dependent on the researchers knowledge

Voluntary Sampling

Sampling in which participants self-select (volunteer) Frequently used by radio and television Over represent people with strong opinions

Convenience Sampling

Sampling where we select elements because they are convenient to sample (cause of time, population, etc.) Not a probability sample

Sample Space

Set of all possible experimental outcomes.

Event

Set of sample space outcomes

Probaility of an event

Sum of all probabilities of corresponding sample space outcomes

probability

The ............... of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

Conditional probability

The probability that one event will occur given that we know another event has already occurred.

binomial

The requirement that the probability of success remains constant from trial to trial is a property of the ................ distribution.

50 students

There are 100 students who took the test. How many student's scores are between 6 and 16?

Non-probaility sampling

These methods are biased.

Dichotomous Questions

Two possible answers (e.g., Yes/No)

Relative frequency method

Uses long-run frequency to estimate probability Ex: Estimate the probability that a randomly selected consumer prefers coca-cola to all other soft drinks. 1000 consumers selected 140 said that they prefer Coca-cola The probability is 140/1000 =.14

21

What is the highest score of test 1?

50%

What is the interquartile range of test 1?

3

What is the lowest score of test 1?

12

What is the median score of test 1?

.15

Whats the unknown probability?

poisson

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

All of the other answers are correct

Which of the following is a type of question used in survey research?

Weight

Which of the following variables is quantitative?

Sum of probabilities

All experimental outcomes must total 1

Classical method

Assigns probability of 1/n for n outcomes Ex: Rolling a die Sample space: S=(1,2,3,4,5,6) Probabilities: Each sample has a ⅙ chance of occurring

Expected Value

Average outcome of a random variable. (Sigma formula)

Poisson Distribution

Consider the number of times an event occurs over an interval of time or space, and assume that: the probability of occurrence is the same for any intervals of equal length and The occurrence in any interval is independent of an occurrence in any non-overlapping interval. (Discrete distribution for number of occurrences.) Ex: number of typos on a printed page, Ex: number of cars arriving at a toll booth in one hour

Cross-sectional Data

Data collected at a single point in time from different subjects or entities (e.g., survey responses from people in 2023).

Continuous random variables

Decimal values; may assume any numerical value in one or more intervals (Ex: number of minutes required to run 1 mile)

Stratified Random Sampling

Divide the population into groups called strata, then take a certain number of elements from each stratum

Multistage Cluster Sampling

Divides the population into clusters and randomly selects clusters, then samples within them.

P(E) = 0

Event E can never occur

P(E) = 1

Event E is certain to occur

mutually exclusive

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are

Simple Random Sampling

Every member has an equal chance of being selected

Probability Sampling

Every member of the population has a known, non-zero chance of being selected

Union

Everything shaded in the Venn diagram (A U B) (A or B or Both)

Sample space outcomes

Experimental outcomes in the sample space.

No outliers

How many outliers?

P(A|B)=P(A)

If P(A)>0 and events A and B are independent, then

median would be less than the mean

If a population distribution is skewed to the right, then, given a random sample from that population, one would expect that the ....

The probability of event A is not influenced by whether event B occurs, or P(A|B)=P(A)

In which of the following are the two events A and B always independent?

Population

The entire group of individuals or items of interest in a study (e.g., all college students)

Mode

The measurement in a sample or population that occurs most frequently?

Sample Size

The number of individuals or observations in a sample; a larger sample size typically provides more accurate results.

.45

if we define the event E. = {a,b,c}, what is P(E)?

Experimental outcomes

possible outcomes for an experiment