Data Final

Facts about continuous variable:

-we can only use probability of a range -the probability (cont.) is found by area under the curve -does not matter if it is < or <= -total area has to add up to 1 under the curve

If A and B are any two events with P(A) = .8 and P(BlA) = .4, then the joint probability of A and B is:

.32

Suppose that we have two events, A and B, with P(A) = 0.5, P(B) = .6, and P(A and B) = .4 Find P(AlB)

.67

if events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to:

0

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The 10 female students in the class averaged:

higher than the males

Conditional Probability:

if we know that B has occurred, the probability of event A might change!

If P(A) = P(AlB), then events A and B are said to be:

independent

the difference between the first and third quartile is called the:

interquartile range 75-25=IQR

Discrete probability distribution:

table or formula that lists probability of each element (outcome) of the random variable

Statistics:

the art and science of collecting, analyzing, presenting, and interpreting data

Data:

the facts, figures, numbers, sounds, images, that are collected, analyzed, and summarized for the presentation and interpretation

Why can you not always take data from the entire population?

the issue of $ and time

The law of large numbers:

the larger the sample size (the longer the experiment), the closer the relative frequency is to the truth probability

Cumulative probability:

the probability that X is less than or equal to a particular value

What is an experiment?

the process by which an observation was made

What is a sample space?

the set of all possible outcomes -Heads or tails

Continuous random variable graph:

PDF on Y and RV on X

Measure of variabilities: Range

R=max-min

A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population:

TRUE

A variable (or field or attribute) is a characteristic of members of a population, whereas an observation (or case or record) is a list of all variable values for a single member of the population.

TRUE

Abby has been keeping track of what she spends to stream movies. The last seven week's expenditures, in dollars, were 6, 4, 8, 9, 6, 12, and 4. The mean amount Abby spends on streaming movies $7:

TRUE

Age, height, and weight are examples of numerical data.

TRUE

Comparing a numerical variable across two or more subpopulations is known as a comparison problem:

TRUE

Suppose A and B are mutually exclusive events where P(A)= 0.2 and P(B)= 0.5, then P(A or B)= 0.70.

TRUE

The mean is a measure of central tendency:

TRUE

The number of car insurance policy holders is an example of a discrete random variable:

TRUE

The sum of all probabilities for a random variable must be equal to 1:

TRUE

The temperature of the room in which you are writing this test is a continuous random variable:

TRUE

The time students spend in a computer lab during one day is an example of a continuous random variable:

TRUE

The value of the mean times the number of observation equals the sum of all the data values:

TRUE

variance of expected value:

(xi-Mu)^2 * p(xi)

double check but based on #6 of WS, AUB formula:

+

Examples of comparison problems:

-a cost of living broken down by region of a country -recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo -salary broken down by male and female subpopulations -starting salary of recent graduates broken down by academic majors

Rule of Complement:

-event A -> it will rain today -event Ac -> no rain today everything outside of it raining is a complement of A

What is the difference between uncertainty and risk?

-risk depends on your position -uncertainty is beyond your control and is random

Addition Rule:

-union of two events -AuB = "or" = union =AnB = "and" = intersection

Two events are said to be independent when knowledge of one event is of no value when assessing the probability of the other:

TRUE

Two or more events are said to be exhaustive if one of them must occur.

TRUE

Ptile:

# of values below / n x 100

If A and B are mutually exclusive events with P(A)=0.30 and P(B)=0.40, then the probability that either A or B occur is:

0.70

If two events are collectively exhaustive, what is the probability that one or the other occurs?

1

Sum of all frequencies should =

1

The probability of an event and the probability of its complement always sum to:

1

3 structures of data:

1. cross-sectional: data collected over a sample unit in a particular time period -- data 201.04 (variables: name, gender, final grade (taken once) 2. time scores: observed over time -- GDP over 10 yrs (variables: year, average min wage, unemployed) 3. panel data: person A and B through 3 yrs with 3 incomes

Characteristics of a good sample:

1. representative of population 2. random

Normal distribution:

1. symmetric around the mean 2. can be completely defined by mean (Mu) and st.dev. 3. asymptotic- the tails get closer and closer to horizontal axis but never touches it (mean must be between 0 and 1) (if the st.dev. is smaller, it will be skinnier and taller)

If a value represents the 95th percentile, this means that:

95% of all values are below this value

Variation pop:

=Z(xi-mu)^2 / n

Variation samp:

=Z(xi-xbar)^2 * # of observations / n-1

Conditional probability is the probability that an event will occur, with no other events taken into consideration:

FALSE

If A and B are independent events with P(A) = .4 and P(B) = .5, then P(AlB) is .50:

FALSE

If A and B are two independent events with P(A) = .20 and P(B) = .60, then P(A and B) = .80

FALSE

If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive:

FALSE

The number of cars produced by GM during a given quarter is a continuous random variable:

FALSE

P(AlB) if not independent:

P(AnB) / P(B)

Population mean:

Mu: average of all x values in the entire population M=NZi=1 Xi / N (pop size)

Conditional probability:

P(AlB)=P(AnB)/P(B) P(AlB)=P(A) if they are indepedent

P(BlA):

P(AnB) / P(A)

Histogram:

a graphic that gives an idea of the shape of a sample indicating regions where sample points are concentrated and regions where they are dispersed -variable of interest is on horizontal axis (x) -height of rectangles correspond to intervals frequency -symmetry and skewness -not symmetric is skewed -thinner ends of distribution are tails -positively or negatively skewed depending on which side the tail is going towards

What is probability?

a numerical value that measures the likelihood that an uncertain event occurs -value of probability is between 0 and 1 -% odds chance

Frequency Distribution:

a tabular summary of data showing the number (frequency) of observations in each of the several nonoverlapping categories (class). -the objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data -mostly used to summarizing categorical variables

Random variable:

a variable whose value is determined by a random experiment. it is a function that assigns value to every element in the sample space

What is an event?

any subset of the sample space -denoted by A,B,C etc

Mean (sample xbar):

average of all data values, central location, sample mean, population mean Xbar =nZi=1 Xi / n

Gender and states of residence are examples of ______ data:

categorical

What is qualitative data?

categorical -- major, grades, religion, status, etc.

Variation means:

deviation from mean

The number of people entering a shopping mall on a given day is an example of a _______ random variable?

discrete

There are two types of random variables, they are:

discrete and continuous

Characteristics of quantitative (numerical) variables

discrete: all possible values can be listed, even if it goes to infinity -- number of apples continuous: you can't count it because it is so many... when there is an infinite amount of decimals -- pounds of apples

Mean of RV:

expected value MU: x1+p1 * x2+p2 * x3+p3 E(x) = Zxi * P(xi)

Relative frequency of class:

frequency/# of observations -- frequency/n

The interquartile range (IQR) encompasses what percent of the observations?

middle 50%

The median can also be described as the:

middle observation when the data value are arranged in ascending order

Interquartile range (IQR):

middle of info from Q1-Q3 IQR: Q3-Q1 -this shows the middle 50% of the data

If two events are independent, what is the probability that they both occur?

must have more information

Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are:

mutually exclusive

What is quantitative data?

numerical -- scores, mow much or how many, height, age, weight, etc.

Know how to make rescued chart!

oh yes girl you know it

Know contingency tables!

okay queen

2 types of categorical data:

ordinal: natural order -- ABC nominal: no natural order -- F vs. M

percentile rank:

p= P/100 x (n+1)

Mode:

piece of data that occurs most frequently in the data set -if the data has 2 modes, bimodel -if data has more than 2 modes, multimodel

Expected value:

population mean (MU), value that we expect on average. not based on sample but on a distribution

PDF:

probability density function- must be >=0. how likely something is in random variable (y-axis) -the higher the f(x), the more likely it has to be

2 types of data:

qualitative and quantitative

As a measure of variability, what is defined as the maximum value minus the minimum value?

range

In order for characteristics of a sample to be generalized to the entire population, the sample should be:

representative of the population

P(Abar)= 1-P(A) is the:

rule of complements

Researchers may try to gain insight into the characteristics of a population by examining a(n) _______ of the population.

sample

Z-Value:

x-Mu / st.dev. -Mu=0 -st.dev.=1 -the farther away towards negative it is, the worse -teachers use this to look at grading things

A variable is classified as ordinal if:

there is a natural ordering of categories

Mutually Exclusive events:

this is when you exhaust all of the possibilities -rain or no rain -sleeping or awake -it must be complements... cannot be something like sleeping or watching a movie or rain and clouds

Multiplication rule:

to find an intersection, multiply P(A) * P(B) -P(AnBnC)=P(A)*P(B)*P(C)

Addition rule:

to find union -P(PuB)=P(A)+P(B) - P(AnB) (unless mutually exclusive)

Percentile:

value below which a percentage of data falls

Median:

value in the middle when data items are arranged in ascending order. it measures the location most often and is for reported annual income and property values -- number from smallest to largest (use median when there is an outlier for mean)

To find a %:

values of meeting characteristics / total # of observations x 100

example of when to use expected value:

when finding out what you expect like in the lottery

Quartile:

when we calculate the 25th, 50th, 75th p-tile for a data set, we are dividing data into 4 parts