Lecture 1

What is population?

• Descriptive Statistics: a summary of the raw data (histograms, numerical data). If

We are provided with descriptive statistics, we can only describe the data (sample).

• Inferential Statistics: allows us to make statements about the population. If we are

provided with inferential statistics then we can make inferences about our

population of interested based on the given data (sample).

Lecture 2

•

Population: entire collection of objects of interest.

o For example: If we want to test how many freshmen are taking STAT 301 at

CSU, then our population would be all of the CSU students.

Sample: a subset of the interested population.

O Denote sample size as "n"

o For example: If we were to do the same test stated above, then our sample

would be a group of CSU students.

• Census: the sample collected is the population

What is addition rule of probability?

• Population parameter: a numeric characteristic of population

Types of studies:

O Experimental: deliberately imposes some treatment on individuals (can be

manipulate)

o Observational: observes individuals and measures variables of interest but

does not attempt to influence the response (survey, questionnaire, simple

observing, no manipulating)

•

Bias: a result that systematically favors a certain outcome. Bias can occur when a

sampling procedure is not properly done. For example, samples are not randomly

obtained can cause bias.

Confounding variable: Occurs when two variables are associated in such a way If you want to learn more check out bpa and phthalates are known _________.

that their effects on the response variable cannot be distinguished between each

other. It is a variable that is important in understanding the data, but is not

accounted for in our study.

What is union in mathematics?

Types of data:

O Qualitative or categorical:

. Nominal: no ordering, Yes/No

. Ordinal: ordering, poor/fair/ good

o Quantitative or numerical

• Discrete: whole numbers

. Continuous: decimal values

•

Proportion: fraction of responses in a category out of the total

o Denote sample proportion as p Don't forget about the age old question of bio 203 liver answers

O Denote population proportion as

Sample size

• Sigma (): sum of....

Sample mean (x): average of a sample

. Sample median (7): middle value of an ordered list of data values If you want to learn more check out what is the term for the process by which information is initially recorded in a form usable to memory?

o

If the sample size is equally split (n is even), then sample median is the

average of two middle values of the ordered list:

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• Range: largest value - smallest values

• Sample variance (s?): measure spread of the data about the mean.

•

Standard deviation (S): square root of the sample variance

• Histogram shape:

Bell-shaped

Right-skewed

Uniform

• 5 number summary:

O

plin

O 01:25 percentile

O Qz: Median, 50 percentile O Q: 75th percentile

• IQR (Inner Quartile Range): Q: - Qi

are se desilly rules Lecture

AP Statistics Basic Probability rules

3

1. All probabilities are proportions that fall between 1 and 0.

OSP(A) 51

2. All of the possible outcomes added together must have a probability of 1.

3. The probability that an event does not occur is 1 minus the probability that it does

occur.

P(A)=1 - P(A) Compliment: the compliment of an event A is the is the probability of A not happening. Written as: A' or not A or AC.

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4. If two events have no outcomes in common, the probability that one or the other If you want to learn more check out which of the following is a strip of the parietal lobe involved in the processing and perception of sensory information from the body, especially temperature, touch, pressure, and pain?

occurs is the sum of their individual probabilities. This is called the addition rule of probability. This is also called the UNION.

P(Aor B) = P(AUB) = P(A) + P(B) Mutually Exclusive or Disjointed: Two events have nothing in common, in other words they cannot occur simultaneously. - If they have a quality in common and they can occur at the same time, they

are not mutually exclusive and the following equation must be used:

P(Aor B) = P(AUB) = P(A) + P(B)- P(Aand B) * Probability of King + Hearts in 52 cards?

PCK UH). PIK) +PCH) - P(K+H)2+-5..307 5. If two events are independent of each other, the probability that they can happen

together is the product of the two events. This is called the multiplication rule of probability. This is also called the INTERSECTION.

P(A and B) = P(ANB) = P(A) P(B)

If the events are dependent on each other, this would mean that one event depends on the outcome of the other, the equation changes to:

P(Aand B) = P(ANB) = P(A)P(BA) Here P(BA) represents the conditional probability that B occurs given the outcome of A

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6. Conditional probability is used when given information effects an outcome.

P(BIA) = P(Aand B)

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P(A) This equation is used for the probability of B given A. *"or" - DLAUB) :PIA) + PIB)- PIANB) Don't forget about the age old question of asynchronous communication occurs when team members

"and P(ANB). PIA)* PIB) "given". PLAIB). P(A and B)

PIA)

Lecture 4

• Expected values E(x): the mean of a random variable:

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O F(x) = 1 = ( x + f(x)dx

Variance of a random variable: amount a random variable deviates about its

expected value

O Denoted as o?

o Var(x) - q? - (-u) f(x)dx

Lecture 5

. Combination: order does not matter

on Choose k-nlk = win-k)!

• Permutation: order does matter

• Expected value fro binomial random variable

Lecture 6

• Probabilities and percentiles for normal distributions can be found by using a z

chart

•

The values given in the Z-chart only give areas to the LEFT of the z-value.

• PC-z) = P(z)

• 2 =*

Empirical rule:

O 68% of the data falls within 1 Standard deviation of the mean Don't forget about the age old question of vaterr

0 95% of the data falls within 2 Standard deviation of the mean

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О

99of the data falls within 3 Standard deviation of the mean

Lecture 7

•

Population entire collection of interest

o We often assume that the population distribution is normal

o Population mean: u

o Population standard deviation: 0

These are called population parameters

o

Population proportion!

Lecture 8

• SRS: simple random sample

o Gathering data method so that every population member has an equal

chance.

•

Sampling variability: the variation in a statistic from sample to sample.

Sampling distribution: the probability distribution formed by considering all

possible values of a statistics for a given sample size and probabilities of these

values.

Sample mean, X

o Denote as E(X) =

• Sample Variance:

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Var(x) =

• Standard deviation of X:

O4 - /Var(1)

• Central limit theorem

1. If the population is normally distributed, then the sample average is also

vel

normally distributed.

2. If the population is not normally distributed, then as long as the sample size

is big enough (n230), the sample average is approximately normal

distributed