Unit 5

Question 1

what is random behavior?

Answer 1

unpredictable in the short-run, but has a regular and predictable distribution in the long-run
for example, if we only have 10 samples of an x value then it will be unpredictable, but in the long run if we have 1000000 samples then its more predictable because the shape starts to get created (probability)

Question 2

when do we use a density curve?

Answer 2

continuous quantitative variables

Question 3

when do we call a phenomenon random?

Answer 3

if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions

Question 4

what is the probability of any outcome of a random phenomenon?

Answer 4

the proportion of times the outcome would occur in an infinitely long series of trials

Question 5

what is the difference between proportions and probability?

Answer 5

proportion: known or observed value. present tense.
probability: theoretical value of a proportion after an infinitely long series of trials that can never be observed. it relates to future events.

Question 6

what is the mathematical model used to describe random behavior?

Answer 6

probability model

Question 7

what are two components of the probability model?

Answer 7

a list of possible outcomes
a probability for each outcome

Question 8

what is probability?

Answer 8

the probability that an event occurs is the long run proportion of times we would see that event occur in a very long series of trials

Question 9

what is a sample space?

Answer 9

(S) of a random phenomenon is the set of all possible outcomes.
ex. if we toss a coin twice S={HH,HT,TH,TT}

Question 10

what is an event?

Answer 10

any subset of outcomes in the sample space.
ex. the event sum is 9 for rolling two dice would be
B={36,45,54,63}

Question 11

what is the complement of an event?

Answer 11

(A^c) of an event (A) consists of all outcomes in the sample space which are not contained in A.
basically, the complement is everything opposite of A.

Question 12

random variable

Answer 12

a variable whose value is a numerical outcome of a random phenomenon

Question 13

what are the two types of random variables?

Answer 13

discrete and continuous

Question 14

what is a discrete random variable?

Answer 14

has a countable number of possible outcomes

Question 15

what is a continuous random variable?

Answer 15

takes on all possible values in an interval
ex. weight or distance

Question 16

probability distribution

Answer 16

gives the values of some variable, as well as the probability of each value

Question 17

what does the probability distribution of a random variable X tell us ?

Answer 17

tells us what values X can take and how to assign probabilities to those values
if X~N(µ, σ) we say that X follows a normal probability distribution

Question 18

what is sampling distribution of the sample mean x̄?

Answer 18

x̄~N( μ, σ/ √n)

Question 19

are averages less or more variable than individual observations?

Answer 19

less variable (therefore, are skinny and tall in a density curve)

Question 20

what happens to the sampling distribution of x̄ as n increases?

Answer 20

the sampling distribution of x̄ approaches a normal distribution

Question 21

what is the central limit theorem state?

Answer 21

if a variable represents a sample mean, then the sampling distribution of the variable is approximately normal when n is high

Question 22

when is it safe to apply the central limit theorem?

Answer 22

when n is bigger than 30

Question 23

what is true population proportion?

Answer 23

p
its a parameter

Question 24

what is the sample proportion?

Answer 24

p̂
is a statistic and an estimate for p

Question 25

when talking about proportions what needs to be met?

Answer 25

n x p needs to be bigger than 10
n (1-p) needs to be bigger than 10

Question 26

what is probability?

Answer 26

the probability that an event occurs is the long run proportion of times we would see that event occur in a very long series of trials

Question 27

when would the answer be approximate?

Answer 27

when using the central limit theorem
its approximate because we will never get the exact values regardless of how much n increases.