4-7

Question 1

Probability

Answer 1

Numerical measure between 0 and 1 that describes the likelihood that an event will occur. Probabilities closer to 1 indicate that the event is more likely to occur. Probabilities closer to 0 indicate that the event is less likely to occur.

Question 2

P(A) - probability of event A

Answer 2

P(A) = 1, event is certain to occur
P(A) = 0, event is certain not to occur

Question 3

Intuition

Answer 3

Incorporates past experience, judgement, or opinion to estimate likelihood of an event

Question 4

Relative frequency

Answer 4

Uses formula:

Probability of event = f/n

Where f = frequency of event in a sample of n outcomes

Question 5

Equally likely outcomes

Answer 5

Uses formula:

Probability of event =

of outcomes favorable divided by total number of outcomes

Question 6

Law of large numbers

Answer 6

As sample size increases and increases, the relative frequencies of outcomes get closer and closer to the theoretical or actual probability value

Question 7

Statistical experiment

Answer 7

Any random activity that results in definite outcome

Question 8

Event

Answer 8

A collection of one or more outcomes of a statistical experiment or observation

Question 9

Simple event

Answer 9

One particular outcome of a statistical experiment

Question 10

Sample space

Answer 10

Set of all simple events

Question 11

Sum of probabilities

Answer 11

Always equal to 1

Question 12

Compliment of event A

Answer 12

Event that A does not occur

Question 13

Independent events

Answer 13

If occurrence or nonoccurence of one event does not change the probability that the other event will occur.

Question 14

Multiplication rule for INDEPENDENT events

Answer 14

P(A and B) = P(A) x P(B)

Question 15

Conditional probability

Answer 15

P(A and B) = P(A) • P(B | A)

P(A and B) = P(B) • P(A | B)

Question 16

Mutually exclusive events

Answer 16

Don’t occur together

Addition rule: P(A or B) = P(A) + P(B)

Question 17

General addition rule for any events A and B

Answer 17

P( A or B) = P(A) + P(B) - P(A and B)

Question 18

Permutations

Answer 18

Number of ways to arrange in order n distinct objects taking them r at a time

    n!
-------
(n - r)!

Question 19

Combinations

Answer 19

Number of combinations of n objects taken at r time (grouping)

      n! ---------------- r!( n - r )!

Question 20

Random variable

Answer 20

If the value that x takes on in a given experiment or observation is a chance or random outcome

Question 21

Discrete random variable

Answer 21

Can take on only a FINITE number of values or a countable number of values

Ie: whole numbers

Question 22

Continuous random variable

Answer 22

Can take on any of the countless number of values in a line interval

Ie: measurements - weight, Length, temperature, elapsed time

Question 23

Binomial experiment

Answer 23

Fixed number of trials (n)

Trials are independent and repeated under same conditions

Two outcomes Success (p) , Failure (q)

Probability of success is the same for each trial

P + q = 1; q = 1 - p

Want to find probability of r successes out of n trials

Question 24

Mean of binomial experiment (u)

Answer 24

U = np

Where:
n = # of trials
p = probability of success

Question 25

Standard deviation of binomial

Answer 25

Square root of (npq)

Question 26

Unusual values

Answer 26

U + 2.5o

U - 2.5o

Question 27

Variance of binomial probability distribution

Answer 27

O^2 = npq

Question 28

Normal curve

Answer 28

1) bell shaped
2) symmetrical about vertical line thru u (mean)
3) curve approaches horizontal axis
4) inflection points between cupping upward and downward occur above u + o and u - o
5) area under curve equals 1

Question 29

Empirical rule

Answer 29

1) 68% of data values lie within 1 std deviation
2) 95% of data values lie within 2 std deviation
3) 99.7% of data values lie within 3 std deviation

Question 30

Out of control signals

Answer 30

Out of control signal 1:
One point falls beyond the 3o level

Out of control signal 2:
A run of 9 consecutive points on one side of center line (u)

Out of control signal 3:
At least 2 of 3 consecutive points lie beyond 2o level on same side of center line

Question 31

Z value / z score

Answer 31

Difference between the measurement and the mean divided by std deviation

Z = x - u
———
O

Question 32

Raw score x

Answer 32

x = zo + u

Question 33

Statistic

Answer 33

Numerical descriptive measure of a SAMPLE

Question 34

Parameter

Answer 34

Numerical descriptive measure of a POPULATION

Question 35

Estimation

Answer 35

Estimate value of population parameter

Question 36

Testing

Answer 36

Formulate a decision about value of the population parameter

Question 37

Regression

Answer 37

Make predictions or forecasts about the value of a statistical variable

Question 38

Sampling distribution

Answer 38

Probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population

Question 39

Normal approximation of the binomial distribution

Answer 39

Conditions

If

1) np > 5
2) nq > 5

Then:
R has a binomial distribution that is approximated by a normal distribution with

U = np and o = sq root npq

Question 40

Mean of std deviation of a discrete population probability distribution

Answer 40

U = summation of (xP(x))

Question 41

Std deviations of a discrete population probability distribution

Answer 41

Steps:

1) Find x(given)
2) Find P(x) (percentage given, turn to decimal)
3) Multiple x and P(x)
4) Calculate u by adding up xP(x) values
5) x - u for all values
6) square values
7) multiply by P(x)
8) add together to find variance/ square root the sum to find the std deviation

Question 42

Find sample size n for estimating u when std deviation is known

Answer 42

n = ( z score times std deviation divided by E) all squared

Where E is error

Question 43

T variable

Answer 43

T =

     X - u
-----------
       S 
      ---
      n^1/2

Degrees of freedom = n - 1

Question 44

Binomial distribution

Answer 44

P = r/n

q = 1 - p

N = # of trials , r = number of successes