Statistics (Math 1342)

Front 1

Population

Back 1

Entire group of people to be studied

Front 2

Sample

Back 2

Subset of population that is being studied

Front 3

Statistic

Back 3

Numerical summary of sample

Front 4

Parameter

Back 4

Numerical summary of population

Front 5

Qualitative data

Back 5

Non-numeric or numeric but cannot perform arithmetic operations

Front 6

Quantitative data

Back 6

Numbers, can perform arithmetic operations with meaning

Front 7

Discrete data

Back 7

"Number of," can be counted

Front 8

Continuous data

Back 8

No space between; measurements

Front 9

Random

Back 9

Every outcome has an equally likely chance of ocurring

Front 10

Relative frequency

Back 10

Part / whole

Front 11

Pie chart

Back 11

Multiply relative frequency by 360 to get degrees

Front 12

Lower class limit

Back 12

Smallest value

Front 13

Upper class limit

Back 13

Highest value

Front 14

Class width

Back 14

Subtract consecutive lower class limits

Front 15

Range

Back 15

Maximum - minimum

Front 16

Variance

Back 16

(X1 - μ)^2

Front 17

Z score

Back 17

(x - μ) / σ

Front 18

IQR

Back 18

Q3 - Q1

Front 19

Lower fence

Back 19

Q1 - 1.5(IQR)

Front 20

Upper fence

Back 20

Q3 + 1.5(IQR)

Front 21

Probability

Back 21

Measure of chance behavior

Front 22

Experiment

Back 22

Anything done with an unknown outcome

Front 23

Sample space

Back 23

All possible outcomes

Front 24

Event

Back 24

Collection of outcomes

Front 25

Empirical probability

Back 25

Comes from data, equals relative frequency

Front 26

Classical method

Back 26

Treat everything equally as likely

Front 27

Subjective probability

Back 27

Probability obtained from personal judgement

Front 28

Disjoint / mutually exclusive

Back 28

2 events with no outcomes in common

Front 29

Addition rule for disjoint

Back 29

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

Front 30

Addition rule if not disjoint

Back 30

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

Front 31

Complement (E^c)

Back 31

All outcomes in sample space s that are not outcomes of event E. P(E^c) = 1 - P(E)

Front 32

Independent events

Back 32

Events whose occurrence do not affect each other

Front 33

Multiplication rule for independent

Back 33

P(A and B) = P(A) * P(B)

Front 34

Multiplication rule for dependent

Back 34

P(A and B) = P(A) * P(B|A)

Front 35

Conditional probability for independent

Back 35

P(B|A) = P(A & B) / P(A)

Front 36

Conditional probability for dependent

Back 36

P(E & F) = P(F)P(F|E)

Front 37

0!

Back 37

1

Front 38

1!

Back 38

1

Front 39

Permutation

Back 39

nPr = n!/(n-r)!
Order is important

Front 40

Combination

Back 40

nCr = n!/r!(n-r)!
Order is not important

Front 41

Mean - discrete random variables

Back 41

μ = Σ[x*P(x)]

Front 42

Criteria for binomial probability experiment

Back 42

Performed fixed number of times, trials are independent, 2 mutually exclusive outcomes, probability of success is the same for each trial

Front 43

Binomial probability distribution

Back 43

Binompdf(n,p,x)
For "x = ..."

Front 44

Binomial cumulative distribution

Back 44

Binomcdf(n,p,x)
For "x < ..." or "x ≤ ..." or "x > ..." or "x ≥ ..."

Front 45

Mean - binomial

Back 45

μ = n*p

Front 46

Standard deviation - binomial

Back 46

σ = √(npq)

Front 47

Normal probability distribution

Back 47

μ = 0, σ = 1

Front 48

Area for standard normal variables

Back 48

Normalcdf(lower bound, upper bound, μ, σ)

Front 49

Critical value

Back 49

Invnorm(area to left)

Front 50

Sample proportion

Back 50

P-hat = x/n

Front 51

90% confidence - critical value

Back 51

1.645

Front 52

95% confidence - critical value

Back 52

1.96

Front 53

99% confidence - critical value

Back 53

2.575

Front 54

Sample size (T)

Back 54

n = ([Zα/2 * σ]/E)^2

Front 55

E (Z interval)

Back 55

E = Zα/2*√[P(1-p)/n]

Front 56

Sample size (Z) [with prior estimates]

Back 56

N = p(1-p){[(Zα/2)/E]}^2

Front 57

Sample size (Z) [no prior estimates]

Back 57

N = .25{[Zα/2]/E}^2

Front 58

Χ^2 distribution

Back 58

X^2 = [(n-1)s^2]/σ^2

Front 59

Unusual event

Back 59

P(x<0.05)

Front 60

Standard normal distribution

Back 60

μ=0, σ=1

Front 61

Finding percentiles

Back 61

Invnorm(percentage in decimal form, μ, σ)

Front 62

Finding area to left (standard normal dist.)

Back 62

Normalcdf(-∞, z, μ, σ)

Front 63

Finding area to right (standard normal dist.)

Back 63

Normacdf(z, ∞, μ, σ)

Front 64

Finding area between 2 z-scores

Back 64

Normalcdf(z1, z2, μ, σ)

Front 65

Finding area - P(x=...)

Back 65

Binompdf(n, p, x)

Front 66

Finding area - P(x≥...)

Back 66

Binomcdf(n, p, [x-1])
1 - ans

Front 67

Finding area - P(x≤...)

Back 67

Binomcdf(n, p, x)

Front 68

Finding area - P(x<...)

Back 68

Binomcdf(n, p, [x-1])

Front 69

Confidence interval - X^2

Back 69

√{[(n-1)s^2]/X^2*1-α/2} < σ^2 < √{[(n-1)s^2]/X^2*1-α/2}

Front 70

Hypothesis testing - mean

Back 70

Use t-distribution

Front 71

Hypothesis testing - population

Back 71

Use z-distribution

Front 72

Hypothesis testing - standard deviation

Back 72

Use X^2 distribution

Front 73

Check for outliers - mean

Back 73

Box plot

Front 74

Check for outliers - p & z

Back 74

np(1-p)≥10

Front 75

P(TI)

Back 75

α

Front 76

P(not TI)

Back 76

1-α

Front 77

P(Type II)

Back 77

β

Front 78

P(not Type II)

Back 78

1-β

Front 79

Test statistic in critical region

Back 79

Reject hypothesis

Front 80

Test statistic not in critical region

Back 80

Don't reject hypothesis

Front 81

Don't reject hypothesis

Back 81

There is not sufficient evidence...

Front 82

Reject hypothesis

Back 82

There is sufficient evidence...

Front 83

Confidence interval - μ - σ known

Back 83

Use z-interval

Front 84

Confidence interval - μ - σ unknown

Back 84

Use t-interval

Front 85

Confidence interval - p

Back 85

Use 1-prop-Z-interval

Front 86

Confidence interval - σ

Back 86

Use X^2

Front 87

Hypothesis test - μ

Back 87

Use t-test

Front 88

Hypothesis test - p

Back 88

Use 1-prop-z-test

Front 89

Hypothesis test - σ

Back 89

Use X^2

Front 90

Dependent hypothesis test

Back 90

L1-L2 > L3

Front 91

Dependent hypothesis test - null hypothesis

Back 91

H0: μ1=0

Front 92

Dependent hypothesis test/interval

Back 92

Use t-test & t-interval

Front 93

Independent hypothesis test - null hypothesis

Back 93

H0: μ1 = μ2

Front 94

Independent hypothesis test - test/interval

Back 94

2-samp-t-test & 2-samp-t-interval

Front 95

2 population proportions - null hypothesis

Back 95

H0: p1 = p2

Front 96

2 population proportions - test/interval

Back 96

Use 2-prop-z-test & 2-prop-z-interval

Front 97

Sample size - 2 population proportions [with prior estimates]

Back 97

n = [p1(1-p1)+p2(1-p2)][(Zα/2)/E]^2

Front 98

Sample size - 2 population proportions [no prior estimates]

Back 98

n = .25[(Zα/2)/E]^2

Front 99

Predictor/explanatory variable

Back 99

X

Front 100

Response variable

Back 100

Y

Front 101

To find r (correlation coefficient)

Back 101

(L1 - x-bar)/Sx > L3
(L2 - y-bar)/Sy > L4
(L3 + L4) > L5
Linreg(ax+b)

Front 102

R close to 1

Back 102

Strong positive correlation

Front 103

R close to -1

Back 103

Strong negative correlation

Front 104

R close to 0

Back 104

Weak correlation

Front 105

Residual

Back 105

Observed - predicted

Front 106

Equation of Least-squares regression line

Back 106

Y-hat = b1x + b0

Front 107

B1 (least-squares regression line)

Back 107

r * (Sy/Sx)

Front 108

B0 (least-squares regression line)

Back 108

Y-bar - b1*x-bar

Front 109

Sum of square residuals

Back 109

Sum of (y - y-hat)^2

Front 110

Pareto chart

Back 110

Bar chart drawn in decreasing order of frequency or relative frequency

Front 111

Bar chart/graph

Back 111

Bars do not touch

Front 112

Histogram

Back 112

Bars touch

Front 113

Graph interpretation - μ & median at same line

Back 113

Symmetric

Front 114

Graph interpretation - μ to left of median

Back 114

Skewed left

Front 115

Graph interpretation - μ to right of median

Back 115

Skewed right

Front 116

Relative frequencies/probabilities must add to equal...

Back 116

1

Front 117

Confidence interval for a parameter

Back 117

An interval of numbers combined with the likelihood the interval contains the unknown parameter

Front 118

Margin of error for confidence interval with known σ

Back 118

±Zα/2 * (σ/√n)