Satistical Summary Table

Condition

Find

Tool

Formula

(known σ)

Normal distribution

or any distribution  n ≥ 30

[pic 1]

Z

[pic 2]

(known σ)

Normal distribution

or any distribution  n ≥ 30

n > 5% N

[pic 3]

Z

[pic 4]

(unknown σ)

Normal distribution  n < 30

[pic 5]

t

[pic 6]     df = n - 1

n is large

np > 5

nq > 5

p

Z

[pic 7]

Normal distribution

[pic 8]

[pic 9]

[pic 10]

want to find [pic 11]

n

Z

[pic 12]

want to find [pic 13]

n

Z

[pic 14]

2-tailed

1-tailed

α

Confidential Interval

probability

Z

probability

Z

.005

99.5%

.4975

2.81

.495

2.575

.010

99%

.495

2.575

.49

2.3267

.025

97.5%

.4875

2.24

.475

1.96

.050

95%

.475

1.96

.45

1.645

.100

90%

.45

1.645

.4

1.2817

Condition

Hypothesis

Tool

Formula

(known σ)

Normal distribution

or any distribution  n ≥ 30

Two-tailed

[pic 15]

One-tailed

[pic 16] or [pic 17]

or [pic 18] or [pic 19]

Z

[pic 20]

(known σ)

Normal distribution

or any distribution  n ≥ 30

n > 5% N

[pic 21]

Z

[pic 22]

(unknown σ)

Normal distribution  n < 30

[pic 23]

t

[pic 24]     df = n - 1

n is large

np > 5

nq > 5

[pic 25]

Z

[pic 26]

Normal distribution

[pic 27]

[pic 28]

[pic 29]

Null True

(e.g. Good Man)

Null False

(e.g. Bad Guy)

Not Reject Null

(i.e. Accept Null)

Accept Correctly

(e.g. married a good man)

Type II error (β)

(e.g. married a bad guy)

Reject Null

Type I error (α)

(e.g. rejected a good man)

Reject Correctly

(e.g. rejected a bad guy)

Condition

Hypothesis

Tool

Formula

Independent samples

(known σ)

Normal distribution

or any distribution  

n1 ≥ 30

n2 ≥ 30

Two-tailed

[pic 30]

One-tailed

......

Z

[pic 31]

Independent samples

 (unknown σ)

Normal distribution

σ1 =σ2

[pic 32]

t

[pic 33]

Independent samples

 (unknown σ)

Normal distribution

σ1 ≠σ2

[pic 34]

t

[pic 35]

Related samples

(e.g. Any improvement?)

[pic 36]

t

[pic 37]          [pic 38]

[pic 39]

n is large

n1 p1 > 5

n1 q1 > 5

n2 p2 > 5

n2 q2 > 5

[pic 40]

Z

[pic 41]

Normal distribution

Two-tailed

[pic 42]

One-tailed

[pic 43]

F

[pic 44]          [pic 45]

[pic 46]