Download Choosing the Correct Hypothesis Test

AP Statistics: Choosing the Correct Hypothesis Test
Data is Means
Test Statistic is t
1 Sample?
1 Sample t Test
(t Test)
2 Samples?
If Independent
Use 2-Sample t Test
If paired
Find differences,
use t-Test
Data is Proportions
Test Statistic is z
1 Sample?
1-Prop z Test
2 Samples?
2-Prop z Test
Categorical Data
Test Statistic is χ2
1 Variable?
χ2 GOF Test
(Uses List)
Two-Way Table?
χ2 Test of Association
(Uses Matrix)
AP Statistics – Hypothesis Test Statistics
Name
Formula
Conditions or Assumptions*
One-sample
z-test
z=
x−μ
σ n
(Normal distribution or n > 30)
and σ known.
One-sample
t-test
t=
x − μ0
s n
(Normal population or n > 30)
and σ unknown
df = n-1
Paired
t-test
t=
d − d0
sd n
(Normal population of differences
or n > 30) and σ unknown
df = n-1
lp − p
0
p0 (1 − p0 )
n
n .p > 10 and n (1 − p) > 10
z=
One-proportion
z-test
lp − lp
1
2
z=
lp(1 − lp) ⎛ 1 + 1 ⎞
⎜
⎟
⎝ n1 n2 ⎠
Two-proportion
z-test
lp = x1 + x2
n1 + n2
Chi-Square Test
x1 − x 2
t=
Two-sample
t-test
2
2
s1 s2
+
n1 n2
(O − Ei ) 2
χ =∑ i
Ei
i =1
2
n
n1.p1 > 5 AND n1(1 − p1) > 5 and
n2.p2 > 5 and n2(1 − p2) > 5 and
independent observations
(Normal populations or n1+n2 > 30)
and independent observations
and σ1 and σ2 unknown
All expected counts > 0 and
no more than 20% are 5 or less
df = n-1 for Goodness of Fit test
df = (r-1)(c-1) for Test of Association
* Note that it is common to all tests that we require the sample to be an SRS
Definition of Symbols Used
n = sample size
= sample mean
s = sample standard deviation
μ0 = population mean
σ = population standard deviation
n1 = sample 1 size
p1 = proportion 1
n2 = sample 2 size
p2 = proportion 2
s1 = sample 1 std. deviation
μ1 = population 1 mean
s2 = sample 2 std. deviation
μ2 = population 2 mean
= sample mean of differences
t = t statistic
d0 = population mean difference
df = degrees of freedom
sd = std. deviation of differences
O = observed count
E = expected count
AP Statistics – Confidence Interval Formulas
Name
Conditions or Assumptions
s
n
(Normal population or n > 30)
and σ unknown
df = n-1
x ±t*
One-sample
t interval
l
l
lp ± z * p (1 − p )
n
One-proportion
z interval
Two-sample
t interval
Two-proportion
z interval
Formula
( x1 − x2 ) ± t *
s12 s2 2
+
n1 n2
lp (1 − lp ) lp (1 − lp )
1
2
+ 2
( lp1 − lp 2 ) ± z * 1
n1
n2
p > 10 and n (1 − lp ) > 10
n.l
(Normal populations or n1+n2 > 40)
and independent observations
and σ1 and σ2 unknown
p 1 > 5 AND n1(1 − lp 1) > 5 and
n1. l
n2. l
p 2 > 5 and n2(1 − lp 2) > 5 and
independent observations
* Note that it is common to all intervals that we require the sample to be an SRS
Definition of Symbols Used
n = sample size
= sample mean
1=
sample 1 mean
lp = sample proportion
2=
sample 2 mean
lp 1 = sample proportion 1
s = sample standard deviation
n1 = sample 1 size
σ = population standard deviation
n2 = sample 2 size
t* = t-statistic critical value
s1 = sample 1 std. deviation
z* = z-statistic critical value
df = degrees of freedom
Commonly used z* values:
C-Level
80%
90%
95%
98%
99%
z* value
1.282
1.645
1.960
2.326
2.576
s2 = sample 2 std. deviation
lp 2 = sample proportion 2