Download Hypothesis Testing for Population Means and Proportions and more Cheat Sheet Statistics in PDF only on Docsity!
Mean of a Population (known standard deviation)
Mean of a Population (unknown standard deviation)
Matched Pairs
Means of Two
Populations
Parameter
μdi↵
Statistic
x ¯
x ¯
x ¯di↵
x ¯ 1 x¯ 2
Null Hypothesis in Hypothesis Test
μdi↵ = 0
Standard Error
p n s p n
sdi↵
p
n
Test Statistic for Hypothesis Test
x ¯ μ
s/
p n
x ¯ μ
/
p n
x ¯ μ
sdi↵/
p n
z or
t? z t t t
Conditions for Inference
df =
s^21
n 1 +^
s^22 n 2
1 n 1 1
s^21 n 1
1 n 2 1
s^22 n 2
Degrees of Freedom
n 1
n 1
known
n < 15
n < 15
n 15
n 40
: OK
Same as above, replacing
n with n 1 + n 2
n 1 5 n 2 ^5
n 1 , n 2 roughly the same size
&
s
s
2 1
n 1
s
2 2
n 2
¯x 1 x¯ 2
q
s^21
n 1 +^
s^22 n 2
Parameter
Statistic
Null Hypothesis in Hypothesis Test
Standard Error for Confidence Interval
Test Statistic for Hypothesis Test
z or t ?
z
Conditions for Inference
Proportion of a Population
Proportion of a Population (plus four)
Proportion of
Two Populations
(plus four)
Proportion of
Two Populations
z
z
z
p
p
p ˆ
p ˜
p 1 p 2
p 1 p 2
p ˆ 1 pˆ 2
p ˜ 1 p˜ 2
p = p 0
p 1 = p 2
Standard Error for Hypothesis Test
r pˆ(1 pˆ)
n
r p˜(1 p˜)
n + 4
s p ˆ 1 (1 ˆp 1 )
n 1
ˆp 2 (1 pˆ 2 )
n 2
s p ˜ 1 (1 ˜p 1 )
n 1 + 2
˜p 2 (1 p˜ 2 )
n 2 + 2
r p 0 (1 p 0 )
n
p ˆ p 0 r p 0 (1 p 0 )
n
p ˆ 1 pˆ 2 s
p ˆ(1 pˆ)
✓ 1 n 1
1 n 2
◆
s
p ˆ(1 pˆ)
✓ 1 n 1
1 n 2
◆
n > 10
Confidence Level 90%
CI: at least 15 successes and 15 failures
HT:
np 0 10
n(1 p 0 ) 10
n 1 5
n 2 5
CI: at least 10 successes and 10 failures in each sample
HT: at least 5 successes and 5 failures in each sample
