Formula significance tests

Question 1

1 sample z significance test

Answer 1

z=𝒙̅ -µ0/

𝜎/√n

Question 2

2 sample z significance test

Answer 2

𝑧 =(𝑥̅1 − 𝑥̅2) − (µ1 − µ2)/

√(𝜎1²/n1)+(𝜎2²/n2)

Question 3

1 sample t significance test

Answer 3

𝑡 =𝑥̅− µ0/

𝑠/√n

Question 4

2 sample t significance test (matched pairs)

Answer 4

𝑡 =𝑥̅d − 0/

𝑠d/√n

Question 5

2 sample t significance test (pooled)

Answer 5

t=(𝑥̅1 − 𝑥̅2)/
√(𝑠𝑝²/𝑛19+(𝑠𝑝²/𝑛2)

sp=√(𝑛1 − 1)𝑠1² + (𝑛2 − 1)𝑠2²/
𝑛1 + 𝑛2 − 2

Question 6

2 sample t significance test (non-pooled [Welch])

Answer 6

t=(𝑥̅1 − 𝑥̅2)/

√(𝑠1²/𝑛1)+(𝑠2²/𝑛2)