Formula confidence interval

Question 1

1 sample z confide interval

Answer 1

𝑥̅± m | m=(𝜎/√𝑛)∗z*

Question 2

2 sample z confidence interval

Answer 2

𝑥̅± m | m=(√(𝜎1²/𝑛1)+(𝜎2²/𝑛2))∗z*

Question 3

1 sample t confidence interval

Answer 3

𝑥̅± m | m= (𝑠/√𝑛)∗z*

Question 4

2 sample t confidence interval (matched pairs)

Answer 4

𝑥̅± m | m=(𝑠d/√𝑛)∗𝑡*

Question 5

2 sample t confidence interval (pooled)

Answer 5

𝑥̅± m | m=(√(𝑠𝑝²/𝑛1)+(𝑠𝑝²/𝑛2))∗𝑡*
sp=√(𝑛1 − 1)𝑠1² + (𝑛2 − 1)𝑠2²/
𝑛1 + 𝑛2 − 2

Question 6

2 sample t confidence interval (non pooled[Welch])

Answer 6

𝑥̅± m | m=(√(𝑠1²/𝑛1)+(𝑠2²/𝑛2))∗𝑡*