There are two tails that we exclude this is why we

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: upper percentage point ) P (Z ≥ zα ) = α The reason P [|Z | ≤ zα/2 ] = 1 − α is that P [|Z | ≤ zα/2 ] = P [−zα/2 ≤ Z ≤ zα/2 ] = 1 − P [Z ≤ −zα/2 ] − P [Z ≥ zα/2 ] = 1 − 2 · α = 1−α 2 Even better, look at the drawing posted separately. There are two tails that we exclude, this is why we need α/2. From (4.1), we read that with probability 1 − α −zα/2 ≤ X −µ σ √ n σ σ σ σ ≤ zα/2 ⇐⇒ −zα/2 √ ≤ X − µ ≤ zα/2 √ ⇐⇒ X −zα/2 √ ≤ µ ≤ X +zα/2 √ n n n n CONCLUSION: With probability 1 − α, ￿ ￿ σ σ (4.2) µ ∈ X − zα/2 √ , X + zα/2 √ n n One sample. Say we choose n = 100, α = 0.05 and we measure x = 2.501. Then zα/2 = z0.025 = 1.96 and the above interval is ￿ ￿ 0.01 0.01 2.501 − 1.96 √ , 2.501 + 1.96 √ = [2.4...
View Full Document

Ask a homework question - tutors are online