{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ams572_notes_5 - AMS 572 Lecture Notes#5 Quiz 1 Let be a...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
AMS 572 Lecture Notes #5 September 24, 2010 Quiz 1. Let be a random sample from a normal population with mean , variance . Please (1) Derive the distribution of (2) Derive the 100(1- α )% confidence interval for μ Solution: (1) First we derive the mgf of Now we derive the mgf of 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
m.g.f. of Thus we have shown that (2) Based on the PDF of the pivotal quantity for μ We have: Thus 2
Background image of page 2
the 100(1- )% C.I. for is α μ <Today’s Topic> Power Calculation (Inference on one population mean) Truth Decision Type II error Type I error = P(Type II error) = P(Fail to reject |) Power Calculation (Inference on one population mean) 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
1. 1 st scenario, Normal population, is known. Test statistic : At the significance level , we reject if Power of the test = P(reject |) = 1- Power = 1- = P(reject |) = P( = , If , = = , 4
Background image of page 4
2 nd scenario, Normal population, is un known. Test statistic : At the significance level , we reject if Power of the test = P(reject |) = 1- Power = 1- = P(reject |) = P( = = = , Here 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Recall that the Shapiro-Wilk test : can be used to determine whether the population is normal.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}