# 409Quiz4Cans - p-value = area of the right tail = P Z ≥...

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

STAT 409 Fall 2011 Version C Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Assume that the population of adult white rhinoceros weights is normally distributed, and the overall (population) standard deviation of the weights is 400 pounds. A random sample of n = 25 adult white rhinos had an average weight of 5,820 pounds. We wish to test H 0 : μ = 5,700 pounds vs. H 1 : μ > 5,700 pounds, where μ is the overall average weight of adult white rhino. a) (3) Find the p-value of this test. Test Statistic: σ is known. 25 400 700 , 5 820 , 5 X Z σ μ 0 - = - = n = 1.50 . Right – tailed test.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: p-value = ( area of the right tail ) = P ( Z ≥ 1.50 ) = 0.0668 . b) (7) If α = 0.095 is used, find ( the significance level ) and ( the power of the test if the true value of the overall average weight of adult white rhino is μ = 5,840 ). Significance level = α = 0.095 . Test Statistic: σ is known. 25 400 700 , 5 X X Z σ μ-=-= n . Rejection Region: Right - tailed. Reject H if Z > z α = 1.31. 25 400 31 . 1 700 , 5 X ⋅ + > = 5,804.8. Power ( μ = 5,840 ) = P ( Reject H | μ = 5,840 ) = P ( X > 5,804.8 | μ = 5,840 ) = -> 25 400 840 , 5 5,804.8 Z P = P ( Z > – 0.44 ) = 0.6700 ....
View Full Document

## This note was uploaded on 11/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

Ask a homework question - tutors are online