Q9. A random sample of size n= 64 from a population with variance o? = 256 is to be used to test Ho: u < 40 against H1: u > 40 where u is the population mean. The null is to be rejected if and only if the sample mean X> 43.5. Find (a) Probabilities of type I error when u = 37.0, 38.0, 39.0 and 40.0 (b) Probabilities of type II error when µ = 41.0, 42.0, 43.0, 44.0, 45.0, 46.0, 47.0 and 48.0. (c) Plot the power function of the test.

Q9. A random sample of size n= 64 from a population with variance o? = 256 is to be used to test Ho: u < 40 against H1: u > 40 where u is the population mean. The null is to be rejected if and only if the sample mean X> 43.5. Find (a) Probabilities of type I error when u = 37.0, 38.0, 39.0 and 40.0 (b) Probabilities of type II error when µ = 41.0, 42.0, 43.0, 44.0, 45.0, 46.0, 47.0 and 48.0. (c) Plot the power function of the test.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q9. A random sample of size n = 64 from a population with variance o? = 256 is to be used
to test Ho: H < 40 against H,: u > 40 where u is the population mean. The null is to be rejected
if and only if the sample mean X > 43.5. Find
(a) Probabilities of type I error when µ = 37.0, 38.0, 39.0 and 40.0
(b) Probabilities of type II error when u = 41.0, 42.0, 43.0, 44.0, 45.0, 46.0, 47.0 and 48.0.
(c) Plot the power function of the test.

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