Answered: Let X1, X2, ... , Xn denote a random…

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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Let X1, X2, ... , Xn denote a random sample from a normal population distribution

with a known value of sigma. For testing the hypotheses HO: mean = mean0 versus Ha: mean > mean0 where mean0 is a fixed number, the test procedure consists of test statistics X(bar) and rejection region x(bar)>102.33. Assume mean0 = 100, n = 25, and sigma = 5.

a) What is the probability of committing a type 1 error when mean = 99?

b) What is the probability of committing a type 1 error when mean = 98?

c) In general, what can be said about the probability of a type 1 error when the actual mean value is below the mean0 value?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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