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When X1, X2,..., X, are independent Poisson variables, each with parameter μ, and n is large, the sample mean X has approximately a normal distribution with μ = E(X) and VX)/n. This implies that Z= X-μ Vμ/n has approximately a standard normal distribution. For testing Hoμ=μo, we can replace μ by μ in the equa- tion for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator S/Vn (when the X's are Poisson) because it is tailored explicitly to the Poisson assumption. If the number of requests for consulting received by a certain statistician during a 5-day work week has a Poisson distribution and the total number of consulting requests during a 36-week period is 160, does this suggest that the true average num- ber of weekly requests exceeds 4.0? Test using a = .02.

When X1, X2,..., X, are independent Poisson variables, each with parameter μ, and n is large, the sample mean X has approximately a normal distribution with μ = E(X) and VX)/n. This implies that Z= X-μ Vμ/n has approximately a standard normal distribution. For testing Hoμ=μo, we can replace μ by μ in the equa- tion for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator S/Vn (when the X's are Poisson) because it is tailored explicitly to the Poisson assumption. If the number of requests for consulting received by a certain statistician during a 5-day work week has a Poisson distribution and the total number of consulting requests during a 36-week period is 160, does this suggest that the true average num- ber of weekly requests exceeds 4.0? Test using a = .02.

MATLAB: An Introduction with Applications
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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When X1, X2,..., X, are independent Poisson variables, each with parameter μ, and n is large, the sample mean X has approximately a normal distribution with μ = E(X) and VX)/n. This implies that Z= X-μ Vμ/n has approximately a standard normal distribution. For testing Hoμ=μo, we can replace μ by μ in the equa- tion for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator S/Vn (when the X's are Poisson) because it is tailored explicitly to the Poisson assumption. If the number of requests for consulting received by a certain statistician during a 5-day work week has a Poisson distribution and the total number of consulting requests during a 36-week period is 160, does this suggest that the true average num- ber of weekly requests exceeds 4.0? Test using a = .02.
Transcribed Image Text:When X1, X2,..., X, are independent Poisson variables, each with parameter μ, and n is large, the sample mean X has approximately a normal distribution with μ = E(X) and VX)/n. This implies that Z= X-μ Vμ/n has approximately a standard normal distribution. For testing Hoμ=μo, we can replace μ by μ in the equa- tion for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator S/Vn (when the X's are Poisson) because it is tailored explicitly to the Poisson assumption. If the number of requests for consulting received by a certain statistician during a 5-day work week has a Poisson distribution and the total number of consulting requests during a 36-week period is 160, does this suggest that the true average num- ber of weekly requests exceeds 4.0? Test using a = .02.
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