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) u/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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
help please answer in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working
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) u/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) u/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.
Expert Solution
steps

Step by step

Solved in 2 steps with 5 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman