A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.74 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information. r 0 1 2 3 4 5 or more O 13 13 32 17 17 8 (a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = e−λλr r! Here λ = 2.74 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) P(0) = P(1) = P(2) = P(3) = P(4) = P(5 or more) = (b) Compute the expected number of colonies E = 100P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to one decimal place.) E(0) = E(1) = E(2) = E(3) = E(4) = E(5 or more) = (c) Compute the sample statistic χ2 = (O − E)2 E and the degrees of freedom. (Round your test statistic to three decimal places.) d.f. = χ2 =

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Description: A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.74 bacteria colonies per field. Let r

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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A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.74 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information.

r	0	1	2	3	4	5 or more
O	13	13	32	17	17	8

(a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below.

P(r) =

e^−λλ^r

Here λ = 2.74 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.)

P(0)	=
P(1)	=
P(2)	=
P(3)	=
P(4)	=
P(5 or more)	=

(b) Compute the expected number of colonies E = 100P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to one decimal place.)

E(0)	=
E(1)	=
E(2)	=
E(3)	=
E(4)	=
E(5 or more)	=

χ² =

(O − E)²

and the degrees of freedom. (Round your test statistic to three decimal places.)

d.f.	=
χ²	=

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