A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.64 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. 4 or more 26 24 14 14 12 (a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below. P(r) = r! Here A = 1.64 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.) P(0) = P(1) = P(2) - P(3) P(4 or more) = (b) Compute the expected number of accidents E = 90P(r) forr = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.) E(0) = E(1) = E(2) - E(3) = E(4 or more) = (c) Compute the sample statistic X = E((0 - E)/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) %3D df = x2 =

A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.64 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. 4 or more 26 24 14 14 12 (a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below. P(r) = r! Here A = 1.64 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.) P(0) = P(1) = P(2) - P(3) P(4 or more) = (b) Compute the expected number of accidents E = 90P(r) forr = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.) E(0) = E(1) = E(2) - E(3) = E(4 or more) = (c) Compute the sample statistic X = E((0 - E)/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) %3D df = x2 =

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of
1.64 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed
accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information.
4 or more
26
24
14
14
12
(a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is given below.
P(r) =
r!
Here A = 1.64 is the average number of accidents per day. Compute P(r) for r = 0, 1, 2, 3, and 4 or more. (Round your answers to three decimal places.)
P(0) =
P(1) =
P(2) -
P(3)
P(4 or more) =
(b) Compute the expected number of accidents E = 90P(r) forr = 0, 1, 2, 3, and 4 or more. (Round your answers to two decimal places.)
E(0) =
E(1) =
E(2) -
E(3) =
E(4 or more) =
(c) Compute the sample statistic X = E((0 - E)/E) and the degrees of freedom. (Round your sample statistic to three decimal places.)
%3D
df =
x2 =

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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.78 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.60 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.60 grams? Use ? = 0.05. Compute the z value of the sample test statistic. Round two decimal placesFind (or estimate) the P-value. Round four decimal places
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