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. 2 3 4 or more 26 24 14 14 12
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
(a) The civil engineer wants to use a Poisson distribution to represent the
| e−λ λr |
| r! |
Here λ = 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) for r = 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 Χ2 = Σ((O – E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.)
| df = | |
| Χ2 = |
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