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 2.62 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 27 18 22 7 (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 = 2.62 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 and the degrees of freedom. (Round your test statistic to three decimal places.) χ2 = E (O-E)2 E d.f. = χ2 =
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 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 2.62 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 | 27 | 18 | 22 | 7 |
| e−λλr |
| r! |
| 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 and the degrees of freedom. (Round your test statistic to three decimal places.)
| d.f. | = |
| χ2 | = |
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