This problem uses the χ2-distribution for a good- ness of fit test. The following is the distribution of the number of calls received at the switchboard of a government building during 400 five-minute intervales # of calls Frequency 0 95 1 116 2 112 3 41 4 or more 30 Use α = 0.05 (level of significance) to test whether the number of calls received by the switchboard in a five-minute interval is a random variable having the Poisson distribution with λ = 1.5; that is, the probabilities for 0, 1, 2, 3, or 4 or more calls are 0.22, 0.33, 0.25, 0.13, and 0.07
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.
This problem uses the χ2-distribution for a good- ness of fit test. The following is the distribution of the number of calls received at the switchboard of a government building during 400 five-minute intervales
# of calls Frequency 0 95
-
1 116
-
2 112
3 41 4 or more 30
Use α = 0.05 (level of significance) to test whether the number of calls received by the switchboard in a five-minute interval is a random variable having the Poisson distribution with λ = 1.5; that is, the probabilities for 0, 1, 2, 3, or 4 or more calls are 0.22, 0.33, 0.25, 0.13, and 0.07
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