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Probability distribution and hypothesis testing

There are 4 entrances to a building in Philadelphia. The bldg maintenance super would like to know if the entrances are equally utilized. To investigate, 400 people were observed entering the building. The number using each entrance is reported below. At the .01 signficance level, is there a difference in the use of the four entrances?

Entrance Frequency

Main Street 140
Broad Street 120
Cherry St 90
Walnut St 50
Total 400

Solution Preview

Solution. Assume that the entrances are equally utilized, ie., people use these four entrances at equal probability 1/4. Denote the numbers of 400 people who use entrance Main Street, Broad Street, Cherry St and Walnut St by X,Y,Z and W, respectively. Obviously, X,Y,Z and W are random variables and mutually independent. Moreover, they follow the same distribution: Binomial ...

Solution Summary

There are 4 entrances to a building in Philadelphia. The bldg maintenance super would like to know if the entrances are equally utilized. To investigate, 400 people were observed entering the building. The number using each entrance is reported below. At the .01 signficance level, is there a difference in the use of the four entrances?

Entrance Frequency

Main Street 140
Broad Street 120
Cherry St 90
Walnut St 50
Total 400

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