# Probability distribution and hypothesis testing

Not what you're looking for?

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

##### Purchase this Solution

##### 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

##### 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 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

##### Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.