Question

There are four entrances to the Government Center Building in downtown Philadelphia. The building maintenance supervisor would like to know if the entrances are equally utilized. To investigate, 401 people were observed entering the building. The number using each entrance is reported below. At the 0.01 significance level, is there a difference in the use of the four entrances? Entrance Frequency Main Street 81

Answer 1

Yes. We have evidence to support the claim that there is a difference in the use of the four entrances.

Explanation:

The question is incomplete:

Entrance Frequency

Main Street 81

Broad Street 129

Cherry Street 72

Walnut Street 119

Total: 401

The building maintenance supervisor wants to know if the entrances are equally utilized.

This problem can be solved using the Chi-square goodess of fit test.

The expected value for each door is

`E=401/4=100.25`

The degrees of freedom are equal to the number of categories (4 doors) minus one:

`df=n-1=4-1=3`

Then, the value of the chi-square statistic can be calculated as:

`\chi^2=\sum ((O_i-E)^2)/(E)\\\\\\\chi^2=((81-100.25)^2)/(100.25)+((129-100.25)^2)/(100.25)+((72-100.25)^2)/(100.25)+((119-100.25)^2)/(100.25)\\\\\\\chi^2=(370.5625+826.5625+798.0625+351.5625)/(100.25)=(2346.75)/(100.25)=23.41`

The P-value for this test statistic χ^2=23.41 and df=3 is:

`P-value=P(\chi^2_3>23.41)=0.00003`

This P-value is much smaller than the significance level (0.01), so the effect is significant.

We have evidence to support the claim that there is a difference in the use of the four entrances.