There are four entrances to the Government Center Building in downtown Philadelp
ID: 3360832 • Letter: T
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, 675 people were observed entering the building. The number using each entrance is reported below. At the 0.02 significance level, is there a difference in the use of the four entrances? (Round x2 to 3 decimal place. Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round fe,(f0 - fe) and (f0 - fe)2/fe) to 2 decimal places.)
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, 675 people were observed entering the building. The number using each entrance is reported below. At the 0.02 significance level, is there a difference in the use of the four entrances? (Round x2 to 3 decimal place. Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round fe,(f0 - fe) and (f0 - fe)2/fe) to 2 decimal places.)
Explanation / Answer
observed frequncies are Oi
200 125 200 150
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expected frequencies are Ei
= 675/4 = 168.75
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and claiming hypothesis is
null, Ho: 1 = 2 = 3 = 4
alternative, H1: The proportions are not equal.
level of significance, = 0.02
from standard normal table, chi square value at right tailed, ^2 /2 =7.824
since our test is right tailed,reject Ho when ^2 o > 7.824
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table take sum of (Oi-Ei)^2/Ei, we get ^2 o = 24.9999
critical value
the value of |^2 | at los 0.02 with d.f, n - 1 = 3 - 1 = 2 is 7.824
we got | ^2| =24.9999 & | ^2 | =7.824
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0
ANSWERS
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null, Ho: 1 = 2 = 3 = 4
alternative, H1: The proportions are not equal.
reject Ho when ^2 o > 7.824
test statistic: 24.9999
critical value: 7.824
p-value:0
decision: reject Ho , The entrances are not equally preferred.
Observed (Oi ) Expected ( Ei) Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 200 168.75 31.25 976.563 5.787 125 168.75 -43.8 1914.06 11.3426 200 168.75 31.25 976.563 5.787 150 168.75 -18.8 351.563 2.0833Related Questions
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