The table to the right gives a breakdown of the root causes of a sample of 78 in
ID: 3306537 • Letter: T
Question
The table to the right gives a breakdown of the root causes of a sample of
78 industrial accidents. Are there significant differences in the percentage of incidents in the four cause categories? Test using
alphaequals=0.05.
System Cause
Number of Incidents
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Copy to Clipboard
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Open in Excel
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Design
20
Procedures
23
Management
25
Training
10
Total
78
Determine the null and alternative hypotheses for this test. Choose the correct answer below.
A.
Upper H 0 :H0:
p 1 equals p 2 equals p 3 equals p 4 equals 0.25p1=p2=p3=p4=0.25
Upper H Subscript a Baseline :Ha:
p 1 not equals p 2 not equals p 3 not equals p 4p1p2p3p4
B.
Upper H 0 :H0:
p 1 equals p 2 equals p 3 equals p 4 equals 0.25p1=p2=p3=p4=0.25
Upper H Subscript a Baseline :Ha:
At least one of the multinomial probabilities does not equal its hypothesized value.
C.
Upper H 0 :H0:
p 1 not equals p 2 not equals p 3 not equals p 4p1p2p3p4
Upper H Subscript a Baseline :Ha:
At least one of the multinomial probabilities equals its hypothesized value.
Now find the test statistic.
chi squared2equals=
(Round to two decimal places as needed.)
Find the critical value.
chi Subscript alpha Superscript 22equals=
(Round to four decimal places as needed.)
Find the p-value.
(Round to four decimal places as needed.)
Choose the correct conclusion below.
A.
RejectReject
Upper H 0H0.
There is
sufficientsufficient
evidence that there are significant differences in the percentage of incidents in the four cause categories.
B.
Fail to rejectFail to reject
Upper H 0H0.
There is
insufficientinsufficient
evidence that there are significant differences in the percentage of incidents in the four cause categories.
C.
RejectReject
Upper H 0H0.
There is
insufficientinsufficient
evidence that there are significant differences in the percentage of incidents in the four cause categories.
D.
Fail to rejectFail to reject
Upper H 0H0.
There is
sufficientsufficient
evidence that there are significant differences in the percentage of incidents in the four cause categories.
The table to the right gives a breakdown of the root causes of a sample of
78 industrial accidents. Are there significant differences in the percentage of incidents in the four cause categories? Test using
alphaequals=0.05.
System Cause
Number of Incidents
Open in StatCrunch
+
Copy to Clipboard
+
Open in Excel
+
Design
20
Procedures
23
Management
25
Training
10
Total
78
Explanation / Answer
for 1st question : option B is correct
B.
Upper H 0 p1=p2=p3=p4=0.25
Ha: At least one of the multinomial probabilities does not equal its hypothesized value
2) applying chi square goodness of fit on above:
from above chi squared 2=6.8205
critical value =7.8147
p-value =0.0778
option B is correct
B.
Fail to reject
Upper H 0H0.
There is
insufficient
evidence that there are significant differences in the percentage of incidents in the four cause categories.
observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E design 0.250 20.000 19.50 0.01 Procedures 0.250 23.000 19.50 0.63 management 0.250 25.000 19.50 1.55 training 0.250 10.000 19.50 4.63 1 78 78 6.8205Related Questions
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