The table to the right gives a breakdown of the root causes of a sample of 84 in
ID: 3305909 • Letter: T
Question
The table to the right gives a breakdown of the root causes of a sample of
84
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
24
Procedures
23
Management
22
Training
15
Total
84
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:
At least one of the multinomial probabilities does not equal its hypothesized value.
B.
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.
C.
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
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
insufficientinsufficient
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
sufficientsufficient
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
84
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
24
Procedures
23
Management
22
Training
15
Total
84
Explanation / Answer
1) option A is correct for Hypothesis
Ho:p1=p2=p3=p4=0.25
Ha: At least one of the multinomial probabilities does not equal its hypothesized value.
2) applying chi square test on above:
for above test stat p value =0.4972
as p value is very high we can not reject null hypothesis
option B is correct
B.
Fail to reject
Upper H0.
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 24.000 21.00 0.43 procedures 0.250 23.000 21.00 0.19 management 0.250 22.000 21.00 0.05 training 0.250 15.000 21.00 1.71 1 84 84 2.3810Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.