27) Nationally, the distribution of weapons used in robberies is as shown in the
ID: 3322981 • Letter: 2
Question
27) Nationally, the distribution of weapons used in robberies is as shown in the table. Weaporn Gun Knife Other Strong-arm 0.40 Proportion 0.42 0.09 0.09 The following data represent the weapon of choice in 1652 robberies on school property Gun Knife Other Weapon Proportion Strong-arm 857 329 122 344 Does the distribution of weapon choice in robberies in schools follow the national distribution? Use 0.01 significance level. Please answer: 1. State the null and alternative hypotheses 2. Find the test statistic 3. Find the p-value 4. State a conclusionExplanation / Answer
Answer:
1).
Ho: p1=0.42,p2=0.09,p3=0.40, p4=0.09
H1: The distribution is different from national distribution.
2).
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
329
693.840
-364.840
191.843
122
148.680
-26.680
4.788
857
660.800
196.200
58.254
344
148.680
195.320
256.591
Total
1652
1652.000
511.475
511.475
chi-square
3
df
0.0000
p-value
Chi square test statistic = 511.475
3). P=0.0000
4). Ho is rejected.
We conclude that distribution of weapon choice in robberies in schools are different from national distribution.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
329
693.840
-364.840
191.843
122
148.680
-26.680
4.788
857
660.800
196.200
58.254
344
148.680
195.320
256.591
Total
1652
1652.000
511.475
511.475
chi-square
3
df
0.0000
p-value
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