3. Researchers wanted to know if the weight of an automobile influenced the pote
ID: 3245472 • Letter: 3
Question
3. Researchers wanted to know if the weight of an automobile influenced the potential for leg injury in a crash. The researchers measured the amount of load placed on the left femur of crash test dummies in vehicles driven into barriers at 35mi/h. The results are presented below. Is there evidence that leg injury measurements for the four car types are not the same?
Full size
Mid-size
Compact
Sub-compact
1085
629
1051
595
971
1686
1193
1063
996
880
946
885
804
181
984
519
1376
645
584
422
Full size
Mid-size
Compact
Sub-compact
1085
629
1051
595
971
1686
1193
1063
996
880
946
885
804
181
984
519
1376
645
584
422
Explanation / Answer
Full Size
Mid-size
Compact
Sub-compact
1085
629
1051
595
971
1686
1193
1063
996
880
946
885
804
181
984
519
1376
645
584
422
Here we use analysis of variance.
Null and alternative hypothesis:
H0: All the population means are equal.
H1: At least one of the mean differs.
Level of significance is .05
Test Statistics:
To find the test statistics we can use excel here. We type the data in excel then we go to Data tab and under that we select Data Analysis. There we select Single factor Anova. We select the data set and finally we click on OK. The anova output will be ready.
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Column 1
5
5232
1046.4
44277.3
Column 2
5
4021
804.2
306933.7
Column 3
5
4758
951.6
51091.3
Column 4
5
3484
696.8
71753.2
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
360065.8
3
120021.9
1.013
0.4129
3.239
Within Groups
1896222
16
118513.9
Total
2256288
19
F = 1.013
p-value = 0.4129
Decision:
Here the p-value is > level of significance (0.4129>.05); we retain the null hypothesis.
Conclusion:
At 5% level of significance there is not enough evidence to conclude that leg injury measurements for the four cars types are not the same. Therefore we can conclude that they are the same.
Full Size
Mid-size
Compact
Sub-compact
1085
629
1051
595
971
1686
1193
1063
996
880
946
885
804
181
984
519
1376
645
584
422
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