Assignment:
Multinomial Experiments
Q1 Randomly selected deaths from car crashes were obtained and the results are included in the table below. Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week. How might the results be explained? Why does there appear to be an exceptionally large number of car crash fatalities on Saturday?
|
Day
|
Sunday
|
Monday
|
Tuesday
|
Wednesday
|
Thursday
|
Friday
|
Saturday
|
|
# of fatalities
|
132
|
98
|
95
|
98
|
105
|
133
|
158
|
Q2 Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to the data set below and use the sample data to test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.
|
Red
|
Orange
|
Yellow
|
Brown
|
Blue
|
Green
|
|
0.751
|
0.735
|
0.883
|
0.696
|
0.881
|
0.925
|
|
0.841
|
0.895
|
0.769
|
0.876
|
0.863
|
0.914
|
|
0.856
|
0.865
|
0.859
|
0.855
|
0.775
|
0.881
|
|
0.799
|
0.864
|
0.784
|
0.806
|
0.854
|
0.865
|
|
0.966
|
0.852
|
0.824
|
0.840
|
0.810
|
0.865
|
|
0.859
|
0.866
|
0.858
|
0.868
|
0.858
|
1.015
|
|
0.857
|
0.859
|
0.848
|
0.859
|
0.818
|
0.876
|
|
0.942
|
0.838
|
0.851
|
0.982
|
0.868
|
0.809
|
|
0.873
|
0.863
|
|
|
0.803
|
0.865
|
|
0.809
|
0.888
|
|
|
0.932
|
0.848
|
|
0.890
|
0.925
|
|
|
0.842
|
0.940
|
|
0.878
|
0.793
|
|
|
0.832
|
0.833
|
|
0.905
|
0.977
|
|
|
0.807
|
0.845
|
|
|
0.850
|
|
|
0.841
|
0.852
|
|
|
0.830
|
|
|
0.932
|
0.778
|
|
|
0.856
|
|
|
0.833
|
0.814
|
|
|
0.842
|
|
|
0.881
|
0.791
|
|
|
0.778
|
|
|
0.818
|
0.810
|
|
|
0.786
|
|
|
0.864
|
0.881
|
|
|
0.853
|
|
|
0.825
|
|
|
|
0.864
|
|
|
0.855
|
|
|
|
0.873
|
|
|
0.942
|
|
|
|
0.880
|
|
|
0.825
|
|
|
|
0.882
|
|
|
0.869
|
|
|
|
0.931
|
|
|
0.912
|
|
|
|
|
|
|
0.887
|
|
|
|
|
|
|
0.886
|
|
|
|
|
|
|
|
|
Contingency Tables
Q3 The data in the accompanying table summarize results from tests of the accuracy of polygraphs. Use a 0.05 significance level to test the claim that whether the subject lies is independent of the polygraph indication. What do the results suggest about the effectiveness of polygraphs?
|
|
Polygraph Indicated Truth
|
Polygraph Indicated Lie
|
|
Subject actually told the truth
|
65
|
15
|
|
Subject actually told a lie
|
3
|
17
|
Q4 Use the data in the table to test the claim that occupation is independent of whether the cause of death was homicide. Does any particular occupation appear to be most prone to homicides?
|
|
Police
|
Cashiers
|
Taxi Drivers
|
Guards
|
|
Homicide
|
82
|
107
|
70
|
59
|
|
Cause of death other than homicide
|
92
|
9
|
29
|
42
|
Analysis of Variance
Q5 The head injury data (in hic) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?
|
Subcompact
|
55
|
47
|
59
|
49
|
42
|
|
Compact
|
57
|
57
|
46
|
54
|
51
|
|
Midsize
|
45
|
53
|
49
|
51
|
46
|
|
Full-size
|
44
|
45
|
39
|
58
|
44
|