2 In a study on speeding and road safety the government coll

2. In a study on speeding and road safety. the government collects the following data on speeding tickets and accidents from 10,000 drivers over a 1-year period: No. of tickets No accidents 1 accident > 1 accident total (a) Test the hypothesis that there is an association between number of speeding tickets and number of accidents. (b) Does this data show that driving faster increases the risk of accidents? If not, give an alternative possible explanation for the result.

Solution

Null hypothesis: There is no association between number of speeding tickets and number of accidents.

Alternate hypothesis: There is an association between number of speeding tickets and number of accidents.

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Row variable

C1

C2

C3

Total

fo-fe

R1

4852

832

54

5738

276.5188

-187.069

-89.45

R2

2844

746

101

3691

-99.2034

90.4784

8.725

R3

278

198

95

571

-177.315

96.5904

80.725

Total

7974

1776

250

10000

Expected Frequencies

Column variable

Row variable

C1

C2

C3

Total

(fo-fe)^2/fe

R1

4575.481

1019.069

143.45

5738

16.71139

34.33991

55.77764

R2

2943.203

655.5216

92.275

3691

3.343743

12.48829

0.824986

R3

455.3154

101.4096

14.275

571

69.05269

92.00022

456.4992

Total

7974

1776

250

10000

Data

Level of Significance

0.05

Number of Rows

3

Number of Columns

3

Degrees of Freedom

4

Results

Critical Value

9.488

Chi-Square Test Statistic

741.038

Calculated chi square 741.038 > 9.488 the table value of chi square at 0.05 level of significance.

We conclude that there is association between number of speeding tickets and number of accidents.

b).

Col 1

Col 2

Col 3

Total

Row 1

Observed

4852

832

54

5738

% of column

60.8%

46.8%

21.6%

57.4%

Row 2

Observed

2844

746

101

3691

% of column

35.7%

42.0%

40.4%

36.9%

Row 3

Observed

278

198

95

571

% of column

3.5%

11.1%

38.0%

5.7%

Total

Observed

7974

1776

250

10000

% of column

100.0%

100.0%

100.0%

100.0%

From the percentages we conclude that driving faster increases the risk of accidents.

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	C1	C2	C3	Total		fo-fe
R1	4852	832	54	5738		276.5188	-187.069	-89.45
R2	2844	746	101	3691		-99.2034	90.4784	8.725
R3	278	198	95	571		-177.315	96.5904	80.725
Total	7974	1776	250	10000
Expected Frequencies
	Column variable
Row variable	C1	C2	C3	Total		(fo-fe)^2/fe
R1	4575.481	1019.069	143.45	5738		16.71139	34.33991	55.77764
R2	2943.203	655.5216	92.275	3691		3.343743	12.48829	0.824986
R3	455.3154	101.4096	14.275	571		69.05269	92.00022	456.4992
Total	7974	1776	250	10000
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	3
Degrees of Freedom	4
Results
Critical Value	9.488
Chi-Square Test Statistic	741.038