Question

In each of exercises 12.57-12.59, use the technology of your choice to solve the specified problems.

The Scottish Executive, Analytical Services Division Transport Statistics, compiles information on motorcycle accidents in Scotland. During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non built-up), are as presented on the WeissStats CD.
a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of day of the week within each type-of-road category and the marginal distribution of day of the week.
c. Determine the conditional distribution of type of road within each day of the week and the marginal distribution of type of road.
d. Does an association exist between the variables "day of the week" and "type of road" for these motorcycle accidents? Explain your answer.

Short answer

(a) The bivariate data for these two variables into a contingency table is:

(b) The conditional distribution of day of the week within each type-of-road category and the marginal distribution of day of the week is:

(c) The conditional distribution of type of road within each day of the week and the marginal distribution of type of road is:

(d) Yes, there is an association between "day of the week" and "type of road" for these motorcycle accidents because the conditional distribution of type of road within each day of the week are not similar.

Step-by-step solution

Part (a) Step 1. Given Information. 

During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non built-up), are as presented on the WeissStats CD.

Part (a) Step 2. Use MINITAB procedure. 

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select Day, and in columns select counts.

4. Under display, select counts.

5. Click OK.

Part (a) Step 3. MINITAB output. 

Rows: Day Column: Type

	Built-up	Non Built-up	All
Monday	88	70	158
Tuesday	100	58	158
Wednesday	76	59	135
Thursday	98	53	151
Friday	103	56	159
Saturday	85	94	179
Sunday	69	102	171
All	619	492	1111

Cell contents: Count

Part (b) Step 1. Use MINITAB. 

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select Day, and in columns select counts.

4. Under display, select column percent.

5. Click OK.

Part (b) Step 2. MINITAB output. 

Rows: Day Column: Type

	Built-up	Non Built-up	All
Monday	14.22	14.23	14.22
Tuesday	16.16	11.79	14.22
Wednesday	12.28	11.99	12.15
Thursday	15.83	10.77	13.59
Friday	16.64	11.38	14.31
Saturday	13.73	19.11	16.11
Sunday	11.15	20.73	15.39
All	100	100	100

Cell contents: % of columns.

Part (c) Step 1. Use MINITAB.  

By using MINITAB procedure,

1. Choose stat > tables > Cross tabulation and Chi-square.

2. Select Raw data.

3. In rows, select Day, and in columns select counts.

4. Under display, select row percent.

5. Click OK.

Part (c) Step 2. MINITAB output. 

Rows: Day Column: Type

	Built-up	Non Built-up	All
Monday	55.70	44.30	100
Tuesday	63.29	36.71	100
Wednesday	56.30	43.70	100
Thursday	64.90	34.10	100
Friday	64.78	35.22	100
Saturday	47.49	52.51	100
Sunday	40.35	59.65	100
All	55.72	44.28	100

Cell contents: % of rows.

Part (d) Step 1. Relation between "day of the week" and "type of the road". 

Yes, there is an association between "day of the week" and "type of road" for these motorcycle accidents because the conditional distribution of type of road within each day of the week are not similar.