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Chapter 12: Q. 12.58 (page 502)

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

Expert verified

(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

01

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.

02

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.

03

Part (a) Step 3. MINITAB output. 

Rows: Day Column: Type


Built-upNon Built-upAll
Monday8870158
Tuesday10058158
Wednesday7659135
Thursday9853151
Friday10356159
Saturday8594179
Sunday69102171
All6194921111

Cell contents: Count

04

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.

05

Part (b) Step 2. MINITAB output. 

Rows: Day Column: Type


Built-upNon Built-upAll
Monday14.2214.2314.22
Tuesday16.1611.7914.22
Wednesday12.2811.9912.15
Thursday15.8310.7713.59
Friday16.6411.3814.31
Saturday13.7319.1116.11
Sunday11.1520.7315.39
All100100100

Cell contents: % of columns.

06

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.

07

Part (c) Step 2. MINITAB output. 

Rows: Day Column: Type


Built-upNon Built-upAll
Monday55.7044.30100
Tuesday63.2936.71100
Wednesday56.3043.70100
Thursday64.9034.10100
Friday64.7835.22100
Saturday47.4952.51100
Sunday40.3559.65100
All55.7244.28100

Cell contents: % of rows.

08

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.

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