A random sample of individuals who drive to work alone in a large metropolitan a

Question

A random sample of individuals who drive to work alone in a large metropolitan area was obtained. Each individual was categorized with respect to size of car and commuting distance. Do the following data suggest that commuting distance and size of car are related in the population sampled? Commuting Distance 10 km 10-20 km 20 km 28 Subcompact 6 19 35 17 Compact Mid-size 21 44 34 Full-size 14 18 8 What is the null hypothesis for the test? There is no association between car size and commuting distance. There is a association between car size and commuting distance. For a given car size, there is no difference between commuting distances. 1 pt(s)] Submit Answer Tries 0/1 What is the expected count for subcompact cars commuting less than 10 km? [3 pt(5 Submit Answer Tries (0/3 Compute the value of the test statistic. 3 pt(s Submit Answer Tries o/3 How many degrees of freedom are there? [1 pt(s Submit Answer Tries 0/1

Explanation / Answer

The null hypothesis for the test will be:

There is no association between car size and commuting distance.

Option A is correct.

Statistical software output for this problem is:

Contingency table results:
Rows: var7
Columns: None

Chi-Square test:

So,

Expected count for subcompact cars commuting less than 10 kms = 10.31

Test statistic = 12.284768

Degrees of freedom = (Row - 1)* (Column - 1) = (4 - 1)*(3 - 1) = 6

p - value = 0.0559 so 0.05 < p-value < 0.1. Option E is correct.

p - value > 0.05 so we do not reject Ho. Option A is correct.

p - value > 0.01 so we do not reject Ho. Option B is correct.

Full size car commuting less than 10 km shows the largest daviation as there are more cars then expected.

Cell format Count
(Expected count)
(Chi-Square residuals)

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