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 20 km Subcompact 6 Compact 8 Mid-size Full-size 27 34 45 18 16 31 20 14 What is the null hypothesis for the test? For a given car size, there is no difference between commuting distances There is an association between car size and commuting distance. There is no association between car size and commuting distance. [1 pt(s)] Submit Answer Tries 0/1 What is the expected count for full-size cars commuting less than 10 km? [3 pt(s)] Submit Answer Tries 0/3 Compute the value of the test statistic. Tries 0/3 [3 pt (s)] Submit Answer 1 pt(s)] How many degrees of freedom are there? Tries 0/1 Submit Answer Which interval in the table contains the p-value for the test? p-value 0.005 0.005p-value s 0.01 0.01

Explanation / Answer

null hypothesis: there is no assciation between.................

expected count ......... =7.67

test statistic =11.795

degree of freedom =(rows-1)*(column-1) =3*2=6

p value : 0.05 <p value <0.1

conclusion : Do not reject the null hypothesis that there is an association.....

conclusion :don not reject the null hypothessis that there is an association.....

ull size

less then 10 km

fewer cars then expected

Observed O <10 km 10-20 Km >20 Km Total subcompact 6 27 18 51 compact 8 34 16 58 Mid-size 20 45 31 96 Full-size 14 18 7 39 Total 48 124 72 244 Expected E=rowtotal*column total/grand total <10 km 10-20 Km >20 Km Total subcompact 10.03 25.92 15.05 51 compact 11.41 29.48 17.11 58 Mid-size 18.89 48.79 28.33 96 Full-size 7.67 19.82 11.51 39 Total 48 124 72 244 chi square =(O-E)^2/E <10 km 10-20 Km >20 Km Total subcompact 1.6210 0.0452 0.5786 2.245 compact 1.0190 0.6945 0.0726 1.786 Mid-size 0.0658 0.2939 0.2521 0.612 Full-size 5.2191 0.1671 1.7660 7.152 Total 7.925 1.201 2.669 11.795

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