Car manufacturers are interested in whether there is a relationship between the

Question

Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver's famly (that is, whether car size and Famly size are independent). To test this, suppose that 801 car owners were randomly surveyed with the following results. Conduct a test for independence at the 5% level. Family Sie Sub & Compact Mid-sizeFull-size Van &Truck; 36 19 35 79 90 69 3- 4 20 19 50 31 70 G Part (a) Part(B) Partie, Whet are the degrees of freedom? (Entor an exact number as an intogor, fraction, or decma) Part What is the test statisac? (Round your answer to two deomal places A Part t Whetl is the D-vale?(Round your eser to four decrsal places)

Explanation / Answer

Ans:

df=(4-1)*(4-1)=3*3=9

Test statistic=14.84

p-value=CHIDIST(14.840,9)=0.0954

Observed(O) contract mid size full size truck Total 1 19 36 41 35 131 2 21 51 69 79 220 3 20 50 101 90 261 4 19 31 70 69 189 Total 79 168 281 273 801 Expected(E) contract mid size full size truck Total 1 12.92 27.48 45.96 44.65 131 2 21.70 46.14 77.18 74.98 220 3 25.74 54.74 91.56 88.96 261 4 18.64 39.64 66.30 64.42 189 Total 79 168 281 273 801 (O-E)^2/E contract mid size full size truck 1 2.861 2.645 0.535 2.085 2 0.022 0.511 0.867 0.215 3 1.281 0.411 0.973 0.012 4 0.007 1.883 0.206 0.326 Total chi square=14.840

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