The data below shows car model and the color of vehicles sold at a Car dealership. Hyundai Honda Toyota Daihatsu Subaru Total Red 20 11 6 8 5 50 15.40 8.648 13.51 * 4.59 Black 15 6 18 9 7 55 16.95 9.51 14.86 8.62 5.05 White 22 15 26 12 5 ** 24.65 13.84 21.62 12.54 7.35 Total 57 32 50 29 17 185 Chi Sq = 1.37 + 0.64 + 4.18 + 0.00 + 0.04 + 0.22 + 1.30 + *** + 0.02 + 0.75 + 0.28 + 0.10 + 0.89 + 0.02 + 0.75 = 10.47 DF = ****, P-Value = ***** No cells with expected counts less than 5 a) Carefully define the null and alternative hypotheses of the χ2 test underlying the generation of the above table. b) Fill in the missing values ‘*’, ‘**’, ‘***’, ‘****’ and ‘*****’. c) What is the conclusion of this test at the 5% level of significance? Give reasons for your answer.
The data below shows car model and the color of vehicles sold at a Car dealership.
Hyundai Honda Toyota Daihatsu Subaru Total
Red 20 11 6 8 5 50
15.40 8.648 13.51 * 4.59
Black 15 6 18 9 7 55
16.95 9.51 14.86 8.62 5.05
White 22 15 26 12 5 **
24.65 13.84 21.62 12.54 7.35
Total 57 32 50 29 17 185
Chi Sq =
1.37 + 0.64 + 4.18 + 0.00 + 0.04 +
0.22 + 1.30 + *** + 0.02 + 0.75 +
0.28 + 0.10 + 0.89 + 0.02 + 0.75 = 10.47
DF = ****, P-Value = *****
No cells with expected counts less than 5
a) Carefully define the null and alternative hypotheses of the χ2 test underlying the
generation of the above table.
b) Fill in the missing values ‘*’, ‘**’, ‘***’, ‘****’ and ‘*****’.
c) What is the conclusion of this test at the 5% level of significance? Give reasons for your
answer.
d) Name two limitations of this test.
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