Question

A study of sport and compact car colors shows that 15.2% are green, 14.4% are white, 19.8% are red, 11.2% are black, and 39.4% are other colors. When 100 trucks and vans are randomly selected, it is found that 16 are green, 24 are white, 16 are red, none are black, and 44 are other colors. Is there sufficient evidence to support the claim that the color distribution for trucks and vans is different from the color distribution for sport and compact cars? α = .05

Answer 1

Solution:

Claim:  the color distribution for trucks and vans is different from the color distribution for sport and compact cars

Level of significance = α = 0.05

Step 1) State H0 and H1:

H0: the color distribution for trucks and vans is same as the color distribution for sport and compact cars

Vs

H1: the color distribution for trucks and vans is different from the color distribution for sport and compact cars

Step 2) Test statistic:

Color	Oi: Observed frequency	Expected %	Ei: Expected frequency	(Oi-Ei)^2/Ei
Green	16	15.2%	=100X15.2%= 15.200	0.042
White	24	14.4%	=100X14.4%= 14.400	6.400
Red	16	19.8%	=100X19.8%= 19.800	0.729
Black	0	11.2%	=100X11.2%= 11.200	11.200
Other	44	39.4%	=100X39.4%= 39.400	0.537
	N = 100

Thus

Step 3) Find Chi-square critical value:

df = k - 1 = 5 -1 = 4

Level of significance = 0.05

Chi-square critical value = 9.488

Step 4) Decision Rule:

Reject null hypothesis H0, if Chi square test statistic > Chi-square critical value =9.488, otherwise we fail to reject H0.
Since Chi square test statistic =     > Chi-square critical value =9.488, we reject null hypothesis H0 in favor of H1.

Step 5) Conclusion:

At 0.05 level of significance , there is sufficient evidence to support the claim that the color distribution for trucks and vans is different from the color distribution for sport and compact cars