Question

"Top Gear" magazine published an article stating that car brands are purchased in equal numbers. To examine this claim, a sample of cars on a major highway was collected and the numbers of 5 major car brands was reported. The numbers are given in the table. Does this sample contradict the magazine's claim at the 0.10 level of significance.  

Honda	Toyota	Ford	GM	Hyundai
121	105	98	92	102

Answer 1

Answer: Top Gear" magazine published an article stating that car brands are purchased in equal numbers. To examine this claim, a sample of cars on a major highway was collected and the numbers of 5 major car brands was reported. The numbers are given in the table. Does this sample contradict the magazine's claim at the 0.10 level of significance.  

The hypothesis test:

Ho: The car brands are purchased in equal numbers = 1/5

Ha: Some of the car brands purchased is not in equal numbers ≠ 1/5

n = 121 + 105 + 98 + 92 + 102 = 518

Test statistic χ2 = (Observed value - Expected value)^2/ Expected value

Expected value = np

Expected value = 518 * 1/5

Expected value = 103.6

Brands	Observed (O)	Expected (E)	(O-E)^2/E
Honda	121	103.6	2.9224
Toyota	105	103.6	0.0189
Ford	98	103.6	0.3027
GM	92	103.6	1.2988
Hyundai	102	103.6	0.0247
Total	518	518	4.5675

Test statistic χ2 = 4.5675

P-value:

df = (r-1)(c-1)

df = (5-1)(2-1)

df = 4

P-value = 0.3347

Since, P-value (0.33) > α (0.05) significance level.

We do not reject the null hypothesis Ho.

Conclusion:

Do not reject Ho. There is not sufficient evidence to conclude that some of the car brands purchased is not in equal numbers.