Question

Hypothesis Test: Show the 5 Steps. "nascar" 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 I

Answer 1

Step 1:

Ho: The proportion of car brands purchased are equal. i.e. = 1/5

Ha: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

Step 2: Test statistics

Data	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
Honda	121	0.200	103.60	2.922
Toyota	105	0.200	103.60	0.019
Ford	98	0.200	103.60	0.303
GM	92	0.200	103.60	1.299
Hyundai	102	0.200	103.60	0.025
Total	518	1.000	518.00	4.568

$\chi^{2}$ = 4.568

Step 3: Rejection region

df = 5-1 = 4

$\chi^{2}$ critical =CHISQ.INV.RT(0.1,4) = 7.779

Step 4: Decision

As $\chi^{2}$   (4.568) is less than $\chi^{2}$ critical, we fail to reject the Null hypothesis.

Step 5: Conclusion

Hence we do not have sufficient to believe that some population proportions differ from the values stated in the null hypothesis.

The data does not contradict the claim.