Question

Question: Thirty years ago, the Big Three automakers dominated car sales in this country. Backthen, Ford accounted for 28% of sales, GM for 26%, and Chrysler for 16%. Foreign companies accounted for 30% of sales. Data for 158 recent car purchases was collected to see if there is a significant shift in this pattern:

	Car Maker	Ford	GM	Chrysler	Foreign
	Cars Sold	42	25	20	71

a)Use the Goodness of Fit Hypothesis Test to find if the pattern from 30 years ago is still in place, using the 0.05 level of significance.Show all steps of the hypothesis test: Hypotheses, Alpha, Distribution, Sketch with Critical Value, Calculate Test Statistic by hand and put on Sketch, Decision, Conclusion.

b)Would your conclusion change if you changed your level of significance level to 1%? Show why or why not.

Answer 1

a)

null hypothesis:Ho: pattern of car purchase follows which was in place 30 years ago

alternate hypothesis: pattern of car purchase differs from which was in place 30 years ago

alpha=0.05

distribution -chi square:

for (categories-1=3) df and 0.05 level critical value =7.815

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Ford	0.280	42.000	44.240		0.113
GM	0.260	25.000	41.080		6.294
Chrysler	0.160	20.000	25.280		1.103
Foreign	0.300	71.000	47.400		11.750
total	1.000	158	158		19.261

from above chi squae test statistic =19.261

as test statistic falls in rejection region we rject null hypothesis

we have sufficient evidence at 0.05 level to conclude that  pattern of car purchase differs from which was in place 30 years ago

b)

for 0.01 level and 3 df crtiical value =11.345

as test statisitc is higher than critical value out conclusion will remain same at 0.01 level