Question

The shares of the U.S. automobile market held in 1990 by General Motors, Japanese manufacturers, Ford, Chrysler, and other manufacturers were, respectively, 33%, 32%, 23%, 8%, and 4%. Suppose that a new survey of 1,000 new-car buyers shows the following purchase frequencies:

GM	Japanese	Ford	Chrysler	Other
363	226	272	100	39

(a) Show that it is appropriate to carry out a chi-square test using these data.

Each expected value is ≥          

(b) Test to determine whether the current market shares differ from those of 1990. Use α = .05. (Round your answer to 3 decimal places.)

x2x2        

(Click to select)Do not rejectReject H₀ . Conclude current market shares (Click to select)do not differdiffer from those of 1990.

Answer 1

a)  Each expected value is ≥ 5

b) H0: Current market Shares do not differ from those of 1990   

H1: Current market Shares do differ from those of 1990

From the given data

	Observed		Expected
	Freq (Oi)	Probability	Freq. (Ei)	(Oi-Ei)^2 /Ei
GM	363	0.33	330	3.3000
Japanese	226	0.32	320	27.6125
Ford	272	0.23	230	7.6696
chrysler	100	0.08	80	5.0000
Other	39	0.04	40	0.0250
Total:	1000	1.00	1000	43.6071

Num Categories: 5
Degrees of freedom: 4

Test Statistic, Chi-square: 43.6071
Critical Chi-square: 9.48772
P-Value: 0.0000

Here Chi-square value > Chi-square critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that Current market Shares do differ from those of 1990