Question

Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford Focus, Hyundai Elantra, Honda Civic, and Toyota Corolla.† Based on total sales, the market shares for these five compact cars were Chevy Cruze 24%, Ford Focus 21%, Hyundai Elantra 20%, Honda Civic 18%, and Toyota Corolla 17%. Suppose a sample of 400 compact car sales in one city showed the following number of vehicles sold.

Chevy Cruze	109
Ford Focus	92
Hyundai Elantra	63
Honda Civic	85
Toyota Corolla	51

Use a goodness of fit test to determine if the sample data indicate that the market shares for the five compact cars in this city are different than the market shares reported by Motor Trend. Use a 0.05 level of significance.

State the null and alternative hypotheses.

H₀: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend.
H_a: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend

.H₀: The market shares for the five automobiles in this city are 0.24, 0.21, 0.20, 0.18, 0.17.
H_a: The market shares for the five automobiles in this city differ from the above shares.     

H₀: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend.
H_a: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend.

H₀: The market shares for the five automobiles in this city differ from 0.24, 0.21, 0.20, 0.18, 0.17.
H_a: The market shares for the five automobiles in this city are the same as the above shares.

Find the value of the test statistic. (Round your answer to three decimal places.)____

Find the critical value for the test. (Round your answer to three decimal places.)

critical value = _____

State your conclusion.

Do not reject H₀. We cannot conclude that the market shares for the five compact cars in this city differ from the market shares reported.

Reject H₀. We conclude that the market shares for the five compact cars in this city differ from the market shares reported.     

Do not reject H₀. We conclude that the market shares for the five compact cars in this city differ from the market shares reported.

Reject H₀. We cannot conclude that the market shares for the five compact cars in this city differ from the market shares reported.

What market share differences, if any, exist in this city?

Chevy Cruze shows   (a higher a lower or the same) market share in this city. Ford Focus shows ( a higher a lower or the same) market share in this city. Hyundai Elantra shows  (a higher a lower or the same) market share in this city. Honda Civic shows (a higher a lower or the same) market share in this city. Toyota Corolla shows (a higher a lower or the same) market share in this city.

Answer 1

.H₀: The market shares for the five automobiles in this city are 0.24, 0.21, 0.20, 0.18, 0.17.
H_a: The market shares for the five automobiles in this city differ from the above shares.

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.240	109	96.000	1.33	1.760
2	0.210	92	84.000	0.87	0.762
3	0.200	63	80.000	-1.90	3.613
4	0.180	85	72.000	1.53	2.347
5	0.170	51	68.000	-2.06	4.250
total	1.000	400	400		12.7320
test statistic X2 =		12.732

for 0.05 level and 4 df :crtiical value X2 =

9.488

Reject H₀. We conclude that the market shares for the five compact cars in this city differ from the market shares reported.     

Chevy Cruze shows   Higher market share in this city. Ford Focus shows higher market share in this city. Hyundai Elantra shows   lower market share in this city. Honda Civic shows higher market share in this city. Toyota Corolla shows lower market share in this city.