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	64
Honda Civic	84
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 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 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.    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 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.

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

Find the p-value. (Round your answer to four decimal places.)

p-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.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.Reject H₀. We 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  ---Select--- a higher a lower the same market share in this city. Ford Focus shows  ---Select--- a higher a lower the same market share in this city. Hyundai Elantra shows  ---Select--- a higher a lower the same market share in this city. Honda Civic shows  ---Select--- a higher a lower the same market share in this city. Toyota Corolla shows  ---Select--- a higher a lower 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
Chevy Cruze	0.240	109	96.000	1.33	1.760
Ford Focus	0.210	92	84.000	0.87	0.762
Hyundai Elantra	0.200	64	80.000	-1.79	3.200
Honda Civic	0.180	84	72.000	1.41	2.000
Toyota Corolla	0.170	51	68.000	-2.06	4.250
total	1.000	400	400		11.9723
test statistic X2 =		11.972

p value =

0.0176

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