Question

Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus.† The 2017 market shares are: Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models making up the remaining 23%. Suppose a sample of 400 compact car sales in a certain large city showed the following number of vehicles sold.

Honda Civic	97
Toyota Corolla	71
Nissan Sentra	53
Hyundai Elantra	45
Chevrolet Cruze	43
Ford Focus	24
Others	67

Use a goodness of fit test to determine if the sample data indicate that the market shares for compact cars in the city are different than the market shares suggested by nationwide 2017 sales. Use a 0.05 level of significance.

State the null and alternative hypothesis.

H₀: The market shares for the compact cars in the city do not differ from market shares nationwide.
H_a: The market shares for the compact cars in the city differ from market shares nationwide.

H₀: The market shares for the compact cars in the city are not different from any of the nationwide market shares listed.
H_a: The market shares for the compact cars in the city are different for at least one of the nationwide market shares listed.   

H₀: The market shares for the compact cars in the city are different from at least one of the nationwide market shares listed.
H_a: The market shares for the compact cars in the city are not different from any of the nationwide market shares listed.

H₀: The market shares for the compact cars in the city differ from market shares nationwide.
H_a: The market shares for the compact cars in the city do not differ from market shares nationwide.

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

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

p-value =

State your conclusion.

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

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

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

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

Answer 1

H₀: The market shares for the compact cars in the city do not differ from market shares nationwide.
H_a: The market shares for the compact cars in the city differ from market shares nationwide.

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	0.200	97	80.00	1.90	3.613
2	0.170	71	68.00	0.36	0.132
3	0.120	53	48.00	0.72	0.521
4	0.100	45	40.00	0.79	0.625
5	0.100	43	40.00	0.47	0.225
5	0.080	24	32.00	-1.41	2.000
7	0.230	67	92.00	-2.61	6.793
total	1.000	400	400		13.9092
test statistic X2 =		13.91
p value =		0.0307

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