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	107
Ford Focus	92
Hyundai Elantra	65
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 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 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 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 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.

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.

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 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 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

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

Given that ,

Null Hypothesis -

Altrnative Hypothesis -

The total sample size = 107+92+65+85+51 = 400

The expexted frequency for chevy cruze is,

similarly ,

The expexted frequency for Ford Focus is

  

The expexted frequency for Hyundai Elantra is

The expexted frequency for Honda Civic is

The expexted frequency for Toyota Corolla is

The formula for chi - square test sattistic is given as .

	Hypothesized	Observed	Expected	Chi Square
Compact Car	Market Share	Frequency	Frequency	(fi – ei)2 / ei
Chevy Cruze	0.24	107	96	1.26
Ford Focus	0.21	92	84	0.76
Hyundai Elantra	0.20	65	80	2.81
Honda Civic	0.18	85	72	2.34
Toyota Corolla	0.17	51	68	4.25
Total	1	400	400	11.42

=11.42

Degrees of Freedom = k – 1 = 5 – 1

Using the table with df = 4, = 11.42 shows the p–value is between 0.01 and .0.25

Using Excel, the p–value corresponding to = 11.42 is

p–value < .05, reject .

Conclude that the markets shares for the five compact cars in City are differ  from the market shares reported by Motor Trend.

Market share difference for each car is given below :

	Hypothesized	Sample
Compact Car	Market Share	Market Share	Difference
Chevy Cruze	0.24	107/400 = 0.27	0.03
Ford Focus	0.21	92/400 =0.23	0,02
Hyundai Elantra	0.20	65/400 =0.16	–0.04
Honda Civic	0.18	85/400 = 0.21	0.3
Toyota Corolla	0.17	51/400 = 0.13	–0.04

Chevy Cruze (.03) Honda Civic (.03) and Ford Focus (.02) show higher market shares in  City.

Toyota Corolla (–.04) and Hyundai Elantra(–.04) show lower market shares in City.