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 (Motor Trend, November 2, 2011). Base on total sales, the market shares among for these five compact cars were Chevy Cruze 24%, Ford Focus 21% , Hyundai Elantra 20% , Honda Civic 18% , and Toyota Corolla 17% . A sample of  compact car sales in Chicago showed the following number of vehicles sold.

Excel File: data12-27.xlsx

Chevy Cruze	108
Ford Focus	92
Hyundai Elantra	64
Honda Civic	84
Toyota Corolla	52

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

The P value is - _____(between .025 and .05, between .01 and .025)

What is your conclusion?

(Conclude that the markets shares for the five compact cars in Chicago differ from the market shares reported by Motor Trend or Conclude that the markets shares for the five compact cars in Chicago same from the market shares reported by Motor Trend.)

Item 2

What market share differences, if any, exist in Chicago? Round your answers to two decimal places. Enter negative values as negative numbers.

Compact Car	Hypothesized Market Share	Sample Market Share	Difference
Chevy Cruze	.24
Ford Focus	.21
Hyundai Elantra	.20
Honda Civic	.18
Toyota Corolla	.17

Answer 1

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency  
total frequency=   400

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
Chevy Cruze	108	0.240	96.00			1.500
Ford Focus	92	0.210	84.00			0.762
Hyundai Elantra	64	0.200	80.00			3.200
Honda Civic	84	0.180	72.00			2.000
Toyota Corolla	52	0.170	68.00			3.765

chi square test statistic,X² = Σ(O-E)²/E =   11.227              
                  
Degree of freedom=k-1=   5   -   1   =   4
                  
P value =   between .01 and .025

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

b)

category		Hypothesized Market Share		sample market share	difference
Chevy Cruze		0.24		0.27	-0.03
Ford Focus		0.21		0.23	-0.02
Hyundai Elantra		0.20		0.16	0.04
Honda Civic		0.18		0.21	-0.03
Toyota Corolla		0.17		0.13	0.04