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). A sample of compact car sales in Chicago showed the following number of vehicles sold:

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

a. State your null and alternative hypotheses. 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. Show all the steps in your calculations of this test, including the degrees of freedom. Using a 5% level of significance, what is the p‐value for this test? What is your conclusion?

b. What market share differences from others, if any, exist in Chicago?

Answer 1

(a) The hypothesis being tested is:

H0: The market shares for the five compact cars in Chicago are not different than the market shares reported by Motor Trend

Ha: The market shares for the five compact cars in Chicago are different than the market shares reported by Motor Trend

observed	expected	O - E	(O - E)² / E
108	80.000	28.000	9.800
92	80.000	12.000	1.800
64	80.000	-16.000	3.200
84	80.000	4.000	0.200
52	80.000	-28.000	9.800
400	400.000	0.000	24.800
24.80	chi-square
4	df
.0001	p-value

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the market shares for the five compact cars in Chicago are different than the market shares reported by Motor Trend.

(b) All the market share differences from each other.

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