Question

In: Statistics and Probability

Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford...

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). Based on total, the market shares for these five compact cars were Chevy Cruze 24%, Ford Focus 21%, Hyundai Elantra 19%, Honda Civic 18%, and Toyota Corolla 17%. A sample of 400 compact car sales in Chicago showed the following of vehicles sold:

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

NOTE: Be sure to show X^2 and Xcrit^2, if not the p-value for test.

Use a goodness of fit test to determine if the sample data indicate that the market shares dor the five compact cars in Chicago are different that the market shares reported by Motor Trend. Using a .05 level significance. What is the p-value and what is your conclusion? What market shares differences, if any, exist in Chicago? please show the sample market share numbers with the difference

Solutions

Expert Solution

(a)

Calculation of observed value:

Name Observed(O) Expected (E) (O - E)2/E
Chevy Cruze 108 400X24/100=96 1.5
Ford Focus 92 400X21/100=84 0.7619
Hyndai Elantra 64 400X19/100=76 1.8947
Honda Civic 84 400X18/100=72 2
Toyota Corolla 52 400X17/100=68 3.7647
Total = = 9.9213

So,

Observed = 9.9213

(b)

ndf = 5 - 1 = 4

= 0.05

From Table, critical value of = 9.4877

Since the observed value of =9.9213 is greater than critical value of = 9.4877, the difference is significant. Reject Null Hypothesis.

Conclusion:

The data support the claim that the market shares for the five compact cars at Chicago are different than the market shares reported by Motor Trend.

(c)

Test statistic is:

= 9.9213

ndf = 4

By Technology, p-value = 0.0418

Since p-value = 0.0418 is less than = 0.05, the difference is significant as already concluded.

(d) Market share difference for each car is given below:

Name Observed(O) Expected (E) Market Share Difference d = O - E
Chevy Cruze 108 400X24/100=96 12
Ford Focus 92 400X21/100=84 8
Hyndai Elantra 64 400X19/100=76 - 12
Honda Civic 84 400X18/100=72 12
Toyota Corolla 52 400X17/100=68 - 16

orchestra answered 2 years ago
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