question archive 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 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)
Subject:ManagementPrice:2.87 Bought7
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 25%, 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 number of vehicles sold.
| 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 .05 level of significance
The p-value is
What is your conclusion?
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 | .25 | ||
| Ford Focus | .21 | ||
| Hyundai Elantra | .19 | ||
| Honda Civic | .18 | ||
| Toyota Corolla | .17 |
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Answer:
H0: The market shares for the five automobiles in Chicago are .25, .21, .19, .18, .17
Ha: The market shares for the five automobiles in Chicago differ from the above shares
|
Hypothesized |
Observed |
Expected |
Chi Square |
|
|
Compact Car |
Market Share |
Frequency |
Frequency |
(fi – ei)2 / ei |
|
Chevy Cruze |
.25 |
108 |
96 |
1.50 |
|
Ford Focus |
.21 |
92 |
84 |
0.76 |
|
Hyundai Elantra |
.19 |
64 |
76 |
1.89 |
|
Honda Civic |
.18 |
84 |
72 |
2.00 |
|
Toyota Corolla |
.17 |
52 |
68 |
3.76 |
=9.92 Degrees of Freedom = k – 1 = 5 – 1
Using the table with df = 4,
= 9.92 shows the p–value is between .05 and .025.
Using Excel, the p–value corresponding to = 9.92 is
p–value < .05, reject . Conclude that the markets shares for the five compact cars
in Chicago differ from the market shares reported by Motor Trend.
|
Hypothesized |
Sample |
||
|
Compact Car |
Market Share |
Market Share |
Difference |
|
Chevy Cruze |
.24 |
108/400 = .27 |
.03 |
|
Ford Focus |
.21 |
92/400 = .23 |
.02 |
|
Hyundai Elantra |
.19 |
64/400 = .16 |
–.03 |
|
Honda Civic |
.18 |
84/400 = .21 |
.03 |
|
Toyota Corolla |
.17 |
52/400 = .13 |
–.04 |
Chevy Cruze (.03) Honda Civic (.03) and Ford Focus (.02) show higher market shares in
Chicago. Toyota Corolla (–.04) and Hyundai (–.03) show lower market shares in Chicago
