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.t 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 93 Hyundai Elantra 64 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. O Ho: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend. H: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend. O Ho: The market shares for the five automobiles in this city are 0.24, 0.21, 0.20, 0.18, 0.17. H: The market shares for the five automobiles in this city differ from the above shares. O Ho: The market shares for the five automobiles in this city differ from 0.24, 0.21, 0.20, 0.18, 0.17. H: The market shares for the five automobiles in this city are the same as the above shares. O Ho: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend. H: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend.

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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.t 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
93
Hyundai Elantra
64
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.
Ho: The majority of the market shares for the five automobiles in this city are the same as the ones reported by Motor Trend.
H: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend.
Ho: The market shares for the five automobiles in this city are 0.24, 0.21, 0.20, 0.18, 0.17.
H: The market shares for the five automobiles in this city differ from the above shares.
Ho: The market shares for the five automobiles in this city differ from 0.24, 0.21, 0.20, 0.18, 0.17.
H: The market shares for the five automobiles in this city are the same as the above shares.
Ho: The majority of the market shares for the five automobiles in this city differ from the ones reported by Motor Trend.
: 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 Ho. We cannot conclude that the market shares for the five compact cars in this city differ from the market shares reported.
Do not reject Ho. We conclude that the market shares for the five compact cars in this city differ from the market shares reported.
Reject Ho. We conclude that the market shares for the five compact cars in this city differ from the market shares reported.
Do not reject Ho. We cannot 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---
O market share in this city. Ford Focus shows
---Select---
O market share in this city. Hyundai Elantra shows
---Select---
O market share in this city. Honda Civic
shows
---Select---
market share in this city. Toyota Corolla shows
---Select---
O market share in this city.

Expert Solution

Step 1

The given data show that the market share and the number of vehicles sold for a sample of 400 compact cars of five companies in City C.

State the test hypotheses.

Null hypothesis:

H0:pC=0.24,pF=0.21, pH=0.20,pHC=0.18 and pT=0.17.

Alternative hypothesis:

Ha: pC≠0.24,pF≠0.21, pH≠0.20,pHC≠0.18 and pT≠0.17.

Therefore, the correct answer is, “H0: The market shares for the five automobiles in this city are 0.24,0.21, 0.20, 0.18, 0.17 and Ha: The market shares for the five automobiles in this city differ from the above shares.”

The test statistic is calculated by the formula,

$χ^{2} = \sum \frac{{(O - E)}^{2}}{E}$

Where, O represents the observed frequency and E represents the expected frequency.

Methods for finding the expected frequency:

Method 1: If the all the expected frequencies are equal, then E=nk

Method 2: If the expected frequencies are not equal, then E=np for each category.

Where, n is the total number of frequencies, k is the categories and p is the probability of occurrence.

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