Question

Toyota Camry, Honda Accord and Ford F-150 are the top 3 best-selling passenger cars in the U.S for the last 5 years. Data for 2017 is shown in the table below. Your interest is to determine whether the shares in the passenger car market have changed in 2018. Use an alpha of 0.01 on your test.

2017 Market Share Observed in 2018

Toyota Camry 0.40 70

Honda Accord 0.20 70

Ford F-150 0.40 60

total 100% 200

4.A) What is the expected value for each category?

4.B) What is the value of the test statistic you calculated for this problem?

4.C) What is the value of degrees of freedom?

4.D) What is the critical value for the given alpha?

4.E) What is your decision after performing the test? (Accept or Reject)

4.F) What is your conclusion after performing the test? Be specific and relate to the problem.

Answer #1

Applying chi square goodness of fit test:

relative | observed | Expected | residual | Chi square | |

category | frequency |
O_{i} |
E_{i}=total*p |
R^{2}_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

Toyota Camry | 0.400 | 70 | 80.00 | -1.12 | 1.250 |

Honda Accord | 0.200 | 70 | 40.00 | 4.74 | 22.500 |

Ford F | 0.400 | 60 | 80.00 | -2.24 | 5.000 |

total | 1.000 | 200 | 200 | 28.750 |

A) expected value for each category is given in expected column

B) value of the test statistic =28.750

C)

degree of freedom =categories-1= | 2 |

D)

for 0.01 level and 2 degree of freedom :critical value = | 9.210 |

E)

reject Ho as test statistic is higher than critical value

F)we have sufficient evidence to conclude that the shares in the passenger car market have changed in 2018

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