Problem 39E

Largest private companies. IPOs—initial public offerings of stock—create billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 212 Largest Private Companies list is given in the table below.

Company |
Revenue (in billions) |

Enterprise Rent-A-Car |
$14.10 |

Pilot Flying J |
17.77 |

Tenaska Energy |
9.95 |

Wawa |
6.99 |

Gulf States Toyota |
5.1 |

Brookshire Grocery |
2.30 |

BrightStar |
4.61 |

Bose |
2.28 |

Mary Kay |
2.5 |

Drummoend |
3.03 |

Petco |
2.8 |

SAS |
2.43 |

Forever 21 |
2.6 |

Burger King |
2.33 |

Conair |
2.01 |

Source: Data from “America’s Largest Private Companies,” Forbes, Nov. 16, 2011.

a. Describe the population from which the random sample was drawn.

b. Use a 98% confidence interval to estimate the mean revenue of the population of companies in question.

c. Interpret your confidence interval in the context of the problem.

d. What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b?

e. Suppose Forbes reports that the true mean revenue of the 212 companies on the list is $5.0 billion. Is the claim believable?

Solution:

Step 1 of 6:

The data regarding the revenues of a random sample of 15 firms is given.

Company |
Revenue( in billions) |

Enterprise Rent A-Car |
$14.10 |

Pilot Flying J |
17.77 |

Tenaska Energy |
9.95 |

Wawa |
6.99 |

Gulf States Toyota |
5.1 |

Brookshire Grocery |
2.30 |

BrightStar |
4.61 |

Bose |
2.28 |

Mary Kay |
2.5 |

Drummoend |
3.03 |

Petco |
2.8 |

SAS |
2.43 |

Forever 21 |
2.6 |

Burger King |
2.33 |

Conair |
2.01 |

Using this data we need to find the required values.