**Sample problem section** from a previous final exam

**1. Duke is in charge of filling milk bottles at the local dairy. His boss Amy wants to assess the consistency of fill in the bottles by drawing a sample of the bottles. She wants to be 90% confident that her sample is representative. She will allow error of .12 ounces, and from past tests she expects standard deviation of about .03 ounces. How many bottles should Duke draw for Amy's test? Show all work for credit. **

**2. Slushee Company is trying to find out what percent of its customers like the strawberry-kiwi flavor of its patented frozen treat. A similar study last year found that about 65% did. Alan Slushee, the company CEO, want to be 99% sure of his result, and is willing to live with 5% error. How many customers should he survey? **

3**. Coca-Cola is developing a new fruit-flavored soft drink, and is testing various sweetness levels for the new product. A market test of four sweetness levels resulted in the following data:
**

Sweetness Level | Subjects Preferring |

Low | 11 |

Moderately low | 21 |

Moderately high | 37 |

High | 31 |

Frequency of Visits | Male | Female | Totals |

1-5 | 14 | 26 | 40 |

6-14 | 16 | 34 | 50 |

15 and above | 15 | 11 | 26 |

totals | 45 | 71 | 116 |

qtr | ad | sale | ad^{2} |
sales^{2} |
ad X sales |

1 | 400 | 3,200 | 160,000 | 10,240,000 | 1,280,000 |

2 | 510 | 6,700 | 260,100 | 448,900,000 | 3,417,000 |

3 | 320 | 3,020 | 102,400 | 9,120,400 | 966,400 |

4 | 280 | 2,890 | 78,400 | 8,352,100 | 809,200 |

sum | 1,510 | 15,810 | 600,900 | 72,602,500 | 6,472,600 |

avg | 377.5 | 3,952.5 | 150,225 | 18,150,625 | 1,618,150 |

- Compute and interpret the correlation between advertising and sales. (20 points)
- Estimate the regression function, and explain the meaning of the function. (20 points)

**5. Ajax wants to know if there is a statistical difference in effectiveness between three advertising campaigns. Perception scores for the three ad campaigns A, B, and C (scored on a 0-200 scale, 200 points being highest level of perception) were collected and processed. Sam in the research department has plugged the numbers into a statistics package, but the computer shut down before giving the final answer. Take what's left below and answer the question for Ajax, TESTING FOR SIGNIFICANCE AT THE 0.05 LEVEL. (20 points)
**

**Campaign B: **25 subjects rating

**Campaign C: **25 subjects rating

**SSA = 10 SSE = 63.6**