Hypothesis Testing

1.University of Maryland is concerned that out of state students may be receiving lower grades than Maryland students. Two independent random samples have been selected: 175 observations from population 1 (Out of state students) and 187 from population 2 (Maryland students). The sample means obtained are X1(bar)=85 and X2(bar)=86. It is known from previous studies that the population variances are 9.2 and 8.3 respectively. Using a level of significance of .01, is there evidence that the out of state students may be receiving lower grades? Fully explain your answer.

Simple Regression

2. A CEO of a large plastics manufacturing company would like to determine if she should be placing more money allotted in the budget next year for television advertising of a new baby bottle marketed for controlling reflux and reducing gas. She wonders whether there is a strong relationship between the amount of money spent on television advertising for this new baby bottle called Gentle Bottle and the number of orders received. The manufacturing process of this baby bottle is very difficult and requires advanced quality control so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new baby bottle. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.

The use of linear regression is a critical tool for a manager’s decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows:

Month | Advertising Cost | Number of Orders |

1 | $77,430.00 | 5,902,000 |

2 | 62,620 | 3,800,000 |

3 | 69,580 | 3,299,000 |

4 | 50,670 | 2,430,000 |

5 | 69,180 | 3,367,000 |

6 | 73,140 | 5,011,000 |

7 | 83,370 | 6,888,000 |

8 | 78,880 | 4,935,000 |

9 | 64,990 | 5,555,000 |

10 | 77,230 | 4,654,000 |

11 | 61,380 | 5,598,000 |

12 | 62,900 | 2,967,000 |

13 | 63,270 | 2,899,000 |

14 | 89,190 | 4,245,000 |

15 | 60,030 | 4,934,000 |

16 | 79,210 | 3,853,000 |

17 | 65,770 | 5,625,000 |

18 | 84,530 | 6,778,000 |

19 | 79,760 | 5,999,000 |

20 | 82,640 | 7,834,000 |

a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under *Tools > Data Analysis.*The Scatterplot can more easily be generated using the Chart procedure.

NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. It should take about a minute.

b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under *Tools > Data Analysis* to construct this equation.

c. Interpret the meaning of the slope, b_{1}, in the regression equation.

d. Predict the monthly advertising cost when the number of orders is 5,800,000. (Hint: Be very careful with assigning the dependent variable for this problem)

e. Compute the coefficient of determination, r^{2}, and interpret its meaning.

f. Compute the standard error of estimate, and interpret its meaning.

g. Do you think that the company should use these results from the regression to base any corporate decisions on?….explain fully

Hypothesis Testing on Multiple Populations

3.The ABC Tutoring Director wants to use a new tutorial to teach middle school students about basic algebraic techniques. As an experiment she randomly selected 18 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the classroom teachers, WebEx Presentation created by an outside contractor, or a well known tutorial by the EducTrain company. After completing their assigned tutorial, the students are given a basic algebraic methods quiz. At the .01 significance level, can she conclude that there is a difference between how well the different tutorials work for the middle school students?