Obesity is a complex disease caused by the interaction of a myriad of genetic, dietary, lifestyle, and environmental factors, which favors a chronic positive energy balance, and leads to increased body fat mass. Recent researches demonstrated the potential of natural products to counteract obesity. Psychological as well as physical effects often contribute to how well a person responds to the recommended therapy.

In this project, you are given the data set for weight losses (in lbs) of a random sample of 50 males who were randomly divided in to 5 equal groups in an experiment to compare the effectiveness of four new weight-reducing agents to that of an existing agent. Preparation A1 is assigned to group 1, preparation A2 to group 2 and so on. Last group is assigned to the standard (S) agent. The researchers then gave a prestudy physical to each man in the experiment and told him how many pounds overweight he was. A comparison of the mean numbers of pounds overweight for the groups showed no significant differences. Then the researchers gave the assigned agents to each group for a fixed period of time and at the end of that time, they recorded their weight loss in pounds. This is given in the Agents Data file:

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- Use the data provided, study and answer the questions.

A1 | A2 | A3 | A4 | S |

12.4 | 9.1 | 8.5 | 12.7 | 8.7 |

10.7 | 11.5 | 11.6 | 13.2 | 9.3 |

11.9 | 11.3 | 10.2 | 11.8 | 8.2 |

11.0 | 9.7 | 10.9 | 11.9 | 8.3 |

12.4 | 13.2 | 9.0 | 12.2 | 9.0 |

12.3 | 10.7 | 9.6 | 11.2 | 9.4 |

13.0 | 10.6 | 9.9 | 13.7 | 9.2 |

12.5 | 11.3 | 11.3 | 11.8 | 12.2 |

11.2 | 11.1 | 10.5 | 12.2 | 8.5 |

13.1 | 11.7 | 11.2 | 11.7 | 9.9 |

**Required Action**: Based on the data set provided, respond to the following:- Using SPSS, run an ANOVA test to determine whether there are any significant variances among the five weight-reducing agents.
- Do any of the ANOVA assumptions appear to be violated? Explain.
- What conclusions do you reach concerning the mean weight loss achieved using the five different agents?
- Determine the significantly different pairs of means using the Tukey’s W.
- Use a Bonferroni t-test to determine which pairs of means are significantly different.
- Use Scheffe’s S procedure to determine which pairs of means are significantly different.
- Suppose the new weight-loss agents were of the following form:
- A
_{1}: Drug therapy with exercise and counseling. - A
_{2}: Drug therapy with exercise but no counseling. - A
_{3}: Drug therapy with counseling but no exercise. - A
_{4}: Drug therapy with no exercise or no counseling. - Compare the mean for the standard agent to the average of the means for the four new agents.
- Compare the mean for the agents with counseling to those without counseling. (ignore the standard)
- Compare the mean for the agents with exercise to those without exercise. (ignore the standard)
- Compare the mean for the agents with counseling to the standard.
- Use a multiple testing procedure to determine which of the contrasts in question 8. to 12. is significantly different from zero.
- Interpret your findings relative to the researchers’ question about finding the most effective weight loss method
**Create**: Write a statistical report summarizing your findings from above. Be sure to include the summary of your statistical analysis, any charts or graphs in your report. Use the following__outline__as a guide.**Annotate**the output as a report to include any bibliographic citation, any interesting information you found and your interpretation of each summary: