Question

Statistics Problem:

You have been asked to engage in one final project for the political organization for which you have been working. This time you wish to study the nature of the relationship between the ages of the donors to the campaign and the amount of money they plan to donate or have donated. Data is collected from a random sample of supporters of the candidate. This data is shown on the next page. Various questions need to be answered about the results you generate. These questions follow the presentation of the data. You should answer the questions posed in the narrative that should accompany your results.

Data:

                        Age of Supporter                              Donation

                                    22                                            $   75

                                    38                                               135

                                    50                                               100

                                    46                                                 50

                                    60                                               200

                                    28                                                   0

                                    25                                                 10

                                    69                                                 35

                                    75                                                 75

                                    28                                               100

                                    55                                               250

                                    37                                               100

                                    36                                               100

                                    43                                               125

                                    35                                                   0

                                    19                                                   0

                                    48                                                 50

                                    70                                                 25

                                    31                                               115

                                    30                                               105

Part 2 Questions:

h)        Find the sample standard error of the estimate for the above data. Explain its meaning relative to the problem.

i)          Find the sample coefficient of correlation for the above data. Explain its meaning relative to the problem.

j)          Perform a complete residual analysis of this data in order to ascertain whether the conditions that need to be met to use the regression procedure you are using is appropriate for this problem. Be sure to address all issues relating to a residual analysis. Include a Durbin-Watson analysis at the 5% level of significance.

k)         At the 5% level of significance, is there evidence of a significant linear relationship between the age of the supporters and the amount of money donated? Be sure that you explain in some manner the criterion or criteria you have used to arrive at your conclusion.

l)          Find a 95% confidence interval for the slope of the population regression line. Provide an explanation of the meaning of this interval. Show how this interval can be used in order to answer the question posed (at the 5% level of significance) in the previous part of the problem.

m)       Find a 95% confidence interval for the mean donation for supporters of the candidate who are 30 years of age. Provide an explanation of the meaning of this interval.

n)        Suppose a 95% confidence interval for the mean donation for supporters of the candidate who is 50 years of age is desired. Find this interval, explain its meaning, and compare its width to that of the interval computed in the previous part of the problem. Give a reason for any difference in the width between this interval and the one in the previous part of the problem.

o)        Find a 95% prediction interval for the donation of an individual supporter of the candidate who is 30 years of age. Explain its meaning relative to the problem. Compare the width of this interval to that of the interval calculated in part m) of the problem. Give a reason for any difference in the width of this interval and the one you found in part m) earlier.

Answer 1