Reference no: EM13988376

Robert Massey and his family are facing a financial crisis. Robert’s position with a major chemical company has been outsourced to an overseas conglomerate and his wife, Megan, has quit her job because the Masseys are expecting their third child. Their oldest son, Robert Jr., will start college in the fall and the daughter, Megan, is planning a very expensive wedding this summer. The Masseys still owe $225,000 on the mortgage on their five bedroom house and are desperately in need of a new vehicle for Robert, Jr. He wants a Porsche! At 6’3” and 220 pounds, Robert, Jr. has received several offers from universities to attend on a football scholarship. But his high school sweetheart, Suesie, will enroll at State U, and Bobbie, as she calls him, did not receive an offer from there. It appears he may have to take out student loans if he wants to follow Suesie next fall. Robert Sr. consults with several of his former co-workers regarding the amount of student debt their offspring ran up at college. Those families quote the following debt their sons and daughters accumulated (in thousands of dollars) as: 56.3 25.6 65.2 36.8 12.5 54.8 48.3 54.8 82.4 17.5 45.2 26.7 Robert wonders what estimate he can derive from these figures for the debt that his son might incur. He asks his neighbor, Nick, a statistics professor at the local college Bobbie refuses to attend, how he might construct such an estimate and be within $3,000 of the actual debt. Nick says he might want to get a larger sample, but Robert isn’t sure how large that should be. Megan and Suesie peruse Modern Brides magazine and learn that the average wedding based on the last 100 nuptials costs $76,654. The variation, as Modern Brides calls the standard deviation, is $43,895. Megan decides not to worry her husband with this news but would like to estimate Suesie’s wedding bill with a reasonable level of certainty. She too wonders if the sample size is large enough to provide an estimate within $3,000 of the true mean of all weddings. After talking to the mortgage company that holds the balance of their home loan, Robert and Megan learn that 32 out of a sample of 124 loans went into default and the homeowners had to give up their home. They wonder what the probability is that they face a similar fate. Is the sample of 124 loans sufficient to produce an accurate measure of how likely they are to have to move if Robert is unable to find suitable employment with an error not to exceed 5%? The Federal Housing Authority reports that 19.5% of all homes in the nation are in default. They wonder if that figure is more reliable. Does this impact the estimate of the proportion of homes that were lost as opposed to the sample provided by the mortgage company? Finally, in utter frustration, they turn to their good friend Nick to help them resolve some of the statistical issues they face. Prepare a complete report of what information Professor Nick could offer the desperate couple.