Dante Development Corporation is considering bidding on a contract for a new office building complex. Figure 4.17 shows the decision tree prepared by one of Dante’s analysts. At node 1,….

## Estimate the proportion of bags that fail to arrive at the proper destination using a technique for which 95% confidence applies.

For this exercise, submit only one Microsoft Word document with all appropriate output results and graphs from Minitab and Excel into the single Word document.

__Question 1__

Suppose a survey of individuals between the ages of 24 and 74 indicated that 66% of Baby Boomers, 61% of Generation X, and 58% of Millennials expect IRAs to be their primary source of income in retirement. The margin of error was given as ± 5 percentage points.

- Calculate 95% confidence interval for the proportion of Baby Boomers who expect IRAs to be their primary source of income in retirement.
- The sample size for each of the three generations was not given. Assuming the confidence level was 95%, determine the sample size for each of the three generations.

__Question 2__

A local West Lafayette commercial bank issues Mastercard credit cards. As a part of its annual review of the profitability of each type of credit card, the bank randomly samples 36 customers to measure the average annual charges per card. A random sample of 36 Mastercard accounts shows the following annual spending per account (in USD):

2869 | 3770 | 2854 | 2750 | 2574 | 2972 |

2549 | 3267 | 3013 | 2707 | 2794 | 1189 |

2230 | 2178 | 3032 | 3485 | 2679 | 2010 |

1994 | 2768 | 3853 | 2064 | 3244 | 2738 |

2807 | 2395 | 3405 | 3006 | 3368 | 2691 |

1996 | 3008 | 2518 | 2674 | 2730 | 3719 |

- Based on these randomly sampled accounts, what is the best point estimate of the true mean annual spending for Mastercard account holders?
- Develop a 95% confidence interval estimate of the mean annual spending. Interpret this range.
- To encourage more use of the card, the company offers a promotion that costs the bank $5 for each card that carries a balance of $3,000 or more. If the bank has 50,000 total customers, what can be stated about the cost of this program to the bank?

__Question 3__

Big Hitter is a manufacturer of golf products in the United States and Canada. One of the golf accessories it produces at its plant in Winnipeg, Manitoba, Canada, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the file labeled *THeight*.

- Determine if the process is not producing the tees to specification. Use a significance level of 0.01.
- If the hypothesis test determines the specification is not being met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this be?

__Question 4__

Many complaints have been received in the past six months regarding airlines losing fliers’ baggage. The airlines claim that problem is nowhere near as great as the newspaper articles have indicated. In fact, one airline spokesman claimed that less than 1% of all bags fail to arrive at the destination with the passenger. To test this claim, 800 bags were randomly selected at various airports in the United States when they were checked with this airline. Of these, 6 failed to reach the destination when the passenger (owner) arrived.

- Is this sufficient evidence to support the airline spokesman’s claim? Test using a significance level of 0.05. Discuss.
- Estimate the proportion of bags that fail to arrive at the proper destination using a technique for which 95% confidence applies.