Statistics - Descriptive Statistics Projects

Germans who undertook the hardship of a trans-Atlantic voyage to the New World in the mid-18th-century

Germans who undertook the hardship of a trans-Atlantic voyage to the New World in the mid-18th-century were poor, yet the cost of such a voyage was high. Records from a 1753 voyage indicate that the cost of each adult fare was 7.5 pistole. (the equivalent of $2000 today) Children between the ages of 4 and 13 were charged half the adult fare, and children under the age of 4 were not charged. A partially reconstructed passenger list for a ship, the St. Andrew, was discovered. This list contains the names of the head of families, a list of family members traveling with them, their parish of origin, and the number of freights each family purchased. Researchers believe that the demographic parameters of this passenger list are likely to be similar to those of the other voyages taken from Germany to America during that period. Probability distributions constructed from the passenger list are shown below.
1. Using the information provided, describe, through histograms and numerical summaries such as the mean and standard deviation, each probability distribution.
2. Does it appear that, on average, the Neuländers were successful in signing more than one family from a parish? Does it seem likely that most of the families knew one another prior to undertaking the voyage? Explain your answers for both questions.
3. Using the mean number of freights purchased per family, estimate the average cost of the crossing for a family in pistoles and in U.S. dollars.
4. Is it appropriate to estimate the average cost of the voyage from the mean family size? Why or why not?
5. Langenscheidt came across a fragment of another ship’s passenger list. This fragment listed information for six families. Of these six, five families purchased more than four freights. Using the information contained in the appropriate probability distribution for the St. Andrew, calculate the probability that at least five of six German immigrant families purchased more than four freights. Does it seem likely that these families came from a population similar to that of the Germans on board the St. Andrew? Explain.
6. Summarize your findings in a report. Discuss any assumptions made throughout this analysis. What are the consequences to your calculations and conclusions if your assumptions are subsequently determined to be invalid?