Case Study Help (statistics) PLEASE HELP

The Voyage of the St. Andrew
Throughout the picturesque valleys of mid-eighteenth-century Germany echoed the song of the Neuländer (newlander). Their song enticed journeymen who struggled to feed their families with the dream and promise of colonial America. Traveling throughout the German countryside, the typical Neuländer sought to sign up several families from a village for immigration to a particular colony. By registering a group of neighbors, rather than isolated families, the agent increased
the likelihood that his signees would not stray to the equally enticing
proposals of a competitor. Additionally, by signing large groups, the Neuländer fattened his purse, to the tune of one to two florins a head.
Generally, the Germans who chose to undertake the hardship of a trans-
Atlantic voyage were poor, yet the cost of such a voyage was high. Records from a 1753 voyage indicate that the cost of an adult fare (one freight) from Rotterdam to Boston was 7.5 pistole. Children between the ages of 4 and 13 were assessed at half the adult rate (one-half freight). Children under 4 were not charged.To get a sense of the expense involved, it has been estimated that the adult fare, 7.5 pistoles, is equivalent to approximately $2000! For a large family, the cost could easily be well beyond their means. Even though many immigrants did not have the necessary funds to purchase passage, they were
determined to make the crossing. Years of indentured servitude for themselves and other family members were often the currency of last resort.
As a historian studying the influence of these German immigrants on colonial America, Hans Langenscheidt is interested in describing various demographic characteristics of these people. Unfortunately, accurate records are rare. In his research, he has discovered a partially reconstructed 1752 passenger list for a ship, the St. Andrew. 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. Unfortunately, some of the data are missing
for some of the families. Langenscheidt believes that the demographic parameters of this passenger list are likely to be similar to those of the other numerous voyages taken from Germany to America during the mid-eighteenth century. Assuming that he is correct, he believes that it is appropriate to create a discrete probability distribution for a number of demographic variables for this population of German immigrants. His distributions are presented next.

Number of
Families per Parish ------------------------ Probability
2-------------------------------------------- 0.176
3-------------------------------------------- 0.000
4-------------------------------------------- 0.059
5-------------------------------------------- 0.000
6-------------------------------------------- 0.059

Number of Freights ------------------------- Probability
1.0----------------------------------------- 0.075
1.5----------------------------------------- 0.025
2.0 ---------------------------------------- 0.425
2.5 ---------------------------------------- 0.150
3.0 ---------------------------------------- 0.125
3.5 ---------------------------------------- 0.100
4.0 ---------------------------------------- 0.050
5.0 ---------------------------------------- 0.025
6.0 ---------------------------------------- 0.025

Number in Family--------------------------- Probability
1 ---------------------------------------- 0.322
2 ---------------------------------------- 0.186
3 ---------------------------------------- 0.136
4 ---------------------------------------- 0.102
5 ---------------------------------------- .051
6 ---------------------------------------- 0.136
7 ---------------------------------------- 0.034
8 ---------------------------------------- 0.017
9 ---------------------------------------- 0.016

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?