The first question is based off of a study of how spores dispersed from fungi Sordaria fimicola (data from Ingold and Hadland 1959). This fungus grows spores in attached strings, each 8 spores long, in structures called asci. When the spores are mature, they are expelled out from the ascus. Sometimes spores stay stuck together in groups of 8, but they can also break apart into shorter strings; the shorter ones are able to fly longer distances.
Ingold and Hadland (1959) developed a model to predict the probability of the strings breaking into strands with different numbers of spores in them (i.e. 1,2, … 8 spores per strand) in flight. They then collected a large number of strands in an experiment and for each strand counted the number of spores in it. The data set below includes a sample of data from their experiment.
Download the fungus spore data with this link
The data consists of three columns:
nspores: the number of spores in a given string.
nstrings_obs: the number of strings they counted that had nspores in it.
nstrings_prob: the predicted probability of finding a string with nspores spores in it, based on their model.
The scientific question is: “is the observed number of strings with each number of spores in it consistent with the proposed scientific model?”. For this question, you can assume that the authors did not have to estimate any parameters from the data to create the model.
This question is based on a study of the diversity of electric fish in the Amazon River by Fernandes, Podos, and Lundberg (2004), and from assignment question 19 from chapter 12 in your textbook. The researchers were studying how tributaries (small waterways) flowing into the Amazon affected the species richness (i.e. total number of species) of electric fish in the Amazon River. They hypothesized that species richness should be higher downstream of a tributary compared to upstream, as some fish species may not be able to swim upstream. They counted the number of electric fish species present upstream and downstream of 13 different Amazonian tributaries. The data set is given below:
Download the Amazon fish richness data with this link
This data set consists of two columns:
tributary: This is the name of the tributary.
richness_difference: This is the difference in richness between the downstream sampling location and the upstream sampling location. Positive values correspond to sites where species richness is higher downstream of the tributary than upstream.
The scientific questions here are: “Is average species richness higher downstream of tributaries compared to upstream? If so, how large is the change in average species richness?”
This data is from a made-up study, looking at the fraction of people who are pre-diabetic in a Canadian city of 100,000 people. The researchers wanted to know if the rate of pre-diabetes differed from the mean proportion in the Canadian population of 12.4% (based on data from Hosseini, Whiting, and Vatanparast (2019)). They also wanted to estimate possible future medical costs from pre-diabetic treatments, and calculated the cost would be $500 per pre-diabetic resident in the city.
They tested the health status of 300 people, chosen at random based on census information. Of the 300 people, they found 57 of them were classified as pre-diabetic.
There are two scientific questions here: 1. Does the average fraction of pre-diabetic people in the city differ from the Canadian average. 2. What is a plausible range of future healthcare costs due to treating pre-diabetic patients, based on this sample?