STA 240 Take Home Midterm

Due: in class on 23 November.

Assignment:

This midterm contains 3 data sets - Each with a set of questions to address.
I recommend first spending a bit of time understanding the data and making some plots. Then as you begin your analysis, you'll be able to check that your results are sensible.
Feel free to ask me questions via email or in class. I have a running list of questions and answers regarding the midterm here .
Often, there is more than one appropriate way to do the problems. I'm looking to see that your solutions give an appropriate answer, not necessarily the best.
Neatness, style and brevity count here. Don't include every possible test you can think of to answer questions; try to pick a single approach that seems appropriate. If you need to, you can always mention that your results coincide with some other approach in passing, without giving all the details.
For questions 1 and 3, your solution should be organized according to the questions at the end of the problem. Question 2 is less rigid, but keep your writing to a single page; you can attach plots and/or output to the end of this page - and refer to them in your write-up.

1. Bug traps in open water

The data in file bugs.asc show the bug counts recorded from 30 sticky traps placed in the open water zone of a wetland in North Dakota. The traps are floating cylinders that are 25cm tall with a diameter of 6.25cm. The cylinder is coated with a sticky tape that traps any bugs that fly into it. The traps are set and then left for 24 hours. Two counts are recorded for each trap: the number of bugs caught on the lower 12.5cm of the cylinder; and the number of bugs caught on the upper 12.5cm of the cylinder. Hence the data file looks like

count height trap
286   low     1
113   high    1
225   low     2
108   high    2
195   low     3
 :     :      :

which means the count for the lower portion of trap 1 is 286 and the count for the upper portion of trap 1 is 113. Likewise the lower and upper portions of trap 2 have counts 225 and 108 respectively.

In open water, the researchers wish to know whether bugs are more likely to travel near the water surface, or a slight distance away from it.

Give a statistic or plot that gives an idea how many bugs are typically trapped on a given day.
Present a graphical display that sheds light on whether or not there is a difference between the number of bugs caught the high and low trap portions.
Quantify the difference between the counts at the high and low portions. It may be most sensible to report a result that says: there tends to be X times as many bugs in the lower portion of the trap as compared to its upper portion.
Give a plausible range of values for X (ie. a 95% CI).
Comment on the scope of the inference carried out here. No more than 3 sentances please.

2. Ant foraging

The file lfarea.asc holds data on the size for pieces of leaf collected by atta ants upon returning from a foraging expedition. On a number of different nights, between 50 and 200 leaf pieces were collected from ants returning to their colony from a foraging expedition and the area of each piece was measured. This was done on repeated nights for various colonies on two different islands. The data here show the average leaf area over a given night for a given colony. Most colonies have data recorded on a number of different nights. Repeated samples for a given colony were taken at least two weeks apart. Each line of the data file gives:

average size of leaf pieces in square mm;
and colony from which the sample was taken.

Note that colonies have been sampled multiple times. S1-S4 denote colonies from a small island where resources are minimal; M1-M5 denote colonies from a mid-sized island were the resources are less strained.

Researchers have two main questions of interest:

Is there evidence that ant colonies differ from one another in the size of leaf fragemnts they carry when foraging?
Is there any evidence that leaf fragment size differs systematically between colonies from the small island as compared to colonies from the mid-sized island?

Using one page or less, write a summary of your statistical analysis. Be sure to include:

a brief statement of the problems of interst;
a summary of your statistical findings;
some discussion of the scope of inference.

You may include plots and Splus output which do not count against your one page limit; you can attach those to your write-up. But don't write more than a single page! I won't read beyond 1 page.

3. A strawberry trial

Trial was conducted to determine which variety of strawberries produces the most fruit. Plants were cultivated on a lattice of 4 x 8 plots (as shown below), and the pounds of fruit produced for each plot were recorded. A randomized complete block design was used with four 2 x 4 plot blocks as shown below. The data are available in the file berries.asc .

Compute an F test to determine if there is a variety effect after adjusting for the block effect.
Compute 95% confidence intervals for each of the variety effects.
Determine which variety effects are significantly different from one another -- here it is sensible to adjust for the fact that multiple comparisons are being made.
The yields from the rightmost column of plots seem rather low in comparison to the other plot yields. This is likely because the hedge at the end of the field was shading (or otherwise affecting) those plots. In light of this, how would you modify your estimates in 2.
In light of all you've learned about this data, which of the varieties could acutally be the best yielding. What would you recommend to a planter who wanted to maximize his yield. You may assume that the conditions of this experiment are similar to the conditions the planter would grow his strawberries in.

G 5.8	V 6.3	Rl 4.9	F 6.5	Re 4.5	M 5.2	E 6.5	P 3.8	H
E 6.9	P 7.6	M 7.9	Re 5.6	G 7.0	V 5.5	F 4.0	Rl 2.7	E
								D
V 7.6	F 6.4	Rl 5.0	G 6.9	P 7.4	E 5.3	Re 5.2	M 3.0	G
E 7.5	Re 7.0	M 6.1	P 7.2	G 6.5	F 5.6	V 5.8	Rl 1.4	E