MONT 105N – Analyzing Environmental Data Midterm Examination – April 12, 2013

Your Name:

Directions: Do all work on these sheets. You may use the back if necessary, but please alert me with a note if you do. In a case where a later part of a question depends on a previous part, I will give credit for the later part as long as you have a correct approach, even without the correct value from the previous part. There are 100 points, distributed as indicated in the questions.

I. A fertile but short-lived organism has monthly fertility and survival rates as given in this table:

Agegroup  A  B  C
Age(months)  0 − 1 1 − 2 2 − 3
Fertilityrate 0 4 3
Survivalrate  0.3 0.1 0.0

A) (10) Draw the corresponding life-cycle graph.

B) (10) Convert the information in the table (and the life-cycle graph) to a system of difference equations.

C) (5) Given that a(0) = 300, b(0) = 200 and c(0) = 100, determine a(1), b(1), c(1).

II. All parts of this question refer to the following data set with n = 9:

12, 15, 18, 25, 26, 28, 31, 33, 34

A) (10) Find the “5-number summary” and draw the corresponding box plot. B) (5) Is the Bowley measure of skewness positive or negative for this data set? C) (5) Given that the SD is approximately SD = 7.97, how well does the Empirical Rule “fit” this data? (Say what that rule says and then determine how closely this data follows it.)

III. Suppose that a data set of n = 25 Dungeness crab shell length measurements has been collected. The mean shell width in the sample is \overline{x} = 20cm and the SD is 4cm.

A) (5) Would the z-score of a measurement x = 18 be?

B) (5) What width measurement would correspond to a z-score of −1.3?

C) (5) Find a 95% confidence interval for the population mean shell width.

D) (10) Estimate the proportion of the population of crabs with shell widths between 18 and 21cm. State any assumptions you are making to arrive at your estimate.

IV. Essay. (30) Exactly what is the “hockey stick” graph? How was it originally generated? When and where did it first appear in the published scientific record? Have other studies confirmed this general pattern or called into question the original conclusions? When and why did the “hockey stick” become such a contentious issue in the climate change debate? What is the IPCC and what do they do? What was the role of the IPCC here?