GG413 Geological Data Analysis, Fall 2014
Homework #4: Hypothesis Testing with Parametric Statistics
Due Tue. Sept 16
The same requests about explaining your answers, writing out your steps, and labeling plots applies. In this
homework, there’s no need to include any Matlab scripts.
1) Micron-sized particles of dust are suspended in the atmosphere and would remain there indefinitely,
except that they tend to be scrubbed out by snow by because they serve as nuclei for tiny ice crystals. At
the two poles, the ice crystals with the particles fall to the surface and create long-lived icecaps. By
studying the particles in various layers of the ice, we can learn about the geologic and atmospheric
conditions in the geologic past.
Suppose a n=16-point sampling of the concentration of micro-particles in ice cores from the Antarctic
icecap give the following concentrations (in ppb):
x = [3.70 2.00 1.30 3.90 0.20 1.40 4.20 4.90 0.60 1.40 4.40 3.20 1.70 2.10 4.20 3.50]
(a) Estimate the mean concentration (i.e., mean and confidence interval) in this part of the icecap to the
90% confidence level using the normal (z) distribution.
(b) Do the same using the t-distribution. Compare your answers, discuss the reasons for their differences,
and indicate which solution is more statistically sound.
2) It is hypothesized that the time at which the layer of ice sample above was deposited, global atmospheric
mixing was not very efficient and thus the mean concentration of particles in the northern hemisphere
was different than the mean concentration in the southern atmosphere. Extensive studies of Greenland
indicate that the relevant layer of ice in the northern hemisphere has a mean concentration of  = 3.20
ppb with a standard deviation of  = 1.60 ppb. Set up the appropriate null (H0) and alternative (H1)
hypotheses, and test them to see if the sample in problem (1) from Antarctica supports the hypothesis of
poor atmospheric mixing at the (a) 70% confidence level, and at the (b) 95% confidence level.
3) After spending weeks in the field measuring mercury content in two remote rivers, we return to the lab
to analyze the data. We find the following concentrations from the rivers (in ppm):
River A: [9.86 12.02 12.96 10.40 12.43 9.61 11.12 10.64 10.22]
River B: [11.36 10.48 11.06 11.61 13.28 12.72 13.91 12.08 12.38 12.80]
(a) Determine whether the standard deviation of concentration between two rivers differs at the 95%
confidence level.
(b) Determine whether the mean mercury content differs between the two rivers at the 95% confidence
level.
Extra Credit: Given the means and standard deviations from the two samples, plot the estimated normal
probability density functions (pdf’s) for the mercury concentrations in each of the two rivers (i.e., plot
p(x) for each river assuming a normal distribution). Then on the same graph plot the estimated normal
pdf’s of sample means that would be taken from the two rivers (i.e., plot p( x ) versus x for each river).
Describe what you see in context of your answer in (a)
4) A designer of seismometers must know whether or not the standard deviation of the time it takes the
instrument to start recording an event after being triggered by an earthquake is less than 0.010 s. Use the
0.05 level of significance (95% confidence level) to test the null hypothesis H0 : s ≤ 0.010 s against the
alternative hypothesis H1:s > 0.010 on the basis of a random sample of size n = 16 for which the sample
standard deviation was found to be s = 0.012 s.