MA145 Final Exam - Takehome Portion
For each of the problems below, use the MA145 technology guide to perform a statistical analysis.
You should justify your choice of method, including any assumptions made in the use of the method.
You should indicate whether a two-tailed, left-tailed, or right-tailed analysis is appropriate,
and, in hypothesis testing problems, state the null and alternative hypotheses.
If the problem does not specify a level of significance, you should choose one.
Problem 1
A survey of 90 randomly selected Eucalyptus trees in Pacific Grove, California finds
an average of 17.1 monarch butterfly (Danus plexippus) egg masses per tree.
A similar survey conducted the previous year examined 82 trees and found an average
of 19.2 egg masses. Historical records indicate that 3.4 is a reliable estimate
the standard deviation of measurements of this kind. Does the more recent survey
suggest a decline in the monarch population in the area?
Problem 2
Ocean color is known to correlate strongly with phytoplankton levels, green indicating higher
and blue lower levels of phytoplankton. Ocean color in the Gulf of Alaska is measured on a
grid of 120 data points using satelite imagery. The same analysis is performed on an image
taken 3 years earlier by the same satelite, using identical grid points. The average difference in wavelength of the peak absorption color at a point on the grid is -35.8 nanometers with a standard deviation of 23.2. Given that the wavelength of green light is 510 nm and that of blue light is 475 nm, does this data indicate a significant shift in ocean color towards blue (and therefore, a reduction in phytoplankton)?
Problem 3
A large survey indicated that 8% of the Culex species Mosquitoes in the area carry the West Nile pathogen. The following year, a trap collects 250 Culex mosquitoes of which 31 test positive. Does this result support the assertion that the prevalence of the virus in
this species of mosquitoes is increasing?