MA207 Final Exam - Takehome Portion

For each of the problems below, use the 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 researcher wishes to determine whether the presence of entomophthoralean fungus (Entomophaga maimaiga), indicates a reduced level of gypsy moth (Lymantria dispar) infestation. Gypsy moth egg masses are counted in 43 quarter-acre plots where the fungus is detected, and 52 where it is not. The number of egg masses in plots where the fungus is detected has a sample mean of 32.4 and a sample standard deviation of 12.1. In plots where no fungus is detected, the sample mean is 43.1 with a sample standard deviation of 15.0. Does this study support the claim that the fungus lowers the level of gypsy moth infestation?

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 randomly selected coordinate points using satelite imagery from 2005. The same analysis is performed on an lower resolution image taken 3 years earlier, using 80 randomly selected coordinate points. In the 2005 data, the wavelength of the peak absorption color is 492.1 nanometers with a standard deviation of 43.2. The 2002 data has peak absoption at 511 nanometers with a standard deviation of 32.4. 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

Records from a banding station indicate that in 2001, the average weight of a certain species of bird is 18.9 grams with a standard deviation of 3.1, based on 42 individual birds. In 2005, 33 individuals from this species are captured and their average weight is 16.1 grams with a standard deviation of 2.3. Is this data consistent with the claim that the average weight in the population has not changed?