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 researcher counts gypsy moth (Lymantria dispar) egg masses in 76 quarter-acre plots. An much larger survey from the previous season indicated an average of 52.1 egg masses per quarter-acre with a standard deviation of 12.4. If the average number of egg masses per quarter-acre
in the sample is 46.1, does the data support the claim that the level of infestation (as measured by the average number of egg masses per quarter acre) is lower this year?
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
Mosquito traps are placed near 43 small ponds and a count of Culex species in the traps is obtained during a baseline period. At the end of the baseline period a spraying program is conducted. One week after the spraying, the traps are cleaned and a second collection period is initiated. Based on an estimate of the size of each pond, the raw counts are converted to a density of Culex mosquitoes per square foot of pond. The difference between the before and after densities is found to have a sample mean of 9.1 and a sample standard deviation of 12.0.
Test whether or not the data indicates that the spraying was effective in reducing the density of
Culex species mosquitoes.