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 sample of 90 Eucalyptus trees is selected at random in Pacific Grove, California and the number monarch butterfly (Danus plexippus) egg masses found on each tree is counted. The average of these counts is 7.6. A very large survey the previous year found an average of 6.8 egg masses per tree with a standard deviation of 2.1. Does the new data suggest that the average number of egg masses per tree is significantly higher this year than last?
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?