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

In an experiment to evaluate the effect of high temperature and humidity on stored films, 35 identical test films are stored in a climate-controlled environment while another 50 identical test films are exposed to ambient temperature and humidity. After one year, the films are evaluated for loss of transparency using a scale that runs from 0 to 100, 100 indicating no measurable loss of transparency and 0 indicating complete loss of transparency. The average measure for the climate-controlled films is 98.2 with a standard deviation of 0.3. The average measure for the non climate-controlled films is 97.3 with a standard deviation of 0.5. Does this data indicate that climate control is effective in preserving transparency?

Problem 2

A government agency is trying to build a case to support the assertion that ocean dumping of titanium dioxide waste in the Baltimore Canyon is resulting in detectable increases in titanium in the deep sea scallop (Placopecten magellanicus) population in the dumping area. A sample of 75 specimens from the dumping area showed titanimum levels of 12.3 parts per million with a standard deviation of 5.1, while a sample of 68 specimens from a site 20 miles away had an average concentration of 8.6 parts per million with a standard deviation of 4.2. Determine whether this data supports the agency's assertion.

Problem 3

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 wavelength of the peak absorption color is 488.7 nanometers with a standard deviation of 43.2. In 2002 peak absoption was measured at 507 nanometers. 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)?