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
In a sample of 85 households with children under the age of six in a rural area of sub-Saharan Africa, 17 reported a new case of malaria in a child under 6 within the past year. Construct
a 99% confidence interval for the proportion of households with children under the age of six
in which a new case of malaria occurred during the past year.
Problem 2
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?
Problem 3
Ocean color is known to correlate strongly with phytoplankton levels, green indicating higher
and blue lower levels of phytoplankton. An extensive ocean color survey on George's Bank
conducted in 1996 measured an average peak absorption wavelength of 502.3 nanometers with
a standard deviation of 34.7. A color survey of 80 randomly selected grid points conducted
in 2005 found an average peak absorption wavelength of 493.1 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)?