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 45 documents designed to simulate prints is exposed to indirect sunlight
for 1,000 hours. A second sample of 45 identical documents is exposed to indirect fluorescent
light for 1,000 hours. An optical instrument measures the "blackness" of the ink on a scale of
zero to 50, with 50 indicating total absorbtion of all colors and 0 indicating
total reflection of all colors. The blackness index for each document is measured after exposure. At the end of the experiment, the average blackness index for the
sunlight sample is 44.1 with a sandard deviation of 2.8. The average blackness index for
the fluorescent sample is 46.5 with a standard deviation of 3.1. Does this data support the
claim that indirect sunlight fades documents of this type faster than indirect fluorescent
light?
Problem 2
Records indicate that 112 Confederate soldiers out of each 1,000 who fought in the Civil War
was killed. A sample records for soldiers known to be present at Gettysburg indicates that 145 out of 1,289 soldiers
were killed. Does this data support the claim that the average number killed out of every
thousand soldiers is more than 112 at Gettysburg?
Problem 3
Salinity measurements on ocean water conducted in 1960 on George's Bank average 35.2 parts per thousand with a standard deviation of 1.2. In 2005, a research group collected 128 samples
in the area and measured an average of 34.6 parts per thousand. Does this data suggest
that the salinity of this part of the Atlantic is lower in 2005 than it was in 1960?