Two methods for
teaching reading were applied to two randomly selected groups of elementary
school children and then compared on the basis of a reading comprehension test
given at the end of the learning period. For the first group (consisting of 25
children), the sample mean was 64.2 and the sample standard deviation was 7.21.
For the second group (consisting of 30 children), the sample mean was 69.7 and
the sample standard deviation was 8.4. Both sets of sample data look fairly
mound-shaped.
Find a 99%
confidence interval for the difference in the means of the two populations.
Based on this
confidence interval, at the 1% level, would you reject the null hypothesis that
the population means are the same (versus the two-sided alternative)?
A study was
conducted by the Florida Game and Fish Commission to assess the amount of
chemical residues found in the brain tissue of brown pelicans. Specifically,
they are interested in if the mean amount of DDT found in juvenile pelicans is
larger than the mean amount of DDT found in nestling pelicans (this test has
important implications regarding the accumulation of DDT over time).
A random sample
of 10 juvenile pelicans was taken and the sample mean was 0.041 parts per
million (ppm) and the sample standard deviation was 0.017 ppm. A random sample
of 13 nestling pelicans was taken and the sample mean was 0.026 ppm and the sample
standard deviation was 0.006 ppm. Furthermore, assume that both sets of sample
data look mound-shaped.
Carry out the
significance test (state hypotheses, check conditions, calculate test
statistic, calculate P-value). What
do you conclude?