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 assumptions, calculate test statistic, calculate P-value). What do you conclude?