1. A study has been made to compare the nicotine contents of two brands of cigarettes. Ten cigarettes of Brand A have an average nicotine content of 3.1 milligrams with a standard deviation of .5 milligrams, while 8 cigarettes of Brand B have an average nicotine content on 2.7 milligrams with a standard deviation of .7 milligrams. At a level of significance of .05, test whether the average nicotine between the two brands is different or not.
2. Consider the following data samples on ore capacities of coal from two mines ( in millions of calories per ton);
Mine A : 8,500, 8330, 8,480, 7,960 and 8,030
Mine B: 7,710, 7,890, 7,920, 8,270 and 7,860
Test whether the average ore capacities are the same or not.
This solution provides guidelines on how to fine the averages of data samples based on different levels of significance.