Statistics

Note that there are three different scenarios here. Number 1 clearly deals with a single population and is distinct from numbers 2 and 3. The difference between the latter two is, however, more subtle. Note that there is a lack of independence in 2, that is, if we shuffled the numbers in the factory and Haiti columns, we would be losing information. This is not the case in number 3.
Note the difference between a one sided and two sided confidence interval in number 1. (Do both!). Which is more appropriate?
What if the confidence level changes to 99% or 90% in each of these?

The weights (in kg) of 24 male runners are given in the file runners.data.
1. Give a 95 percent confidence interval for the mean weight of male runers μ.
2. Are you sure the mean weight is less than 65 kg? Are you sure the mean weight is less than 63.5 kg?
Researchers are studying vitamin C retention in a wheat-soy blend. A major concern is that some of the vitamin C content is destroyed during shipment and storage. A random selection of bags was tested for vitamin C content and marked in the factory. Five months later each bag was tested again in Haiti. The data vitaminc.data list before and after measurements for each bag.
1. Find a 95% confidence interval for the mean vitamin C content in the factory.
2. Find a 95% confidence interval for the mean vitamin C content in the Haiti.
3. Find a 95% confidence interval for the difference.
4. In terms of what the researchers were studying, what can we say about the vitamin C loss during shipment and storage?
In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pounds per acre. The data are in malathion.data. Is there significant evidence that the mean number of larvae per stem is reduced by Malathion?