Confidence interval for μ 1 –μ 2 , σ1= and σ 2 known In the summer of 1988,

Confidence interval for μ₁–μ₂, σ1= and σ₂ known

In the summer of 1988, Yellowstone National Park had some major fires that destroyed large tracts of old timber near many famous trout streams. Fishermen were concerned about the long-term effects of the fires on these streams. However, biologists claimed that the new meadows that would spring up under dead trees would produce a lot more insects, which would in turn mean better fishing in the years ahead. Guide services registered with the park provided data about the daily catch for fishermen over many years. Ranger checks on the streams also provided data about the daily number of fish caught by fishermen. Yellowstone Today (a national park publication) indicates that the biologists’ claim is basically correct and that Yellowstone anglers are delighted by their average increased catch.

Suppose you are a biologist studying fishing data from Yellowstone streams before and after the fire. Fishing reports include the number of trout caught per day per fisherman. A random sample of n₁= 167reportsfrom the period before the fire showed that the average catch was trout per day. Assume that the standard deviation of daily catch per fisherman during this period was σ₁= 1.9 . Another random sample of n₂= 125fishing reports 5 years after the fire showed that the average catch per day was trout. Assume that the standard deviation during this period was σ₂= 2.3.

(a) Check Requirements For each sample, what is the population? Are the samples dependent or independent? Explain. Is it approriate to use a normal distribution for the distribution? Explain.

(b) Compute a 95% confidence interval for μ₁- μ₂, the difference of population means.

(c) Interpretation What is the meaning of the confidence interval computed in part (b)?