Case Studies: (30 Points Each, Values Individually Marked) Two case studies are presented, and for each you will use concepts we have learned throughout the quarter to perform an analysis of the data and come to some conclusions.
Case Study 1: Researchers with the Department of Fish and Wildlife (DFW) monitor the acidity of lakes in the Cascade Mountains. Pollution in the atmosphere can mix with water and oxygen and create "acid rain". When this falls at high altitudes, the runoff can cause acidity in lakes to rise. A rise in acidity can be harmful to the ecosystems of the lakes at high altitudes.
Acidity is measured on the pH scale, with 7 being neutral, lower pH being more acidic, and higher pH being less acidic (basic). The DFW begins to be concerned about the acidity of freshwater lakes when the pH drops below 6.
The Sampling: Each year, the DFW randomly selects a few new lakes to monitor. Then, over the course of three years, the DFW visits each lake four times/year and takes a random sample of water to test for acidity. For one particular lake, Lake 153, the past three years of samples produced the following pH levels:
Sample W16 Sp16 Su16 F16 W17 Sp17 Su17 F17 W18 Sp18 Su18 F18
pH 6.2 6.4 5.9 5.5 5.9 6.1 6.0 5.8 5.5 5.8 5.4 5.8
1.) [4 pts] Calculate the mean and standard deviation of the pH levels of Lake 153.
2.) [2 pts] As a data analyst for the DFW, you are concerned in pH levels dip below 6.0. How would you formulate this as a formal hypothesis test?
Ho:
Ha:
3.) [4 pts] Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making each one would be.
Type I Error:
Type II Error: