A Researcher takes measurements of water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The collected data is given in the table below.
Oservation 1 2 3 4 5 6
Dates 1/25 3/19 5/30 7/3 9/13 11/7
Initial 37.4 35.9 37.6 47.7 63.3 55.5
After five years 37.8 33.6 37.4 54.0 67.6 54.6
Construct a 95% confidence interval about the population mean difference. Compute the difference as (initial depth of clarity) minus (depth of clarity after five years). Interpret your results.