Divide the data into two groups: one group is annual rainfall for the most recent 20 years and the other is all the earlier years.Compute the sample average for each group, separately.I am using 20 years because meteorologists often use that length of time to define a "current" period of data history.

Use the sample average for the earlier time period as if it were a population average.I am doing that for two reasons.First, to do a one-sample t-test, we need a specific value of the population average.Second, our data size is quite large for the earlier period, large enough that we can for our purposes substitute xbar for mu.

Test for climate change in terms of the annual rainfall for NYC.Let the older data give you "mu", let the newer data give you xbar and s.Use alpha level 5%.Include a graph.

n=20

Group Asample Average46.0735

Group B sample Average40.9815748