Unizor - Statistical Distribution - Task C - Rising Sea Level

Unizor - Creative Minds through Art of Mathematics - Math4Teens



Our random variable takes continuous range of values with theoretically known fixed boundaries - from a to b.



Problem



In order to determine if the claims about climate change are true or false, the daily sea level data (in mm) have been gathered daily at noon for the period from 1933 to 2014 at Crescent City, California, United States (latitude 41.74500, longitude -124.18300) and for the period from 1911 to 2014 at Atlantic City, New Jersey, United States (latitude 39.35000, longitude-74.42000) from the official Web site Sea Level Center of University of Hawaii.



Based on these data about the sea levels at California and New Jersey coasts, determine for each of these two places and for each decade (10-year period) the mean, standard deviation, slope, range and 95% certainty interval of average sea level.

Create a density of probabilities model - probability mass function - of average sea level by decade (divide the range in 5 intervals).

Make a judgement about validity of the claims that sea level was rising.





Solution



The summary data for California coast with some additional calculations in a spreadsheet format can be downloaded from Sea Level in CA.

The corresponding spreadsheet for New Jersey coast is at Sea Level in NJ.



These two spreadsheets contain summary data about average sea level by decades.

These data include:

=AVERAGE(...)

=STDEV(...)

=SLOPE(...)

=MIN(...)

=MAX(...)

It is further supplemented with distribution counts of sea levels for each decade in five intervals.

Examine it.

Here are some conclusions.



CONCLUSION

In short, the sea level in California was stable, while in New Jersey it has risen by about 400 mm in about 100 years. Both statements have 95% certainty.