Glacier name | Rate/m |
---|---|
Breidamerkurjökull | 48 |
Breidamerkurjökull | 108 |
Breidamerkurjökull | 18 |
Falljökull | 18 |
Fjallsjökull | 10 |
Fjallsjökull | 18 |
Fjallsjökull | 16 |
Fláajökull | 22 |
Gígjökull | 75 |
Hrútárjökull | 6 |
Kverkjökull | 42 |
Kvíárjökull | 3 |
Morsárjökull | 9 |
Múlajökull | 48 |
Nathagajökull | 8 |
Öldufellsjökull | 88 |
Sátujökull | 93 |
Síðujökull | 44 |
Skaftafellsjökull | 4 |
Skeiðarárjökull | 27 |
Skeiðarárjökull | 9 |
Skeiðarárjökull | 69 |
Skeiðarárjökull | 21 |
Svínafellsjökull | 3 |
Tungnaárjökull | 23 |
Glaciers are giant sheets of ice and snow that flow like a vast frozen river down high latitude and high altitude mountain valleys. Glaciers move very slowly, typically only a few decimeters per year. Each winter snowfall on the glacier basin replenishes the glacier. At the bottom of the glacier the ice sheet either melts as water or calves off into the ocean. The result is a balance where the glacier remains the same length over long periods of time. Global warming, however, is melting glaciers faster than winter snows can rebuild the glacier. Glaciers exhibit this most by increased melting on the bottom or front of the glacier. The glacier gets shorter with each passing year. The data in the table is the average annual retreat of the glacier front for glaciers in Iceland. Some glaciers have more than one "tongue" and measurements are made for each tongue. Globally, glacial melting is a contributor to sea level rise. While places like Iceland lose their glaciers, places like Micronesia lose their atolls. The data is also available in a data sheet to save you retyping the data.
For the annual retreat rate in meters for the glaciers of Iceland data given in the table (to avoid using negative numbers, this section uses positive numbers for the amount of retreat of the glacier front in meters):
Bins | Frequency | RF p(x) |
---|---|---|
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
Sums: | _________ | _________ |
Write out the 95% confidence interval for the population mean retreat rate:
_________ ≤ μ ≤ _________
__________________ Use the t-statistic to find the p-value. Remember to increase the decimal places in OpenOffice Calc. Use six decimal places.
__________________ What is the maximum level of confidence we can have that the rate of glacier retreat is not zero (that the glaciers are really retreating, shrinking in length).
The following data is also glacier retreat rate data from glaciers in Iceland. Because this data includes glaciers that retreated and glaciers that grew longer, the data includes positive and negative measurements. In this section negative numbers are the distance in meters the glacier retreated (shrank, got smaller) while the positive numbers are the distance in meters that the glacier advanced (grew longer). The paired data is measurements for individual glaciers taken in 1996 and four years later in 2000.
Glacier | 1996 | 2000 |
---|---|---|
Breidamerkurjökull | -20 | -5 |
Breidamerkurjökull | -45 | -40 |
Falljökull | 1 | -37 |
Fjallsjökull | 23 | -63 |
Fjallsjökull | -10 | -5 |
Fjallsjökull | 12 | -20 |
Fláajökull | 10 | -53 |
Gígjökull | 10 | -136 |
Hrútárjökull | -20 | 0 |
Kaldaklofsfjöll | 38 | 0 |
Kvíárjökull | 4 | 0 |
Morsárjökull | -31 | -14 |
Múlajökull | -8 | -50 |
Nathagajökull | -5 | -5 |
Sátujökull | -200 | -51 |
Skaftafellsjökull | 51 | -70 |
Skeiðarárjökull | -33 | -1 |
Skeiðarárjökull | -31 | -10 |
Skeiðarárjökull | -4 | -14 |
Skeiðarárjökull | -13 | -110 |
Svínafellsjökull | 5 | -5 |
Tungnaárjökull | -53 | -19 |
Year | Movement/meters |
---|---|
1996 | -13 |
1997 | -38 |
1998 | -35 |
1999 | -150 |
2000 | -110 |
The data in this section examines whether there is a trend in the retreat rate for the Skeiðarárjökull glacier front. Note that this section the numbers are the retreat rate, a velocity or speed of retreat in meters per year. Negative numbers represent the retreat, shrinking of the length of the glacier.
Basic Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | OpenOffice |
Square root | =SQRT(number) | ||
Sample standard deviation | sx or s | =STDEV(data) | |
Sample Coefficient of Variation | CV | sx/x | =STDEV(data)/AVERAGE(data) |
Confidence interval statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | OpenOffice |
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c;df) | |
Calculate the standard error of the mean | =sx/SQRT(n) | ||
Calculate a margin of error for the mean E for n < 30 using sx. Should also be used for n ≥ 30. | E | =t_{c}*sx/SQRT(n) | |
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E | x - E ≤ µ ≤ x + E | ||
Hypothesis Testing | |||
Relationship between confidence level c and alpha α for two-tailed tests | 1 − c = α | ||
Calculate t-critical for a two-tailed test | t_{c} | =TINV(α;df) | |
Calculate a t-statistic | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate a two-tailed p-value from a t-statistic | p-value | = TDIST(ABS(t);df;2) | |
Calculate a p-value for the difference of the means from two samples of paired samples | =TTEST(data_range_x;data_range_y;2;1) | ||
Calculate a p-value for the difference of the means from two independent samples, no presumption that σ_{x} = σ_{y} | =TTEST(data_range_x;data_range_y;2;3) |
Linear Regression Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | OpenOffice |
Slope | b | =SLOPE(y data; x data) | |
Intercept | a | =INTERCEPT(y data; x data) | |
Correlation | r | =CORREL(y data; x data) | |
Coefficient of Determination | r^{2} | =(CORREL(y data; x data))^2 |