10.4 Calvo RJ Individual Assignment How Wet is the Earth
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Geography
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Dec 6, 2023
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How Wet is the Earth? Activity
Name:
Group 2
How Wet is the Earth?
What proportion of the Earth’s surface is covered in water? The
true proportion is what we are estimating, and we will use
sample data to estimate this proportion. How will the sample
proportions vary? What proportion of 90% confidence intervals
calculated would we expect to contain the true proportion? Note
that the true proportion is about 71%.
Design and Implement a Plan to Collect the Data
Go to
http://www.geomidpoint.com/random/
o
Select: “circular region” and “Select whole earth” (see Figure 1).
Start by randomly generating one point on Earth and click to see it on a map.
o
The map will come up centered on a blue pin. Ignore the blue pin and look for
the red pin.
o
Then, determine whether or not the red pin is on water (you may need to zoom
in). [Note: This single point is generated to illustrate the process to collect data,
and this point will not be used for any future calculations.]
Next, randomly generate 50 points on Earth and click to see them on a map (Figure 2).
How Wet is the Earth? Activity
Figure 1.
Generating 50 random points.
Be careful to not count points more than once. Given the rectangular nature of the map,
you may have to zoom in to make sure each pin is on the map only once. You can take a
screenshot of the map with the 50 points. For example:
How Wet is the Earth? Activity
Figure 2.
Example of screenshot
You can place the screenshot in a Word document, and, if you have a printer, you can
print it out. Go back to the webpage and zoom in to determine how many of the 50
points are on water. Circle pins on the map that are in the water. If you didn’t print the
map, find another way to keep track of how many are in the water. Once you do this,
record the number of pins on water and on land in the “Activity Sheet” section below.
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How Wet is the Earth? Activity
Activity Sheet
We will take random samples of points on the Earth’s surface and see if we can
use these samples to learn about estimating the proportion of the Earth’s surface
that is water.
Do steps 1-6 individually, and then work together to complete the
rest of the steps as a group.
1.
What numeric value (or parameter) are we estimating?
2.
Go to
http://www.geomidpoint.com/random/
and select “circular region” and “select whole
Earth.”
3.
Now, randomly generate a point on Earth and click to see it on a map. The map will come up
centered on a blue pin. Ignore that blue pin and look for the red pin. Determine whether or
not the pin is on water (you may zoom in if you need to).
4.
Now randomly generate 50 points on Earth and click to see the points on a map.
●
Take a screenshot of the map with the 50 points.
●
Open Word and paste the screenshot into a Word file.
●
If you have a printer, you could print the Word file with the map.
●
Go back to the webpage, and determine how many of the 50 points are on water,
zoom in if you need to.
●
Circle pins on the map that are in the water. If you didn’t print the map, find another
way to keep track of how many are in the water.
5.
Record the number of pins on water and on land.
Sample 1 - 50 points:
On Water
On Land
Total
Proportion on Water
36
14
50
36/50
6.
Repeat the process to get a total of 100 pins.
Sample 2 - 50 points:
On Water
On Land
Total
Proportion on Water
34
16
50
34/50
7.
Combine the results of both samples.
Combined Samples 1 & 2 - 100 points:
On Water
On Land
Total
Proportion on Water
How Wet is the Earth? Activity
70
30
100
70/100
How Wet is the Earth? Activity
Second try (Jackie)
Record the number of pins on water and on land.
Sample 1 - 50 points:
On Water
On Land
Total
Proportion on Water
30
20
50
30/50
Repeat the process to get a total of 100 pins.
Sample 2 - 50 points:
On Water
On Land
Total
Proportion on Water
31
19
50
31/50
Combine the results of both samples.
Combined Samples 1 & 2 - 100 points:
On Water
On Land
Total
Proportion on Water
61
39
100
61/100
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How Wet is the Earth? Activity
8.
Calculate the sample proportion of points on water for the group’s total combined samples.
How Wet is the Earth? Activity
Total Combined Group Samples:
On Water
On Land
Total
Proportion on Water
131
69
200
131/200
9.
Compute a 90% confidence interval for the proportion of points on water. This is an estimate
for the proportion of the Earth covered by water. (Show work to get full credit.)
z
1.645
n
200
x
131
p
0.655
SE
Sqrt(p(1-
p)/n)
SE
0.03361361
ME
Z*SE
ME
0.05528935
(
0.5997106
5
0.710289935
)
Answer: (
0.59971065,0.710289935
)
* As you may or may not know, about 71% of the Earth’s surface is covered by water.
10. Suppose we did the activity again and the first sample was of size 100, and the second
sample was size 1,000.
a.
How would this change impact the distribution of the sample proportions?
As the sample size increases, causing a decrease in the standard error, the confidence interval
becomes slenderer. This results in a more accurate estimation of the actual population
proportion.
b.
How would this change impact the 90% confidence interval?
If you gather information from a bigger sample, you can be sure that the range you calculate
is a close estimate of how much of the Earth is covered by water. In simple terms, having
more data it helps to approximate the confidence interval because it helps you get a better
idea of the actual proportion.
How Wet is the Earth? Activity
11. Suppose a student obtained 75 points out of 100 on the water.
Use this data to calculate a
sample proportion of both a 90% and a 95% confidence interval for the proportion of water
on the surface of the Earth. (Show work to get full credit.)
a.
Which interval is wider?
z90%
1.64485
n
100
x
75
p
0.75
SE
Sqrt(p(1-p)/n)
SE
0.04330
1
ME
Z*SE
ME
0.07122
4
Interval
(
0.67877
6,
0.82122
4
)
z95%
1.95996
4
n
100
x
75
p
0.75
SE
Sqrt(p(1-p)/n)
SE
0.04330
1
ME
Z*SE
ME
0.08486
9
Interval
(
0.66513
1,
0.83486
9
)
The 95% z score confidence interval is wider.
b.
Will this always be the case?
Indeed, it is generally accurate regarding confidence intervals: when
the confidence level rises, the interval width also increases.
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