Ocean Energy Kosrae is an independent power producer in the State of Kosrae.
Ocean Energy Kosrae will produce and deliver to the customers in the State of
Kosrae electric power harnessed from ocean waves in order to reduce,
and ultimately eliminate, the state's dependence on fossil fuels,
to improve the quality of life,
minimize the cost and expand the use of electricity in the state of Kosrae,
to achieve an equal access to affordable and sustainable renewable energy
sources in environmentally responsible and commercially viable manner.
The state of Kosrae is poised to become the first island in the world to be
completely powered by wave energy and other renewable energy sources.
Table one
Wave
Height (m)
1.2
1.7
2.4
2.4
2.5
2.7
2.7
2.9
2.9
2.9
2.9
3.2
3.3
3.3
3.4
3.5
4.0
4.2
4.4
4.7
The 1.5 MW clean energy project is based on Ocean Energy Industries'
WaveSurfer™ technology.
Wave energy is a genuinely renewable, clean, safe and efficient energy source.
For island nations land is perhaps the most valuable commodity.
Unlike solar or wind power plants, wave power plant occupies unused ocean surface
out of sight from the shore.
WaveSurfer is a reliable, inexpensive and efficient "point absorber" off-shore system,
that can be installed at different depths by mooring.
WaveSurfer does not contain expensive and complex parts, lubricants, high precision
hydraulics or air pumps.
One of the main advantages of WaveSurfer system is its remarkably high level of survivability.
WaveSurfer is designed to operate in harmony with waves rather than attempting to resist them.
WaveSurfer's main power conversion and generation parts are completely
submerged at a depth of around one-half wavelength of the prevailing waves in the
region where the water is not affected by the waves,
therefore is still or relatively still.
The wave height data is based on data in a report on coastal erosion in Malem.
__________ What is the level of measurement for the data in table one?
__________ Calculate the sample size n.
__________ Calculate the minimum.
__________ Calculate the maximum.
__________ Calculate the range.
__________ Calculate the midrange.
__________ Calculate the mode.
__________ Calculate the median.
x = __________
Calculate the sample mean x.
sx = __________ Calculate the sample standard deviation sx.
__________ Calculate the coefficient of variation.
_________ Determine the class width. Use
5
classes (bins or intervals).
Fill in the following frequency table:
Classes (x)
Frequency f
Rel Freq p(x)
Sums:
Sketch a histogram of the frequency data to the right of the table.
__________________ What is the shape of the distribution?
__________ Using the sample mean and standard deviation from table one calculate the
z-score for a wave with a height of 4.7 meters.
__________ Is the z-score for a 4.7 meter wave ordinary or extraordinary?
SE = _________
Calculate the standard error of the sample mean x
t_{critical} = _________
Calculate t_{critical} for a confidence level c of 95%
E = _________
Calculate the margin of error E for the sample mean x.
Write out the 95% confidence interval for the population mean μ
p(_____________ < μ < ___________) = 0.95
Kosrae has a peak power demand of 1100 Kilowatts.
A WaveSurfer-4 unit requires wave heights of 4 meters to generate 1100 Kilowatts.
Run a hypothesis for whether the data in table one has a population mean
wave height of μ = 4 meters.
at an alpha α of 0.05.
H_{0}: μ = 4
H_{1}: μ ≠ 4
t_{critical} = _________
Calculate t_{critical} at α = 0.05.
t = _________ Calculate the t-statistic t.
p-value = _________ Calculate the p-value.
max c = _________
Calculate the maximum confidence that the data in table one has wave heights of 4 meters.
_____________________
At an alpha α of 5%, would you fail to reject|or|reject the null hypothesis?
___________
Will the Malem site produce 1100 watts?
Table two
Wave H (m)
Malem
Tafunsak
1.2
4.6
1.7
3.4
2.4
3.7
2.4
5.0
2.5
4.3
2.7
4.3
2.7
3.5
2.9
4.1
2.9
3.6
2.9
2.9
2.9
3.9
3.2
2.9
3.3
4.0
3.3
2.5
3.4
3.1
3.5
2.4
4.0
3.7
4.2
4.8
4.4
5.1
4.7
4.5
Part II: Hypothesis Testing using the t-test
Two independent samples of wave data were gathered.
One sample was from offshore of Malem, and the other was from offshore of
Tafunsak. The samples are independent.
_________ Calculate the sample mean
for the Malem wave data.
_________ Calculate the sample mean
for the Tafunsak wave data.
_________ Are the sample means for the two samples arithmetically different?
__________________
What is the p-value? Use the TTEST function with two tails
to determine the p-value for these two independents samples.
__________________ Is the difference in the means statistically significant
at an alpha α = 0.05?
__________________
Would we fail to reject| or |reject
a null hypothesis of no difference
in the sample means?
__________________ What is the maximum level of confidence we can have that the
difference is statistically significant?
__________________
Based on the above analysis, where should the WaveSurfer be located to maximize
power production?
Part III: Linear Regression (best fit or least squares line) Table three
Wave H (m)
Power (Kw)
0.5
16
1.0
63
1.5
143
2.0
254
2.5
397
3.0
572
3.5
778
4.0
1016
4.5
1286
5.0
1366
5.5
1443
6.0
1528
The data in the table provides the estimated power output of a WaveSurfer™ unit.
The first column is the height of the waves in meters.
The second column is the power output in KiloWatts.
_________ Calculate the slope of the linear regression (best fit line).
_________ Calculate the y-intercept of the linear regression (best fit line).
_________ Is the relation positive, negative, or neutral?
_________ Calculate the linear correlation coefficient r for the data.
______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
______________ Determine the coefficient of determination.
______________ What percent variation in
Wave H (m)
"explains" the variation in
Power (Kw)
?
___________
Use the slope and intercept above to predict the power generated by a
3.8
meter high wave.
___________
Use the slope and intercept above to predict the wave height needed to produce
1200 Kilowatts.
n 20
min 1.2
max 4.7
range 3.5
midrange 2.95
mode 2.9
median 2.9
mean 3.06
stdev 0.86
cv 0.28
classes 5
width 0.7
cul f rf
1.9 2 0.1
2.6 3 0.15
3.3 9 0.45
4 3 0.15
4.7 3 0.15
5.4 0 0
6.1 0 0
20
SE0.19
tc 2.09
E0.4
lower 2.66
upper 3.46
mean 3.06
Part II
Malem Tafunsak
n 20 20
mean 3.06 3.82
stdev 0.86 0.79
ttest 0.00635
y = 313.53846x + -280.500
count 12
slope: 313.54
intercept: -280.50
correl: 0.98754
coef det 0.98
y given x 910.95
x given y 4.72
ttest: 19.84
p-value: 0.0000000 Probably have to omit this due to values.
max c 1.0000000