Ocean Energy Kosrae ♒ Name:

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.

Data sheet

Part I: Basic Statistics

1. __________ What is the level of measurement for the data in table one?
2. __________ Calculate the sample size n.
3. __________ Calculate the minimum.
4. __________ Calculate the maximum.
5. __________ Calculate the range.
6. __________ Calculate the midrange.
7. __________ Calculate the mode.
8. __________ Calculate the median.
9. x = __________ Calculate the sample mean x.
10. sx = __________ Calculate the sample standard deviation sx.
11. __________ Calculate the coefficient of variation.
12. _________ Determine the class width. Use 5 classes (bins or intervals).
13. Fill in the following frequency table:
Classes (x)Frequency fRel Freq p(x)
Sums:
14. Sketch a histogram of the frequency data to the right of the table.
15. __________________ What is the shape of the distribution?
16. __________ Using the sample mean and standard deviation from table one calculate the z-score for a wave with a height of 4.7 meters.
17. __________ Is the z-score for a 4.7 meter wave ordinary or extraordinary?
18. SE = _________ Calculate the standard error of the sample mean x
19. tcritical = _________ Calculate tcritical for a confidence level c of 95%
20. E = _________ Calculate the margin of error E for the sample mean x.
21. 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.
H0: μ = 4
H1: μ ≠ 4
22. tcritical = _________ Calculate tcritical at α = 0.05.
23. t = _________ Calculate the t-statistic t.
24. p-value = _________ Calculate the p-value.
25. max c = _________ Calculate the maximum confidence that the data in table one has wave heights of 4 meters.
26. _____________________ At an alpha α of 5%, would you fail to reject |or| reject the null hypothesis?
27. ___________ Will the Malem site produce 1100 watts?

Table two
Wave H (m)
MalemTafunsak
1.24.6
1.73.4
2.43.7
2.45.0
2.54.3
2.74.3
2.73.5
2.94.1
2.93.6
2.92.9
2.93.9
3.22.9
3.34.0
3.32.5
3.43.1
3.52.4
4.03.7
4.24.8
4.45.1
4.74.5

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.
28. _________ Calculate the sample mean for the Malem wave data.
29. _________ Calculate the sample mean for the Tafunsak wave data.
30. _________ Are the sample means for the two samples arithmetically different?
31. __________________ What is the p-value? Use the TTEST function with two tails to determine the p-value for these two independents samples.
32. __________________ Is the difference in the means statistically significant at an alpha α = 0.05?
33. __________________ Would we fail to reject | or | reject a null hypothesis of no difference in the sample means?
34. __________________ What is the maximum level of confidence we can have that the difference is statistically significant?
35. __________________ 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)
0.516
1.063
1.5143
2.0254
2.5397
3.0572
3.5778
4.01016
4.51286
5.01366
5.51443
6.01528

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.
36. _________ Calculate the slope of the linear regression (best fit line).
37. _________ Calculate the y-intercept of the linear regression (best fit line).
38. _________ Is the relation positive, negative, or neutral?
39. _________ Calculate the linear correlation coefficient r for the data.
40. ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
41. ______________ Determine the coefficient of determination.
42. ______________ What percent variation in Wave H (m) "explains" the variation in Power (Kw) ?
43. ___________ Use the slope and intercept above to predict the power generated by a 3.8 meter high wave.
44. ___________ Use the slope and intercept above to predict the wave height needed to produce 1200 Kilowatts.
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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
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