Researchers claim that the surface temperature of the world's oceans mainly changes with changing latitude. The warmest waters are near the equator and the coldest waters are in the Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the following data has been collected from coastal areas in the southern hemisphere for 5 consecutive years in the middle of November. The recorded temperatures are all averages across the 5 years of data. Coastal ocean Surface Temperature Latitude 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 14.1 15.2 16.2 17.5 18 21 22.1 23.8 24.5 24.2 24.4 26 26.9 28.2 28.5 28.8 29.8 29.8 31.2 32.5 Coastal Air Temperature 16 17 15 15 18.5 22 24.5 24 25 26.5 30 31.6 30.4 33.5 33 32 32 33.5 34 30 Note: Temperature.xlsx is also attached. a) Convert the latitude numerical variable to a categorical variable with 4 levels (very low, low, moderate, high), using a statistical software package. Find the overall mean, group means, and group standard deviations using the statistical package. Conduct an ANOVA test to find the possible impact of latitude on coastal ocean surface temperature. Write the assumptions of the model, write out the model in cell means/classical/regression form, conduct the analysis in a statistical software package, run the Tukey HSD test if needed, and state a conclusion based on the output.
Researchers claim that the surface temperature of the world's oceans mainly changes with changing latitude. The warmest waters are near the equator and the coldest waters are in the Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the following data has been collected from coastal areas in the southern hemisphere for 5 consecutive years in the middle of November. The recorded temperatures are all averages across the 5 years of data. Coastal ocean Surface Temperature Latitude 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 14.1 15.2 16.2 17.5 18 21 22.1 23.8 24.5 24.2 24.4 26 26.9 28.2 28.5 28.8 29.8 29.8 31.2 32.5 Coastal Air Temperature 16 17 15 15 18.5 22 24.5 24 25 26.5 30 31.6 30.4 33.5 33 32 32 33.5 34 30 Note: Temperature.xlsx is also attached. a) Convert the latitude numerical variable to a categorical variable with 4 levels (very low, low, moderate, high), using a statistical software package. Find the overall mean, group means, and group standard deviations using the statistical package. Conduct an ANOVA test to find the possible impact of latitude on coastal ocean surface temperature. Write the assumptions of the model, write out the model in cell means/classical/regression form, conduct the analysis in a statistical software package, run the Tukey HSD test if needed, and state a conclusion based on the output.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
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Transcribed Image Text:Researchers claim that the surface temperature of the world's oceans mainly changes with
changing latitude. The warmest waters are near the equator and the coldest waters are in the
Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the
following data has been collected from coastal areas in the southern hemisphere for 5
consecutive years in the middle of November. The recorded temperatures are all averages
across the 5 years of data.
Coastal ocean
Surface
Temperature
Latitude
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
14.1
15.2
16.2
17.5
18
21
22.1
23.8
24.5
24.2
24.4
26
26.9
28.2
28.5
28.8
29.8
29.8
31.2
32.5
Coastal Air
Temperature
16
17
15
15
18.5
22
24.5
24
25
26.5
30
31.6
30.4
33.5
33
32
32
33.5
34
30
Note: Temperature.xlsx is also attached.
a) Convert the latitude numerical variable to a categorical variable with 4 levels (very low,
low, moderate, high), using a statistical software package. Find the overall mean, group
means, and group standard deviations using the statistical package. Conduct an ANOVA
test to find the possible impact of latitude on coastal ocean surface temperature. Write
the assumptions of the model, write out the model in cell means/classical/regression
form, conduct the analysis in a statistical software package, run the Tukey HSD test if
needed, and state a conclusion based on the output.
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Transcribed Image Text:b) Plot a scatterplot with coastal ocean surface temperature (horizontal axis) and costal air
temperature (vertical axis). Interpret the output.
Solution
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