1. Hurricanes with lower minimum central pressure (measured in millibars) are more intense because when the pressure at the ocean's surface inside a hurricane is lower, more warm air and moisture is pulled into the eye of the hurricane at a faster rate. We know based on computer simulations that historically (pre-industrial), hurricane intensities have followed a normal distribution with a mean of 934 mb and a standard deviation of 30 mb. Idealized hurricane simulations Aggregate results: 9 GCMs, 3 basins, 4 parametrizations, 6 member ensembles No. of occurrences 160 CATEGORY S 140 GO Control (mean-934.11) 100 80 60 40 20 High CO, (mean-923.68) 880 00000 900 920 CATEGORY 4 CATEGORY 940 Minimum Central Pressure (mb) a. What is the probability of a hurricane being less than 900 mb? Use the z-score % b. Climate model simulations can simulate hurricane frequency and intensity under different emissions scenarios. Simulations of hurricane intensity under high-CO, scenarios through year 2050 resulted in the distribution of intensity values plotted above (black lines and points). This represents about 700 simulations, with a sample mean of 923 mb and sample standard deviation of 25 mb. Compare this with the historic (pre-industrial) average intensity. i. What is the null hypothesis? Ο μ = 934 ☐ <934 ii. What is the one-sided alternative hypothesis? Ο μ = 934 Ο μ < 934 Ο μ > 934 934 Ο μ > 934 Ο μ. 934 iii. Test this hypothesis at 1% significance level assuming the historic (i.e., population) standard deviation is 30 mb. What is the value of your test statistic? (2 sig fig) What is the outcome of your test? Value of test statistic: Reject the null hypothesis Fail to reject the null hypothesis iv. Test this hypothesis at 1% significance level assuming that we don't know/aren't sure of the population standard deviation for preindustrial hurricanes since they are simulated (and thus can have artificially large n-values). What is the value of your test statistic? (2 sig fig) What is the outcome of your test? Reject the null hypothesis Value of test statistic: Fail to reject the null hypothesis 2
1. Hurricanes with lower minimum central pressure (measured in millibars) are more intense because when the pressure at the ocean's surface inside a hurricane is lower, more warm air and moisture is pulled into the eye of the hurricane at a faster rate. We know based on computer simulations that historically (pre-industrial), hurricane intensities have followed a normal distribution with a mean of 934 mb and a standard deviation of 30 mb. Idealized hurricane simulations Aggregate results: 9 GCMs, 3 basins, 4 parametrizations, 6 member ensembles No. of occurrences 160 CATEGORY S 140 GO Control (mean-934.11) 100 80 60 40 20 High CO, (mean-923.68) 880 00000 900 920 CATEGORY 4 CATEGORY 940 Minimum Central Pressure (mb) a. What is the probability of a hurricane being less than 900 mb? Use the z-score % b. Climate model simulations can simulate hurricane frequency and intensity under different emissions scenarios. Simulations of hurricane intensity under high-CO, scenarios through year 2050 resulted in the distribution of intensity values plotted above (black lines and points). This represents about 700 simulations, with a sample mean of 923 mb and sample standard deviation of 25 mb. Compare this with the historic (pre-industrial) average intensity. i. What is the null hypothesis? Ο μ = 934 ☐ <934 ii. What is the one-sided alternative hypothesis? Ο μ = 934 Ο μ < 934 Ο μ > 934 934 Ο μ > 934 Ο μ. 934 iii. Test this hypothesis at 1% significance level assuming the historic (i.e., population) standard deviation is 30 mb. What is the value of your test statistic? (2 sig fig) What is the outcome of your test? Value of test statistic: Reject the null hypothesis Fail to reject the null hypothesis iv. Test this hypothesis at 1% significance level assuming that we don't know/aren't sure of the population standard deviation for preindustrial hurricanes since they are simulated (and thus can have artificially large n-values). What is the value of your test statistic? (2 sig fig) What is the outcome of your test? Reject the null hypothesis Value of test statistic: Fail to reject the null hypothesis 2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:1.
Hurricanes with lower minimum central pressure (measured in millibars) are more intense because when the
pressure at the ocean's surface inside a hurricane is lower, more warm air and moisture is pulled into the eye of the
hurricane at a faster rate. We know based on computer simulations that historically (pre-industrial), hurricane
intensities have followed a normal distribution with a mean of 934 mb and a standard deviation of 30 mb.
Idealized hurricane simulations
Aggregate results: 9 GCMs, 3 basins, 4 parametrizations, 6 member ensembles
No. of occurrences
160
CATEGORY S
140
GO Control (mean-934.11)
100
80
60
40
20
High CO, (mean-923.68)
880
00000
900
920
CATEGORY 4
CATEGORY
940
Minimum Central Pressure (mb)
a. What is the probability of a hurricane being less than 900 mb? Use the z-score
%
b. Climate model simulations can simulate hurricane frequency and intensity under different emissions scenarios.
Simulations of hurricane intensity under high-CO, scenarios through year 2050 resulted in the distribution of
intensity values plotted above (black lines and points). This represents about 700 simulations, with a sample
mean of 923 mb and sample standard deviation of 25 mb. Compare this with the historic (pre-industrial)
average intensity.
i. What is the null hypothesis?
Ο μ = 934
☐ <934
ii. What is the one-sided alternative hypothesis?
Ο μ = 934
Ο μ < 934
Ο
μ > 934
934
Ο μ > 934
Ο μ. 934
iii. Test this hypothesis at 1% significance level assuming the historic (i.e., population) standard deviation is 30
mb. What is the value of your test statistic? (2 sig fig)
What is the outcome of your test?
Value of test statistic:
Reject the null hypothesis
Fail to reject the null hypothesis
iv. Test this hypothesis at 1% significance level assuming that we don't know/aren't sure of the population
standard deviation for preindustrial hurricanes since they are simulated (and thus can have artificially large
n-values). What is the value of your test statistic? (2 sig fig) What is the outcome of your test?
Reject the null hypothesis
Value of test statistic:
Fail to reject the null hypothesis
2
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