SUMMARY

We will work on this exercise with a new data set (i.e., “fema_claims_random.csv Download fema_claims_random.csv”). First, a little story about this data set: in 1968, the Congress of the US passed the National Flood Insurance Act, creating the National Flood Insurance Program (NFIP) to reduce future flood losses through flood hazard identification, manage floodplains, and provide insurance protection. In other words, the NFIP offers insurance coverage for building structures as well as for contents and personal property within the building structures to eligible and insurable properties. The data you’ll be using is derived from the NFIP system of record, staged in the NFIP reporting platform, and redacted to protect policyholders’ personally identifiable information. The original dataset has more than 2.5 million observations, but here you will use a 5% random sample stratified by the state where the property is located. That is, within each state, we took a 5% random sample of every NFIP record. Each row in the data set represents a record, and you can look at the description of each variable in the workbook Download workbook. For this homework, we will be using just a subset of variables. Imagine you are working for a planning research group that is trying to understand the consequences of flood on the real estate market. For your annual report, you would like to provide the reader with a general description of FEMA’s NFIP program across space and time.

Setting up working environment
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Create a new table of data from the “MASSZONG.xls”

masszoning <- read_xls("MASSZONING.xls")
femaclaim <- read.csv("fema_claims_random.csv")

1. Basic Statistics of the National Flood Insurance Program

• What’s the mean, median, and standard deviation of the total insurance amount paid in dollars on the building (variable: totalbuildinginsurancecoverage) and the total insurance amount paid in dollars on the contents
view(femaclaim)

building_insurance <- femaclaim$totalbuildinginsurancecoverage
content_insurance <- na.omit(femaclaim$totalcontentsinsurancecoverage)

#find the sample mean
x_hat_building <- mean(building_insurance)
x_hat_building
## [1] 157332.1
x_hat_content <- mean(content_insurance)
x_hat_content
## [1] 30321.81
#find the median
median_building <- median(building_insurance)
median_building
## [1] 100000
median_content <- median(content_insurance)
median_content
## [1] 11500
#find sd 
sd_building <- sd(building_insurance)
sd_building
## [1] 1176810
sd_content <- sd(content_insurance)
sd_content
## [1] 49813.11

The amount paid in dollars on building is significantly larger (~5 times) than the total insurance amount paid in dollars on the contents

• Graph the total number of flood claims by year of loss (variable: yearofloss). That is, on the y-axis the total number of claims by year and on the x-axis the year of loss.
ggplot(data = femaclaim, aes(yearofloss))+geom_bar()

##### • What’s the year with the highest number of flood claims? What extreme weather event could explain this pattern? 2005 has the highest number of flood claims due to Hurricane Katrina

2. The ever-increasing cost of the National Flood Insurance Program over time: a colleague of yours suggests providing the reader with proof of whether the average total insurance amount paid in dollars on the building has changed over time. For each of the following questions, please provide the null and alternative hypotheses, the p-value of the test, and answer whether you can reject the null hypothesis at the 5% level.

Is the average total insurance amount paid in dollars on the building different between the year of loss in 2000 and 2010?

Ho: avg insurance paid are same Ha: avg insurance paid are different

a <- 0.05

fema_subset_2000 <- femaclaim %>% filter(yearofloss == 2000) %>% select(yearofloss, totalbuildinginsurancecoverage)
fema_subset_2010 <- femaclaim %>% filter(yearofloss == 2010) %>% select(yearofloss, totalbuildinginsurancecoverage)
fema_subset_2020 <- femaclaim %>% filter(yearofloss == 2020) %>% select(yearofloss, totalbuildinginsurancecoverage)

t.test(fema_subset_2000, fema_subset_2010)
## 
##  Welch Two Sample t-test
## 
## data:  fema_subset_2000 and fema_subset_2010
## t = -0.77039, df = 5303.8, p-value = 0.4411
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -127728.76   55661.36
## sample estimates:
## mean of x mean of y 
##  103766.3  139800.0
t.test(fema_subset_2010, fema_subset_2020)
## 
##  Welch Two Sample t-test
## 
## data:  fema_subset_2010 and fema_subset_2020
## t = -0.61511, df = 5541.3, p-value = 0.5385
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -120275.11   62824.09
## sample estimates:
## mean of x mean of y 
##  139800.0  168525.5
t.test(fema_subset_2000, fema_subset_2010)$p.value < a
## [1] FALSE
t.test(fema_subset_2010, fema_subset_2020)$p.value < a
## [1] FALSE

Because the p values are larger than the critical value, we can not reject the null hypothesis. The average total insurance amount paid in dollars on the building has not changed over time.

3. For the year of loss in 2005, you would like to show that the distribution of occupancy type (variable: occupancytype) of the filed claims is statistically different between the states (variable: state) of Louisiana (i.e., LA) and Mississippi (i.e., MS).
• Is the number of flood claims between the states of Louisiana and Mississippi independent of the occupancy type? Please state the null and alternative hypothesis and show whether we can reject the null at the 1% level.

Ho: Number of flood claims between the states of Louisiana and Mississippi are NOT independent of the occupancy type;

Ha: Number of flood claims between the states of Louisiana and Mississippi are independent of the occupancy type

a = 0.01

fema_subset_types <- femaclaim %>% filter(state %in% c('MS', 'LA') & yearofloss == 2005) %>% select(state, occupancytype)

#inspect the new table
head(fema_subset_types)
##   state occupancytype
## 1    LA             1
## 2    LA             1
## 3    LA             1
## 4    LA             1
## 5    LA             1
## 6    LA             1
fema_subset_types_chisqtest <- chisq.test(fema_subset_types$state, fema_subset_types$occupancytype)
## Warning in stats::chisq.test(x, y, ...): Chi-squared approximation may be
## incorrect
fema_subset_types_chisqtest
## 
##  Pearson's Chi-squared test
## 
## data:  fema_subset_types$state and fema_subset_types$occupancytype
## X-squared = 73.182, df = 6, p-value = 9.084e-14
# p-value of our test is < 2.2e-16, which is smaller than critical value a 0.01
fema_subset_types_chisqtest$p.value < a
## [1] TRUE

We reject the null hypothesis. The number of flood claims between the states of Louisiana and Mississippi are independent of the occupancy type.