Question 1

The precipitation data in "precip.txt" are precipitation values for Boulder, CO from

https://www.esrl.noaa.gov/psd/boulder/Boulder.mm.precip.html. Precipitation includes

rain, snow, and hail. Snow/ice water amounts are either directly measured or a ratio of

1/10 applied for inches of snow to water equivalent.

The purpose of this analysis is to assess the null hypothesis that the total annual rainfalls in

the early portion and the total annual rainfalls in the recent portion of the data are each

independent identically distributed (i.i.d.) samples from Normally distributed populations

with equal means, Normal(µ, arly) and Normal(μ, recent).

Unlike in a class setting, in practice, data formatting is often a major component of a data

analysis project. Some basic formatting of the data in "precip.txt" is included below for

reference.

The symbol "Tr" represents a trace amount of precipitation. Observations marked by a "*"

were made at a non-standard site. Some light-duty data formatting appears below that sets

"Tr" values to 0 and drops years that include an observation made at a non-standard site.

The code provided below reads in the precipitation data. The values are tab-separated.

Most columns are assigned the string class.

dat<-read.table("precip.txt", sep="\t",header = TRUE)

The following replaces all column names with lower case versions. For example, "TOTAL"

becomes "total". The command "names(dat)" is used to verify that the replacement has

succeeded./n1.a.

(10 points)

Since values in successive years may be related by persistent weather patterns, the data are

thinned to every third entry in "dat.s"

Please provide a visual assessment of the consistency with Normality of the first 15 values

for "year.total" in "dat.s" and of the consistency with Normality of the last 15 values for

"year.total" in "dat.s". Please give a verbal assessment based on the visualization.

dat.s<-filter (dat.trim, year%%3==2)/n1.b.

(5 points)

Please provide a visualization to examine whether the "year.total" values show smooth

variation over time or the "year.total" values at consecutive time points in "dat.s" appear to

be independent. Please state your assessment./n1.c.

(10 points)

Please perform a test of the null hypothesis that the total annual rainfalls in the early

portion and the total annual rainfalls in the recent portion are each i.i.d. samples from

Normally distributed populations with equal means, Normal(μ, early) and

Normal(μ, ocent). Please state your conclusion based on 1.a. and 1.b. regarding the null

hypothesis that the means in the two populations are equal.