l.hydro <-
  scan('http://math.uttyler.edu/nathan/classes/statistics/data/hw2-add.data')

summary(l.hydro)
boxplot(l.hydro)
#boxplot(l.hydro,rnorm(30,mean=mean(l.hydro),sd=sd(l.hydro)))

hist(l.hydro)

t.test(l.hydro)

#	One Sample t-test
#
#data:  l.hydro 
#t = 3.6799, df = 9, p-value = 0.005076
#alternative hypothesis: true mean is not equal to 0 
#95 percent confidence interval:
# 0.8976775 3.7623225 
#sample estimates:
#mean of x 
#     2.33 

# we are 95% confident that the average number of extra hrs of sleep of
# l.hydro takers is between .90 and 3.76

t.test(l.hydro,conf.level=.9)
# we are 95% confident that the average number of extra hrs of sleep of
# l.hydro takers is at least 1.17.


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### Problem Two


labor <-
  scan('http://math.uttyler.edu/nathan/classes/statistics/data/hw2-labor.data')

labor
boxplot(labor)
hist(labor)
summary(labor)

# t.test confidence interval the hard way
# method 1 -- not quite correct
mean(labor) - 1.96*sd(labor)/sqrt(length(labor))
mean(labor) + 1.96*sd(labor)/sqrt(19)

# method 2 -- correct
mean(labor) - qt(.975,df=18)*sd(labor)/sqrt(length(labor))
mean(labor) + qt(.975,df=18)*sd(labor)/sqrt(19)
  #### note qt(.975,df=18) is the analogue of 1.96 for the appropriate
  #### t distribution

# confidence interval the easy way:
t.test(labor)


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### Problem Three

labor.1 <-
  read.table('http://math.uttyler.edu/nathan/classes/statistics/data/hw2-labor1.data',header=TRUE)

names(labor.1)
increase <- labor.1$X1972-labor.1$X1968

t.test(increase)
#	One Sample t-test
#
#data:  increase 
#t = 2.4577, df = 18, p-value = 0.02435
#alternative hypothesis: true mean is not equal to 0 
#95 percent confidence interval:
# 0.004889895 0.062478527 
#sample estimates:
# mean of x 
#0.03368421 

# an increase of between .48% and 6.2% in female labor force
# participation is suggested by this data set (with 95% confidence)


t.test(increase,conf.level=.9)$conf.int
#[1] 0.009917895 0.057450526

# with 95% confidence we have an increase in female labor force
# participation of at least .99%