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


t.test(Sleep)


#	One Sample t-test
#
#data:  Sleep 
#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 


#alternative hypothesis: true mean is not equal to 0 
# H1: mu =/= 0
# H0: mu = 0
#
#p-value = 0.005076

# With such a small p-value, the null hypothesis seems to be very
# unlikely (our sample would have to be about 1/200) so it seems
# reasonable to conclude that the null is wrong and the alternative
# hypothesis is true.

### Statistics speak:

### With a p-value of .005076 we reject the null hypothesis in favor of
### the alternative hypothesis that mu =/= 0.


### To test H1: mu =/= 1 versus H0: mu = 1 do:
t.test(Sleep,mu=1.5)

t.test(Sleep,mu=.8976775)

### To test H1: mu > 0 versus H0: mu <= 0 do:
t.test(Sleep,alternative='greater')

### with a p-value of .002538 we reject the null hypothesis in favor of
### the alternative and conclude that the true mean is greater than 0

t.test(Sleep,conf.level = .9)


### H0: mu <= 2   H1: mu > 2
t.test(Sleep,mu=2,alternative='greater')

### with a p-value of .3074 we fail to reject the null hypothesis and
### are unable to conclude that the true mean is larger than 2