Question

4. Chapter 12: Using the attached dataset “Chapter 12 Data Set 1” to determine whether there was a change in tons of paper before vs. after a recycling program in these 25 districts. a. Is this a directional or non-directional hypothesis? b. Should you use a one-tailed or two-tailed test? c. Is a dependent samples t-test an appropriate way to analyze these data? d. Conduct the between groups t-test using Excel (either method). Use the .05 confidence level. What is your conclusion?

District   Before Recycling   After Recycling
District1   20   23
District2   6   8
District3   12   11
District4   34   35
District5   55   57
District6   43   76
District7   54   54
District8   24   26
District9   33   35
District10   21   26
District11   34   28
District12   33   31
District13   54   56
District14   23   22
District15   33   35
District16   44   41
District17   65   56
District18   43   34
District19   53   51
District20   22   21
District21   34   31
District22   32   33
District23   44   38
District24   17   15
District25   28   27

Answer 1

( a ) This is non-directional hypothesis

( b )  use a two-tailed test

( c ) yes dependent samples t-test an appropriate way to analyze these data

( d )

For the given data using t-Test: Paired Two Sample for Means in Excel we get output as

t-Test: Paired Two Sample for Means
	before	after
Mean	34.44	34.8
Variance	218.7567	259.75
Observations	25	25
Pearson Correlation	0.88013
Hypothesized Mean Difference	0
df	24
t Stat	-0.23453
P(T<=t) one-tail	0.408283
t Critical one-tail	1.710882
P(T<=t) two-tail	0.816566
t Critical two-tail	2.063899

So from the above output  

P value > l.o.s

0.8166 > 0.05

so fail to reject H0

Conclusion :

At alpha = 0.05 l.o.s there is no evidence to support the claim that  there was a change in tons of paper before vs. after a recycling program in these 25 districts