t Test Write-up: Matched Pairs
Problem 11.12
Growing Tomatoes
Problem 11.12. Growing Tomatoes: An agricultural field trial
compares the yields of two varieties of tomatoes for commercial
use. The researchers divide in half each of 10 small plots of land
in different locations and plant each tomato variety on half of each
plot. After harvest, they compare the yields in pounds per plant
per location. The 10 differences (Variety A-Variety B) give
x 0.34 and s0.83. Is there convincing evidence that Variety A
has the higher mean yield?
We will now make a 7-step write-up for this problem. This
example follows a matched pairs design. We treat the differences
as our sample data. Each pair of data points is used to find a
difference. This cannot be computed by merely subtracting the
means of the two groups.
Step 1:
H0:  = 0
The mean difference in yield between
Varieties A and B is zero.
Ha:  > 0
The mean difference in yield between
Varieties A and B is positive.
 = (yield of Variety A ) - (yield of Variety B)
Step 2:
Assumptions:
•We have a simple random sample, provided there was random
allocation of varieties to the positions in each plot.
•We are uncertain of meeting the requirement for normal
distribution and lack data to analyze.
Step 3:
t
x  0 .34  0

1.295
s
.83
n
10
df=9

Step 4:
This graph is made on the TI-83 by using Shade_t. To use this
command first clear drawings. Press <2nd> <DRAW>
<1:ClrDraw>.
Then <2nd> <DISTR> <DRAW> <2:Shade_t(>. Then enter
1.295,100,9). The format is Shade_t(lower bound, upper
bound,degrees of freedom).
Step 5:
P-value = P(t>1.295)=0.1137.
Step 6:
Fail to reject H0, a value this extreme will
occur by chance alone 11% of the time.
Step 7:
We lack strong evidence of a higher
yield for Variety A. While there is some
evidence of a higher yield, it was not
significant at the 10% level. We were
not able to verify that the population of
differences was normally distributed so
this is a further concern.
THE END