Hypothesis test: T-Test
µ
1
-
µ
2
A farmer compared the 15-day mean weight of two sets of chicks, one group receiving feed
supplement A and the other supplement C. Twenty two chicks only one day old were assigned
randomly to the two groups. To distinguish between the two groups of eleven, which were caged
together to minimize other influences, the heads of the chicks were stained red and purple
respectively with a harmless vegetable dye.
The individual weights were recorded in the table below. From the means at the end of the table it
appears that supplement A produces a higher mean weight.
Weights
x
X
σ
Supp.
A 57 120 101 137 119 117 104 73 53 68 118 97 27.75
Supp.
C 89 30 82 50 39 22 57 32 96 31 88 56 26.54
The farmer wishes to know, at the 1% test level, whether this is statistically significant.
Our hypotheses are:
H
0
:
The effects are the same
(
µ
=
µ
)
ie. There is no effect from the supplement.
1
2
H
A
:
Supplement A is better
(
µ
>
µ
)
1
2
Enter the data into columns
C1
and
C2
of the Statistics aplet.
We are dealing with two independent samples in this case and so we
need to choose from those tests which involve two samples.
again use a Student-t test.
view to
ed.
Since we know the standard deviations of only these samples, we must
We then change to the
NUM SETUP
import the summary statistics. The import screen can be seen on the
The results of the importation can be seen right. Since the two standard
deviations for the samples are similar, and the sample sizes are the
same, a more accurate estimate of the population standard deviation will
right.
be obtained if the data is pooled, so ensure that this option is
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