Using Lists & Spreadsheet 233
This test is useful in determining if the difference between a sample
mean and a population mean is statistically significant when you know
the true deviation for a population.
t-test (tTest)
t-Test (one-sample t test) performs a hypothesis test for a single unknown
population mean, m, when the population standard deviation, s, is
unknown. It tests the null hypothesis H
0
: m=m
0
against one of the
alternatives below.
•H
a
: mƒm
0
(m:ƒm0)
•H
a
: m<m
0
(m:<m0)
•H
a
: m>m
0
(m:>m0)
This test is similar to a z-test, but is used when the population is small and
normally distributed. This test is used more frequently than is the z-test
because small sample populations are more frequently encountered in
statistics than are large populations.
This test is useful in determining if two normally distributed populations
have equal means, or when you need to determine if a sample mean
differs from a population mean significantly and the population
standard deviation is unknown.
2-SampZTest (zTest_2Samp)
2-SampZTest (two-sample z test) tests the equality of the means of two
populations (m
1
and m
2
) based on independent samples when both
population standard deviations (s
1
and s
2
) are known. The null
hypothesis H
0
: m
1
=m
2
is tested against one of the alternatives below.
•H
a
: m
1
ƒm
2
(m1:ƒm2)
•H
a
: m
1
<m
2
(m1:<m2)
•H
a
: m
1
>m
2
(m1:>m2)
2-SamptTest (tTest_2Samp)
2-SamptTest (two-sample t test) tests the equality of the means of two
populations (m
1
and m
2
) based on independent samples when neither
population standard deviation (s
1
or s
2
) is known. The null hypothesis
H
0
: m
1
=m
2
is tested against one of the alternatives below.
•H
a
: m
1
ƒm
2
(m1:ƒm2)
•H
a
: m
1
<m
2
(m1:<m2)
•H
a
: m
1
>m
2
(m1:>m2)
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