Calculate the upper bound of the 95% range of likely sample means for this onesided hypothesis test
using the CONFIDENCE.NORM function.

CONFIDENCE.NORM finds the margin of error for a twosided hypothesis test but we are
interested in the upper bound of a onesided test. To find the upper bound for the onesided test
we must first determine what twosided test would have a 5% rejection region on the right side.
Since the distribution of sample means is symmetric, a twosided test with a 10% significance
level would have a 5% rejection region on the left side of the normal distribution and a 5%
rejection region on the right side. Thus, the upper bound for a twosided test with alpha=0.1 will
be the same as the upper bound on a onesided test with alpha=0.05. The margin of error is
CONFIDENCE.NORM(0.1,C3,C4)=0.33. The upper bound of the 95% range of likely sample
means for this onesided hypothesis test is the population mean plus the margin of error, which
is approximately 6.7+0.33=7.03.
Performing a onesided hypothesis test using Excel
is very similar to performing a twosided test. To calculate the pvalue for the sample mean we use the
same function we learned about earlier. The only difference in setting up a onesided test versus a two
sided test is the number we assign to the tails argument: 1 for a onesided test and 2 for a twosided
test.
=T.TEST(array1, array2, tails, type)
array1
is a set of numerical values or cell references. We will place our sample data in this
range.
array2
is a set of numerical values or cell references. We have only one set of data, so we will
use the historical mean, 6.7, as the second data set. To do this, we create a column with each
entry equal to 6.7.
tails
is the number of tails for the distribution. It can be either 1 or 2. Now that we are
performing a onesided test, we will enter a 1 instead of a 2.
type
can be 1, 2, or 3. Type 1 is a paired test and is used when the same group is tested twice
to provide paired “before and after” data for each member of the group. Type 2 is an unpaired
test in which the samples are assumed to have equal variances. Type 3 is an unpaired test in
which the samples are assumed to have unequal variances. The variances of the two columns
are clearly different in our case, so we use type 3. There are ways to test whether variances are
equal, but when in doubt, use type 3.
Alternative Excel Functions
T.TEST replaces the function:
=TTEST(array1, array2, tails, type)
Throughout the course we will provide alternative functions that existed prior to Excel 2010 that can
still be used in Excel 2010.
3.2.6 – Comparing two populations
So far, we have conducted
singlepopulation
hypothesis tests, collecting a sample from one
population and testing to see if its average was significantly different from the historical average.