# Calculate the upper bound of the 95 range of likely

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Calculate the upper bound of the 95% range of likely sample means for this one-sided hypothesis test using the CONFIDENCE.NORM function. - CONFIDENCE.NORM finds the margin of error for a two-sided hypothesis test but we are interested in the upper bound of a one-sided test. To find the upper bound for the one-sided test we must first determine what two-sided test would have a 5% rejection region on the right side. Since the distribution of sample means is symmetric, a two-sided 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 two-sided test with alpha=0.1 will be the same as the upper bound on a one-sided 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 one-sided hypothesis test is the population mean plus the margin of error, which is approximately 6.7+0.33=7.03. Performing a one-sided hypothesis test using Excel is very similar to performing a two-sided test. To calculate the p-value for the sample mean we use the same function we learned about earlier. The only difference in setting up a one-sided test versus a two- sided test is the number we assign to the tails argument: 1 for a one-sided test and 2 for a two-sided 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 one-sided 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 single-population hypothesis tests, collecting a sample from one population and testing to see if its average was significantly different from the historical average.
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