the difficult step of drawing inferences from a result if the sample data results are

the same as those in the examples in the book.

If you do not see this option, then use TOOLS / ADD-INS to activate the Add-In for

27

data analysis. Refer to section 41.4.

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Chapter 11: Hypothesis Testing

test: Two“Sample Assuming Unequal Variances.” The relevant dialog is

shown in the next figure.

The range must consist of a single column or row and contain the same

number of data points as the first range.

Figure 152: T-test for Paired Samples

Place the hypothesized difference in means into the checkbox

“Hypothesized Mean Difference.” In this example, one is using the

hypothesis:

“H0 (Null Hypothesis): mean difference > 5”. See the next figure for

an example of setting the hypothesis for testing. Set a

hypothesized mean difference of zero to test the standard

hypothesis that the “Means for the two groups/samples are

statistically different.”

The level of significance for the hypothesis tests should be placed in

the checkbox “Alpha.” If you desire a significance level of “alpha =

.05” (that is, a Confidence level of 95%), then write in “.05” into the

checkbox Alpha. The next figure illustrates this.

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Statistical Analysis with Excel

Possible hypothesis for testing

u1 is the mean of sample one. u2 is the mean for sample two. The critical

regions are based on a 5% significance level (or, equivalently, a 95%

Confidence Interval)

(a) Two“tailed

The hypothesis

” H0 (Null Hypothesis): u1” u2 = 0

” Ha (Alternate hypothesis): u1” u2 <> 0

Critical region:

” “Fail to accept” the null hypothesis if the absolute value of the

calculated T is higher than 1.96. Examples of such T values are:

“+2.12” and ““2.12.”

” “Fail to reject” the null hypothesis if the absolute value of the

calculated T is lower than 1.96. Examples of such T values are:

“+1.78,” “0.00” and ““1.78.”

In short, if the absolute value of the T is higher than 1.96, then one may

conclude (with 95% Confidence) that the means of the samples differ by

the hypothesized difference.

(b) One“tailed (left-tail)

The hypothesis:

” H0 (Null Hypothesis): u1” u2 >= 0

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Chapter 11: Hypothesis Testing

” Ha (Alternate hypothesis): u1” u2 < 0 (one“tailed)

Critical region:

” “Fail to accept” the null hypothesis if the value of the calculated

T is lower than ““1.64.” Examples of such T values are: ““2.12”

and ““1.78.”

” “Fail to reject” the null hypothesis if the absolute value of the

calculated T is greater than ““1.64”. Examples of such T values

are: “+1.78” and “0.00.”

In short, if the T is lower than ““1.64,” then one may conclude (with 95%

Confidence) that the means of the samples differ by the hypothesized

difference.

(c) One“tailed (right-tail)

The hypothesis:

” H0 (Null Hypothesis): u1” u2 <= 1

” Ha (Alternate hypothesis): u1” u2 > 1 (one“tailed)

Critical region:

” “Fail to accept” the null hypothesis if the value of the calculated

T is greater than “+1.64.” Examples of such T values are: “+2.12”

and “+1.78.”

” “Fail to reject” the null hypothesis if the absolute value of the

calculated T is less than “+1.64.” Examples of such T values are:

““1.78” and “0.00.”