Enter the hypothesized mean difference (that is, the Null Hypothesis) into

the text-box “Hypothesized Mean Difference.” Enter the variances for the

two populations.

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

17

data analysis. Refer to section 41.4.

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Figure 150: Z-test for mean differences when population variance is known

The next table shows the result of a Z-test18.

Table 32: Output for Z-test for mean differences when population variance is known

Z-test: Two Sample for Means

s119 s2

Mean 7.3202 7.2345

Known Variance 32 40

Observations 168 168

Hypothesized Mean Difference 1.0

“1.397

P (Z< = z) one“tail 0.081

Z Critical one“tail 1.645

I do not supply the sample data for most of the examples in chapter 42 to chapter 46.

18

My experience is that many readers glaze over the examples and do not go through

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.

s1 and s2 are the labels, picked up from the first row in the range b1:b25 and c1:c25.

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Statistical Analysis with Excel

Z-test: Two Sample for Means

P (Z< = z) two“tail 0.163

Z Critical two“tail 1.960

Interpreting the output

The P value (that is “P (Z<= or >= z) two“tail”) of 0.081 implies that we

fail to reject the null for the two one“tail hypothesis. Moreover, Z= “1.397

implies that we “fail to reject” the null hypothesis because the Z is in the

acceptance region (“1.96,” ““1.96”) for the two“tail hypothesis.

The P value (that is “P (Z<>z) two“tail”) of 0.163 implies that we fail to

reject the null for the two“tail hypothesis. In addition, if we use a one“

tailed (left tail) test, we again fail to reject the null hypothesis because the

Z is in the acceptance region (“> “1.645”) for the left“tail hypothesis. If

we use a one“tail (right tail) test, we fail to reject the Null because the Z

is in the acceptance region (“< +1.645”) for the right“tail hypothesis.

T-TESTING MEANS WHEN THE TWO SAMPLES ARE

11.2

FROM DISTINCT GROUPS

11.2.A THE PRETEST” F-TESTING FOR EQUALITY IN VARIANCES

The T-test is used most often to test for differences in means across

samples from distinct groups. The respondents in the two samples differ.

An example is a pair of samples from two surveys on earnings, one survey

in country A and the other in country B. The formula used in estimating

the T statistic depends on the equality of variance for the data series

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across the two samples. In particular, if the variances of the two samples

are unequal the formula takes into account this difference across the

samples. An F-test is used to test for unequal variances.

The “F-test Two“sample for Variances” performs a test to compare the

variances across two groups of data. Launch the procedure by accessing

the menu option TOOLS/DATA ANALYSIS20 and selecting the “F-test

Two“sample for Variances.”

The relevant dialog is reproduced in the next figure.

Figure 151: F-test Two“Sample for Variances

Choose the “alpha” for level of significance. A 0.05 level sets up a 95%

confidence test.

The hypothesis:

” H0 (Null Hypothesis): σ12” σ 22 = 0