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 = 1

” Ha (Alternate hypothesis): u1” u2 <> 1

Critical region:

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

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

“+2.12” and ““2.12.”

183

Statistical Analysis with Excel

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

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

“+1.78,” “0.00” and ““1.78.”

In short, if the absolute value of the Z 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 >= 1

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

Critical region:

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

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

and ““1.78.”

” “Fail to reject” the null hypothesis if left-tail)

The value of the calculated Z is greater than ““1.64.” Examples of such Z

values are: “+1.78” and “0.00.”

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

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

difference.

184

Chapter 11: Hypothesis Testing

(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

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

and “+1.78.”

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

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

““1.78” and “0.00.”

In short, if the Z is greater than “+1.64,” then one may conclude (with 95%

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

difference.

Excel calculates the P or Significance value for each test you run.

” If P is less than 0.10, then the test is significant at 90%

Confidence (equivalently, the hypothesis that the means are

equal can be rejected at the 90% level of Confidence). This

criterion is considered too “loose” by some.

185

Statistical Analysis with Excel

” If P is less than 0.05, then the test is significant at 95%

Confidence (equivalently, the hypothesis that the means are

equal can be rejected at the 95% level of Confidence). This is the

standard criterion used.

” If P is less than 0.01, then the test is significant at 99%

Confidence (equivalently, the hypothesis that the means are

equal can be rejected at the 99% level of Confidence). This is the

strictest criterion used.

You should memorize these criteria, as nothing is more helpful in

interpreting the output from hypothesis tests (including all the tests

intrinsic to every regression, ANOVA and other analysis).

Go to TOOLS/DATA ANALYSIS17. Select the option “Z-test.” The dialog