# Z-Test two sample for means in Excel using the QI Macros

### When to use the Z-Test two sample for means

• to compare population and sample means to determine if there is a significant difference
• to compare means between two samples,
• to compare the mean of one sample to a given constant.

The Z-test is typically used in evaluating the results of standardized tests. Are the results from a sample of students outside of or within the standard test performance? Consider the following example taken from Statistical Analysis in Excel for Dummies by Joseph Schmuller.

### Example: New Training Technique Designed to Increase IQ

Imagine a new training technique designed to increase IQ. Take a sample of 25 people and train them using the new technique. Take another sample of 25 people and give them no special training.

Now, conduct a test with the two samples and input their scores into Excel:

Then, select the data with the mouse and click on the QI Macros Menu to select the Z-Test two sample for means test:

The QI Macros will prompt for a significance level (default = 0.05):

a hypothesized mean difference (in this case 0 ):

and variances for variables 1 and 2

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The QI Macros Z-Test will perform the calculations and interpret the results for you:

### What's Cool About Z-Test Calculations in the QI Macros?

When you run the Z-Test, the QI Macros will compare the p-value (0.192) to the significance level (0.05) and interpret the results for you. Cannot Reject the Null Hypothesis because p > 0.05" and that the "Means are the same".

### Interpreting the Z-Test results manually

• The null hypothesis H0 is that the mean difference = 0
or in other words the means are the same
• The alternative hypothesis Ha is that the mean difference is > 0
or in other words that the mean of the trained population is larger
 If Then test statistic > critical value  (i.e. z> zcrit) Reject the null hypothesis test statistic < critical value  (i.e. z< zcrit) Cannot Reject the null hypothesis p value < a Reject the null hypothesis p value > a Cannot Reject the null hypothesis

Since the null hypothesis is that the means are the same this is a two-sided test. Therefore, use the two-tail values for your analysis.

Since the z statistic < zcritical (1.305 < 1.960) and p value > a ( 0.192> 0.05) , we cannot reject the null hypothesis that the means are the same.

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### One-Sample Z-Test

To do a one-sample z-test on the New data above, use native Excel formulas in an empty cell:

=ztest(A1:A26,100)
Gives p=0.015
Since the p-value is < 0.05, we can reject the null hypothesis.