# Struggling to Run a Z-Test in Excel?

## QI Macros can run a z test and interpret the results for you in seconds!

### 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?

### z Test Example using QI Macros add-in for Excel

New Training Technique Designed to Increase IQ - This example was taken from Statistical Analysis in Excel for Dummies by Joseph Schmuller.

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. Input the results in Excel.

#### To conduct a z test using QI Macros add-in:

1. Click and drag over your data to select it. 2. Now click on QI Macros Menu > Statistical Tools > f and t tests > Z-Test two sample for means test.
3. QI Macros will prompt you to enter a significance level (default = 0.05) and a hypothesized mean difference (in this case 0).  4. QI Macros will calculate the variance for each data set selected and give you the opportunity to type in another value if appropriate.  5. Q Macros will perform the z test calculations AND interpret the results for you:
6. 7. QI Macros will also draw a Values Plot to help you visualize the data.

### Interpreting the z test Results

QI Macros compares the p-value (0.192) to the significance level (0.05) and interprets the result for you. In this example we "Cannot Reject the Null Hypothesis because p > 0.05 (Means are not Different)."

• 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 (Accept the null hypothesis) p value < a Reject the null hypothesis p value > a Cannot Reject the null hypothesis (Accept 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 (accept 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 (Means are Different/Means are not the Same).