# Z-Test Two Sample for Means in Excel

## QI Macros Add-in for Excel Makes Conducting Z tests a Snap

### 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: 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:

- Select the data, then click on QI Macros Menu-> Statistical Tools -> f and t tests, then Z-Test two sample for means test:

- QI Macros will prompt you to enter:
- a significance level (default = 0.05):
- a hypothesized mean difference (in this case 0 ):

- QI Macros will calculate the variance for each data set selected and give you the opportunity to type in another value if appropriate.
- Q Macros will perform the z test calculations AND interpret the results for you:
- In the July 2022 version of QI Macros, the Box & Whisker Plot output was removed and replaced with a Values Plot output, as Values Plots provide simpler visual representations of your data.:

**Interpreting the z test Results**

**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:"Cannot Reject the Null Hypothesis (Accept the Null Hypothesis) because p > 0.05 (Means are the Same/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.

### 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).

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