# 1-sample z-test

The one sample *z*-test is a test for a difference in mean between a sample and hypothesised mean, when the population standard deviation is known.

The requirements of the test are:

- A sample measured on a continuous scale from a population with normal distribution.
- Known population standard deviation.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain a continuous scale variable.

When entering new data we recommend using New Dataset to create a new **1 variable** dataset ready for data entry.

**Using the test**** **

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Distribution**on the**Analyse-it**tab, then click**z-test**. - Click
**Variable**and select the variable to compare. - Enter
**Hypothesised mean**. - Enter
**Population standard deviation**. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Enter
**Confidence interval**to calculate for the mean. The level should be entered as a percentage, between 50 and 100 without the % sign. - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Distribution** then click **z-test**.

X ≠ hypothesised mean to test if the mean is not equal to the hypothesised mean. |

X > hypothesised mean to test if the mean is greater than the hypothesised mean. |

X < hypothesised mean to test if the mean is less than the hypothesised mean. |

The report shows the number of observations analysed, number of missing values excluded, summary statistics for the sample, and the hypothesised mean and population standard deviation.

The mean of the sample and confidence interval are shown.

The Z statistic and hypothesis test are shown. The *p*-value is the probability of rejecting the null hypothesis, that the sample mean is the same as the hypothesised mean, when it is in fact true. A significant *p*-value implies that the sample mean is different from the hypothesised mean.

## Further reading & references

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 121.

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