The 1-Sample Z conducts a hypothesis test of the mean based on sampled data when the population standard deviation, s is known. It also calculates a confidence interval of the mean. This procedure is based on normal distribution. For larger samples (>30), the sample standard deviation may be used in the absence of the population standard deviation. For smaller samples, make sure the data is drawn from a normal distribution or the t-test may be more appropriate.
| Test | Null Hypothesis, H0 | Alternate Hypothesis, H1 |
| One-tailed | m = m0 | m < m0 or m > m0 |
| Two-tailed | m = m0 | m <> m0 |
where m is the population mean and m0 is the hypothesised population mean
At the Excel Menu (For Excel 2007, go to Add-ins first)
Choose ProcessMA > Statistics > Basic Statistics > 1-Sample Z
In Variable, select the column containing the data (Numeric)
In Test Mean, enter hypothesized population mean (Numeric)
In Sigma, enter population standard deviation (Numeric, >0)
In Alternate, select the appropriate alternate test
In Confidence Level, enter value for confidence level (Numeric, >0 & <1)
You measured the thickness of 30 new widgets made. You know that the thicknesses of these parts are normally distributed with a standard deviation of 1.4. You want to test if the population mean is 57 and also calculate a 90% confidence interval for the mean.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Statistics > Basic Statistics > 1-Sample Z
In Variable, select K - Thickness
In Test Mean, enter 57
In Sigma, 1.4
In Confidence Level, enter 0.90
Click OK
For a desired a = 0.05, since p = 0.0002 < a, we will reject H0. Therefore, we conclude that there is significant evidence that the population mean is not equal to 57. We can also observe from the dotplot that the hypothesised value falls outside the 90% confidence interval for population mean (55.626, 56.467). Therefore, H0 will also be rejected for a = 0.10.
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