The 1-Sample t conducts a hypothesis test of the mean based on sampled data when the population standard deviation, s is unknown. It also calculates a confidence interval of the mean. This procedure is based on the t-distribution which is derived from a normal distribution. It is more conservative than the Z-test for smaller sample sizes or when s is unknown.
| 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 t
In Variable, select the column containing the data (Numeric)
In Test Mean, enter hypothesized population mean (Numeric)
In Alternate, select the appropriate alternate test
In Confidence Level, enter value for confidence level (Numeric, >0 & <1)
Click OK
You made measurements on 12 parts. You know that the measurements are normally distributed but the population standard deviation is unknown. You want to test if the population mean is less than 4 and calculate the 95% confidence interval for the mean.
Open data worksheet by choosing ProcessMA > Tools > Data
Choose ProcessMA > Statistics > Basic Statistics > 1-Sample t
In Variable, select BK - Measurement
In Test Mean, enter 4
In Alternate, select Less than
Click OK
For a desired a = 0.05, since p = 0.0694 > a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the population mean is less than 4. We can also observe from the Dotplot that the hypothesised value falls within the 95% confidence interval for the population mean.
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