1-Sample t

 

Overview  |  How to  |  Data  |  Example

 

 

 

Overview

 

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  ¹ m0

 

where m is the population mean and m0 is the hypothesised population mean.

 

 

 

 

 

How to

 

1.       Choose ProcessMA > Basic Statistics > 1-Sample t.

 

2.       In Variable, select the column containing the sample.

 

3.       In Test mean, enter the hypothesised population mean.

 

4.       Click OK.

 

 

Optional

 

5.       In Alternate, select the type of test.

 

6.       In Confidence level, enter the desired confidence level for the confidence interval.

 

7.       Check Plot dotplot, if you want to display the Dotplot of the data and the hypothesis test parameters.

 

 

Note       To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.

 

 

 

 

 

Data

 

Variable: Numeric.

               

Test mean: Numeric.

 

Confidence level: Numeric; Between 0 and 100.

 

 

 

 

 

Example

 

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.

 

1.       Open worksheet ProcessMA > Tools > Data Files > Stat.xls.

 

2.       Choose ProcessMA > Basic Statistics > 1-Sample t.

 

3.       In Variable, select B – Measurement.

 

4.       In Test mean, enter 4.

 

5.       In Alternate, select Less than.

 

6.       In Confidence level, enter 95.

 

7.       Check Plot dotplot

 

8.       Click OK.

 

 

 

 

Interpretation

 

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.