## One-sample t Test - Example

#### Data

This data set was collected by Bob Zarr of NIST in January, 1990 from a heat flow meter calibration and stability analysis. The response variable is a calibration factor. The motivation for studying this data set is to illustrate a well-behaved process where the underlying assumptions hold and the process is in statistical control.

Source: http://www.itl.nist.gov/div898/handbook/eda/section4/eda4281.htm

#### Analysis

- Open the DataBook
*compare.vstz*

open this data file via the**Help / Open Examples**menu; it is in the Sample Data - Select the sheet
*zarr13* - Choose the menu
**Analyze**and the command**One t-Test** - In
**Variables**, select*Calib*. - In Hypothesized mean, enter 5.
- Click
**OK**

#### Output

By default, R code is printed after parsing and before
evaluation.

You can avoid this in **File / Option / Advanced**
menu.

DataSheet is converted to DataFrame, in the form *
DataBook.DataSheet*

> ## Summary Statistics: > summary.vst(zarr13.Sheet1[,c('Calib')], statistics = c('mean','semean','sd','nobs')) nobs mean sd semean 195 9.261461 0.0227888 0.00163194 > ## Perform one sample t-test: > t.test(zarr13.Sheet1$Calib, alternative = 'two.sided', mu = 5, conf.level = 0.95) One Sample t-test data: zarr13.Sheet1$Calib t = 2611.286, df = 194, p-value < 2.2e-16 alternative hypothesis: true mean is not equal to 5 95 percent confidence interval: 9.258242 9.264679 sample estimates: mean of x 9.261461 > ## Find two-tailed critical values: > qt(0.975,194) [1] 1.972268

#### Results

We are testing the null hypothesis that the population mean is 5. The alternative hypothesis is that the population mean is not equal to 5. The test statistic t is calculated as 2611.286

We reject the null hypotheses for our two-tailed t-test because the absolute value of the test statistic is greater than the critical value.

The confidence interval provides an alternative to the hypothesis test. If the confidence interval contains 5, then null hypotheses cannot be rejected. In our example, the confidence interval (9.258242, 9.264679) does not contain 5, indicating that the population mean does not equal 5 at the 0.05 level of significance.

#### Resource

- NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm, 10/30/2013
- Probability and statistics EBook