# 17.3.1 One-Sample T-Test

## Introduction

The one-sample Student's t-Test determines whether or not the mean of a sample taken from a normally distributed population is consistent with the hypothetical value for a given confidence level. By choosing a one- or two-tailed t-test, you can test how likely it is that the sample mean is greater than, less than, or equal to the true population mean. Note that the one-sample t-test is appropriate when the standard deviation of the entire population is unknown.

The t statistic value and p-value will be calculated to decide whether or not to reject the null hypothesis. The p-value is the probability that null hypothesis is true, and a small p-value suggests that you should reject it.

The confidence interval provides lower and upper limits for the possible value of the population mean. For a given significance level, $\alpha$, this interval indicates we have $(1-\alpha )\times 100\%$ confidence to say the true population mean falls within the interval.

## Handling Missing Values

The missing values in the data range will be excluded in the analysis

## Performing One-Sample t-test

To perform a one-sample t-test:

1. Select Statistics: Hypothesis Testing: One-Sample t-Test. This opens the OneSampletTest dialog.
2. Specify your Input Data, the Test Mean, and the desired Alternative Hypothesis.
3. Upon clicking OK, a report table sheet is generated to show the degrees of freedom, t statistics, the associated p-value, and the test conclusion. In addition, you can generate confidence intervals for the sample mean; histogram and box chart; and a power analysis, which computes the probability of rejecting the null hypothesis when the alternative hypothesis is true, given the sample size.
 Topics covered in this section: Tutorial