Page 59 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

One Sample t-Test

One sample t-test is also used when a researcher wants to compare
one sample mean value with the population mean value.

Questions answered:

3. Did a particular sample come from a given population?

4. Is a group mean significantly different/greater/less than the
population it represents?

Formula:
̅

√
where ̅ = sample mean
= population mean (given)
= sample standard deviation (given)
= sample size
Main difference between Z-test and t-Test

Most often, the population standard deviation, is not known,
therefore
1. We are unable to calculate the z-score.
2. Luckily, we can estimate with s, the sample standard
deviation.
3. However, one new problem is that we no longer have a
normal distribution by using s as an estimate for .
4. We will now use the t-distribution when the population
standard deviation is not known and sample size is small.

The Theory and Applications of Statistical Inferences 43