Chapter 7 Single Sample Z-Test
Usage: To check for a difference between a sampe mean and a population mean.
Requirements: One variable that is interval/ratio, a population mean, and a population standard error.
Steps to conducting an single samples z-test:
- Write out null and alternative hypotheses
- Determine critical z-value for rejection of null hypothesis
A. Use degrees of freedom (df) and alpha level
- Calculate z-value for your data
A. You must first find the sample mean, population mean, and standard error
- Compare your calculated z-value to the critical z-value
A. If your calculated value is greater than the critical value, you reject the null hypothesis
B. If your calculated value is less than the critical value, you fail to reject the null hypothesis
- Calculate effect size (Cohen’s d)
7.1 Example Setup
7.1.1 Hypotheses
\(\Large H_0: \mu = value\)
\(\Large H_1: \mu \neq value\)
7.1.2 Critical z-Value (CV)
\(\Large df = n - 1\)
\(\Large \alpha = .05\)
\(\Large CV = [check\ table]\)
7.1.3 Calculate z
\(\Large N = number\ of\ scores\)
\(\Large \bar X = \frac{sum}{N}\)
\(\Large \sigma_{\bar X} = \frac{\sigma}{\sqrt{N}}\)
\(\Large z = \frac{\bar X - \mu}{\sigma_{\bar X}}\)
7.1.4 Compare Observed z to CV
If z is greater than the CV, reject the null hypothesis.
If z is less than the CV, fail to reject the null hypothesis.
7.1.5 Calculate Effect Size
\(\Large d = \frac{\bar X - \mu}{\sigma}\)