One-sample t-test

Definition

A one-sample t-test is a statistical test used to determine whether the mean of a single sample is significantly different from a known or hypothesized population mean. This test is particularly useful when the sample size is small and the population standard deviation is unknown, allowing for inferences about the population based on sample data.

5 Must Know Facts For Your Next Test

1. The one-sample t-test assumes that the sample data is normally distributed, particularly important when dealing with smaller samples.
2. It calculates the t-statistic by taking the difference between the sample mean and the hypothesized population mean, divided by the sample standard deviation adjusted for sample size.
3. The resulting t-statistic is then compared to a critical value from the t-distribution table based on degrees of freedom to determine statistical significance.
4. If the p-value obtained from the t-test is less than the chosen significance level (commonly 0.05), the null hypothesis can be rejected, indicating a significant difference.
5. One-sample t-tests are commonly used in various fields, including psychology and medicine, to evaluate whether treatment effects differ from expected baseline measures.

Review Questions

• How does the one-sample t-test differ from a z-test, and under what conditions would you use each?
  • The one-sample t-test differs from a z-test primarily in that it is used when the population standard deviation is unknown and the sample size is small (typically n < 30). In contrast, a z-test is appropriate when the population standard deviation is known or when dealing with larger sample sizes where normal approximation holds. The choice between these tests hinges on the sample size and knowledge of population parameters.
• Describe how you would interpret the results of a one-sample t-test if you obtained a p-value of 0.03 at a significance level of 0.05.
  • If a one-sample t-test yields a p-value of 0.03 while using a significance level of 0.05, it suggests that there is sufficient evidence to reject the null hypothesis. This indicates that there is a statistically significant difference between the sample mean and the hypothesized population mean. In practical terms, this means that the observed data provides strong support for claiming that the sample's average differs from what was expected based on population assumptions.
• Evaluate how understanding one-sample t-tests can enhance decision-making processes in fields such as healthcare or marketing.
  • Understanding one-sample t-tests equips professionals in fields like healthcare or marketing to make data-driven decisions by assessing whether observed outcomes differ from expected values. For example, healthcare researchers can determine if new treatment protocols lead to significantly different recovery times compared to established norms. Similarly, marketers can assess if consumer responses to new products significantly deviate from historical performance metrics, allowing for informed strategic adjustments and resource allocation based on statistical evidence.

Related terms

Population Mean: The average value of a characteristic or measurement in the entire population, which serves as a benchmark in hypothesis testing.

Null Hypothesis: A statement that there is no effect or no difference, which the one-sample t-test seeks to test against the alternative hypothesis.

Degrees of Freedom: A parameter that represents the number of independent values in a statistical calculation, crucial for determining the critical value in hypothesis testing.