Math
T-intervals.
Definition
A t-interval is a confidence interval for a population mean constructed using the t-distribution instead of the normal distribution, typically when the population standard deviation is unknown and the sample size is small. It gives a range of plausible values for the true population mean based on sample data.
How it works · 5 phases
Step by step.
- Collect a random sample and calculate the sample mean and sample standard deviation.
- Determine the confidence level and find the corresponding t* critical value using degrees of freedom (n − 1).
- Calculate the standard error as s / √n.
- Construct the interval: x̄ ± t* × (s / √n).
- Interpret the interval in context of the problem.
Examples
Real-world.
- 1 Estimating the average test score of all students in a school from a sample of 25 students
- 2 Finding a 95% confidence interval for the mean weight of backpacks carried by middle schoolers
- 3 Determining a plausible range for the average commute time of employees at a company
Key Fact
t-interval formula: x̄ ± t* × (s / √n), where df = n − 1