t-distribution
The t-distribution is a family of distributions indexed by degrees of freedom (df). For a sample of size n, df = n - 1. The t-distribution has heavier tails than the normal distribution, reflecting greater uncertainty when estimating σ from sample data. As df increases, the t-distribution approaches the normal distribution. Use t-distribution when σ is unknown or n < 30 and the population is normal.
Real World
A student dissertation comparing mean exam scores for two teaching methods uses a t-distribution with df = n − 1 because the population standard deviation is unknown and must be estimated from the small sample.
Exam Focus
Always state degrees of freedom when reading t-tables; using the wrong df row gives the wrong critical value and costs accuracy marks.
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