Topic Details (Notes format)

How to Use the t-Distribution for Small Samples

Subject: Mathematics

Book: Maths Mastery

When population standard deviation is unknown and sample sizes are small, the t-distribution replaces the normal (z) distribution in confidence interval and hypothesis testing. T-distributions depend on degrees of freedom (n–1 for a single sample). As sample size increases, the t-curve approaches the normal curve. For example, a 95% CI for a sample mean with 10 observations uses a critical t-value from t-tables. This approach underpins real-life scenarios with limited data, ensuring valid inference. Grasping the t-distribution is crucial in numerous lab measurements, academic research, or pilot studies with small samples.

Practice Questions

A train 150 m long passes a pole in 15 seconds. What is its speed?

View Question

The base of a triangle is 10 cm and its height is 6 cm. What is its area?

View Question

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

View Question

If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

View Question

If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

View Question

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

View Question

If x = 3 and y = 4, what is the value of x^2 + y^2?

View Question

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

View Question