When we do not know the population standard deviation sigma, σ, and the sample size, n, is less than 30, we use the t-test to evaluate a claim. Consider the following problem:

A scientist thinks the mean waste recycled by adults in the US is now more than one pound per person per day. In a random sample of 12 US adults, the mean waste recycled per day per person is 1.9 pounds with a standard deviation of 0.3 pounds. At a 10% significance level, does the sample data support the claim?

In statistics, it is always a good idea to sketch the situation described in the problem:

The sample mean is far to the right of the assumed population mean, µ = 1. [Read more…] about Single-sample t-test & Confidence Interval – Excel & StatCrunch