The *t*-statistic was introduced in 1908 by William Sealy Gosset, a chemist working for the Guinness brewery in Dublin, Ireland. “Student” was his pen name. ^{}Gosset had been hired owing to Claude Guinness’s policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness’s industrial processes. Gosset devised the *t*-test as an economical way to monitor the quality of stout.

When given a t-test question, we must first find the following: the sample, the mean of sample, the standard deviation, the population average and alpha. Here is one example to test:

15 sample n

40.6 mean of sample X̄

6 σ

36.7 population average μ

0.05 alpha

Note: due to the sample size being under 30, we do the t test:

**Step 1: Write the hypothesis**

H0: μ=36.7

H1: μ≠36.7

**Step 2: Calculated value**

t= x̄-μs/n

s= sample standard deviation

t= 40.6-36.76/15 = 3.9/2.128

Calculated value = 2.57

**Step 3: Find the critical value**

1 tailed test

Df: degrees of freedom = n-1

14 and 0.05 = 1.761 critical value

**Step 4: Compare both calculated and critical values**

Reject the null 2.57>1.7