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Simple 4 Step T Test

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. 

William Sealy Gosset.jpg

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

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