One-Sample T-Test

In order to conduct a one-sample t-test, you must first have the following information: 

• Sample Mean (x̄)
• Population Mean ()
• Sample Standard Deviation (s)
• Number of Observations (n)

Once you have the aforementioned values, you can use the following steps to conduct the test:

• Step 1: Write your Null Hypothesis

In a one-sample t-test, the null hypothesis will generally take the following form; “the population mean equals the specified mean value”. 

• Step 2: Write your Alternative Hypothesis

The alternative hypothesis will generally take the following form; “the population mean does not equal the specified mean value”. 

• Step 3: Input the known Information into the T Score Formula

The t-score formula is;

t=x̄-sn

In this step, you must input your sample mean (x̄), population mean  (), sample standard deviation (s), and the number of observations (n) into the formula. Once you’ve done the calculations, you will arrive at your t-score. 

• Step 4: Identify the T-Table Value

To find this value, you must have the following numbers;

1. Alpha level: Generally taken as 0.05
2. Degree of Freedom: The number of items in the sample (n) subtracted by 1 (n-1)

• Step 5: Accept or Reject the Null Hypothesis

In the final step, you must accept or reject your null hypothesis. If the t-score calculated in step 3 does not fall into the range calculated in step 4, the null hypothesis is rejected and the alternative hypothesis is accepted. On the other hand, if the t-score calculated in step 3 does fall into the range calculated in step 4, the null hypothesis is accepted and the alternative hypothesis is rejected.