Single sample t-test is applied when (1) the data is normally distributed, (2) population standard deviation is unknown, and (3) the sample size is reasonably high (over 30).

Assume that someone wants to check the height of U.S. male. Currently, the population mean is about 70 inches, and the standard deviation is unknown. A total of 30 representative samples are taken and the height is measured (Table 1).

Table 2. U.S. Male Height (inches) Sample Data

Step 1

Hypothesis

Step 2

Method

Single sample t-test as it matches all the criteria for a single sample t-test.

MS Excel can be used to find the t value using Equation 2. P-value can be calculated by typing =TDIST(calculated t-value, degrees of freedom, tail).

Equation 2

Any software, such as, Minitab can also be used to analyze the data.

Step 3

Result

Results using MS Excel and Minitab are provided in Equation 4 and Equation 5, respectively.

Figure 4. Manual Analysis Results for a Single Sample T-Test Using MS Excel

Figure 5. Software Analysis Results for a Single Sample T-Test Using Minitab