Single Sample T-Test

Comparing a single sample/population/group/mean with a standard value

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


Step 2


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


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

Statistical Interpretation of the Results

We do not reject the null hypothesis because the p-value (0.53) is larger than the level of significance (0.05).

[p-value = the observed probability for the null hypothesis to happen, which is calculated from the sample data]

Step 4

Contextual Conclusion

Statistically, the height of U.S. male is equal to 70 inches. [rewrite the accepted hypothesis. In this case, the null hypothesis is accepted]