The formula to calculate the t-value is:
\[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]
Where:
Let's say the sample mean is 50, the population mean is 45, the sample standard deviation is 10, and the sample size is 30. Using the formula:
\[ t = \frac{50 - 45}{\frac{10}{\sqrt{30}}} \approx 2.74 \]
So, the t-value is approximately 2.74.
The t-value is a ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing to determine if there is a significant difference between the sample mean and the population mean.