To calculate the test statistic for this scenario, we will use the formula for the t-test statistic:
\[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]
Where:
- \(\bar{x}\) = sample mean
- \(\mu\) = population mean (hypothesized mean)
- \(s\) = sample standard deviation
- \(n\) = sample size
From the information given:
- Sample mean (\(\bar{x}\)) = 55
- Hypothesized mean (\(\mu\)) = 60
- Sample standard deviation (\(s\)) = 20
- Sample size (\(n\)) = 100
Now, we can plug in the values into the formula.
First, calculate the standard error (SE):
\[ SE = \frac{s}{\sqrt{n}} = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2 \]
Next, calculate the test statistic \(t\):
\[ t = \frac{55 - 60}{2} = \frac{-5}{2} = -2.5 \]
Thus, the value of the test statistic is:
\[ \boxed{-2.5} \]