The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with

In this scenario, you are comparing the mean salary of a sample of state employees to a known population mean (federal government employees' salary). Since the sample size is relatively small (n = 30), and the population standard deviation is not known (only the sample standard deviation is provided), you should use the **t distribution** for hypothesis testing.

Here are the steps to conduct the hypothesis test:

1. **State the hypotheses:**
- Null hypothesis (H0): μ_state ≥ μ_federal (The average salary of state employees is greater than or equal to that of federal employees.)
- Alternative hypothesis (H1): μ_state < μ_federal (The average salary of state employees is less than that of federal employees.)

2. **Given data:**
- Population mean (μ_federal) = $59,593
- Sample mean (M) = $58,800
- Sample standard deviation (s) = $1,500
- Sample size (n) = 30
- Significance level (α) = 0.01

3. **Calculate the test statistic:**
You would use the t-test formula:
\[
t = \frac{M - μ_federal}{\frac{s}{\sqrt{n}}}
\]
Substituting the values:
\[
t = \frac{58,800 - 59,593}{\frac{1,500}{\sqrt{30}}}
\]

4. **Find the critical t-value:**
You will need to look up the t-table for α = 0.01 and degrees of freedom (df = n - 1 = 29) to find the critical t-value.

5. **Make a decision:**
If the calculated t-statistic is less than the negative of the critical t-value, you reject the null hypothesis.

In conclusion, you should use the **t distribution** for this hypothesis testing.