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

To determine whether the average salary of state employees is less than that of federal employees, we can perform a hypothesis test.

Let's set up the hypotheses:

- Null Hypothesis (H0): μ_state >= μ_federal (State employees earn on average at least as much as federal employees)
- Alternative Hypothesis (H1): μ_state < μ_federal (State employees earn on average less than federal employees)

Where:
- μ_state = mean salary of state employees
- μ_federal = mean salary of federal employees ($59,593)

Given the information:
- Sample mean of state employees (x̄) = $58,800
- Federal employees mean (μ_federal) = $59,593
- Sample size (n) = 30
- Standard deviation (σ) of state employees = $1,500
- Significance level (α) = 0.01

Next, we need to calculate the test statistic using the formula for the z-test for a single sample mean:

\[
z = \frac{x̄ - μ_federal}{σ / \sqrt{n}}
\]

Substituting the known values:

\[
z = \frac{58,800 - 59,593}{1,500 / \sqrt{30}}
\]

Calculating the standard deviation of the sample mean (σ / √n):

\[
σ / \sqrt{n} = \frac{1,500}{\sqrt{30}} \approx 274.07
\]

Now, calculate the z-value:

\[
z = \frac{58,800 - 59,593}{274.07} \approx \frac{-793}{274.07} \approx -2.89
\]

Next, we need to find the critical z-value for a one-tailed test at the 0.01 significance level. This can be found using a z-table or calculator:

The critical z-value for α = 0.01 (one-tailed) is approximately -2.33.

Now, we can compare our calculated z-value with the critical z-value:

- Calculated z-value: -2.89
- Critical z-value: -2.33

Since -2.89 is less than -2.33, we reject the null hypothesis.

Based on our results:

- Rejecting the null hypothesis suggests there is sufficient evidence to support the alternative hypothesis that state employees earn on average less than federal employees.

Thus, the correct conclusion is:

**c) The sample data support the claim that state employees earn on average less than federal employees.**