Question

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
= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees?

What distribution should be used in hypotheses testing?

Group of answer choices

normal distribution

t distribution

Answer 1

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.