Question

employees in a large accounting firm claim that the mean salary of the firm's accounting is less than that of the competitors mean salary of $45,000. a random sample of 30 of the firm's accountants have a mean salary of $43,500 with a standard deviation of $5,200. test the employees claim at 95% confidence. state your conclusion of the employees claim

Answer 1

To test employees claim let's test null and alternative hypotheses:

$$H _ {0}: \mu = 4 5 0 0 0$$ $$H _ {1}: \mu < 4 5 0 0 0$$

Test statistics:

$$t = \frac {\bar {x} - \mu}{s / \sqrt {n}}$$

In our case:

$$\mu = 4 5 0 0 0$$ $$\bar {x} = 4 3 5 0 0$$ $$s = 5 2 0 0$$ $$n = 3 0$$

Substituting values into the formula we get:

$$t = \frac {\bar {x} - \mu}{s / \sqrt {n}} = \frac {4 3 5 0 0 - 4 5 0 0 0}{5 2 0 0 / \sqrt {3 0}} = - 1. 5 8$$

At $\alpha = 1 - 0.95 = 0.05$ we have such critical value:

$$t _ {\alpha , n - 1} = t _ {0. 0 5, 2 9} = - 1. 7$$

Since $t > t_{\text{critical}}$ we do not reject $H_0$ . There is no sufficient evidence to conclude that salary is less than 45000.