Answer to Question #294445 in Statistics and Probability for Pasty

Question

1.      One of the undersecretary of the Department of Labor and Employment (DOLE) claims that the average salary of Social worker is Php18, 000. A sample of 19 social worker’s salary has a mean of Php17, 350 and standard deviation of Php1, 230. Is there enough evidence to reject the undersecretary’s claim at 𝛼 = 0.01?

Answer 1

Solution:

$H_0:\mu=18000 \\ H_1:\mu\ne18000 \\ n=19 \\ \bar X=17350 \\\sigma=1230$

Test statistics: $\dfrac{\bar X-\mu}{\sigma/\sqrt n}= \dfrac{17350-18000}{1230/\sqrt {19}}=-2.303$

$t_{n-1}=t_{18}=2.878$

This is two-tailed test, so t-value is $\pm2.878$

Our test statistics -2.303 lies between t-values. So, we cannot reject null hypothesis.

Thus, we conclude that the average salary of Social worker is Php18, 000.