Answer to Question #198787 in Statistics and Probability for John

Question

It is claimed that the average monthly income of chemical engineers last year was P27,900. A random

sample of 35 chemical engineers is selected and it is found out that the average monthly salary is P28,000.

Using 0.01 level of significance, can it be concluded that there is an increase in the average monthly income

of chemical engineers? Assume that the population standard deviation is P250.50.

Answer 1

$Here,\\H_0: μ = 27,900\\ H_a: μ > 27,900\\\ \\ Z = \dfrac{\bar{x}-u}{\frac{σ}{\sqrt{n}}}\\\ \\ Z =\frac{28000-27900}{\frac{250.50}{\sqrt{35}}}\\\ \\ Reject \space Ho \space if \space Z > 2.33\\ Reject \space Ho\\ \text{There is\space sufficient\space evidence\space to\space conclude \space the\space average \space salary \space has\space increased, \space for\space α = 0.01}$