Answer to Question #212467 in Statistics and Probability for Marlene Padua

Question

It is claimed that the mean annual salary of call center customer service representatives

is P188,584.00. A researcher randomly selected 45 call center customer service

representatives. He computed the mean of their annual salaries and obtained a mean of

P188,600.00. Does this show that the mean salary of call center customer service

representatives is greater than P188,584 00? Use 0.05 level of significance assume that

the population standard deviation is P39.50

Answer 1

Population standard deviation is known;thus, z-score is used.

$H0:\mu=188,584$

$Ha:\mu>188,584$

$\bar X=188,600$

$n=45$

$\sigma=39.5$

$Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=\frac{188,600-188,584}{\frac{39.5}{\sqrt{45}}}$

$=2.717$

$Cv=z_{0.05}=1.645$ (Right-tailed)

Since z (2.717) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is no enough evidence to support the claim that the mean annual salary of call center customer service representatives is 188,584.