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 \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.

Answer 1

Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  $Z_{\alpha } = - 2.33$

Step-by-step explanation:

From the question we are told that

   The  population mean is  $\mu = \ 59593$

   The sample size is  n =  30

    The  sample mean is $\= x = \ 58800$

     The  standard deviation is  $\sigma = \ 1500$

     The significance level is  $\alpha = 0.01$

   

The null hypothesis is  $H_o : \mu = \ 59593$

 The  alternative hypothesis is  $H_a : \mu < \ 59593$

The critical value of $\alpha$ from the normal distribution table is  $Z_{\alpha } = - 2.33$

 Generally the test statistics is  mathematically evaluated as

            $t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }$

=>         $t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }$  

=>          $t = -2.896$

The  p-value is obtained from the z-table

   $p-value = P(t < -2.896) = 0.0018898$

Since $p-value < \alpha$ , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees