need to find the critical value and Id rejection region An e

An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is $22,300. The annual pay for random sample of 10 full-time male workers over age 25 without over age 25 without a high school diploma is listed. At alpha = 0.01, test the claim that the mean salary is $22,300. Assume the population is normally distribute. Which of the following correctly states H0 and Ha?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   22300  
Ha:    u   =/   22300   [ANSWER, OPTION C]

****************************
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit = 3.249835542, -3.249835542 [ANSWER, CRITICAL VALUES]

***************************

Thus, we reject Ho is t < -3.249835542 or t > 3.249835542. [ANSWER, REJECTION REGION]

*****************************
  
Additional information:

Getting the test statistic, as              
              
X = sample mean =    21823.7          
uo = hypothesized mean =    22300          
n = sample size =    10          
s = standard deviation =    2627.895569          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.573155519          
              
Also, the p value is              
              
p =    0.580575555          
              
Comparing t and tcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.