emplyment information service claims mean annual pay for ful

emplyment information service claims mean annual pay for full-time male worker over age 25 without high school diploma is $22,300. random sample of 10 males over age 25 is as follows: a= 0.05

$20,659, $21,130, $22,352, $24,186, $21,393, $22,971, $16,914, $19,151, $23,198, $26,281

find critical values and standardized test statistics

reject or fail to reject Ho?

Solution

Getting the sample mean and standard deviation,

mean (X) = 21823.5
s = Formulating the null and alternative hypotheses,              
              
Ho:   u   =   22300  
Ha:    u   =/   22300  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    +/-   2.262157163   [ANSWER, CRITICAL VALUE]

******************************************  
              
Getting the test statistic, as              
              
X = sample mean =    21823.5          
uo = hypothesized mean =    22300          
n = sample size =    10          
s = standard deviation =    2628.979745          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.573159724   [ANSWER, STANDARD TEST STATISTIC]      
***************************************                              
Comparing -2.262<t<2.262 , we   FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER]