A United Nations report shows the mean family income for Mex

A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   27150  
Ha:    u   =/   27150  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    29          
tcrit =    +/-   2.756385904      

Thus, we reject Ho if t is not between -2.756 and 2.756. [ANSWER]

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Other info:
              
Getting the test statistic, as              
              
X = sample mean =    29500          
uo = hypothesized mean =    27150          
n = sample size =    30          
s = standard deviation =    11150          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.154392834          
              
Also, the p value is              
              
p =    0.257763731          
              
Comparing t and tcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.