A United Nations report shows the mean family income for Mexican migrants to the

Question

A United Nations report shows the mean family income for Mexican migrants to the United States is $31,140 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 25 Mexican family units reveals a mean to be $38,690 with a sample standard deviation of $12,240. 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.)

(Click to select)Rejec/t HoDo not reject Ho.

This data (Click to select)contradicts/does not contradict the report.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   31140  
Ha:    u   =/   31140   [ANSWER]

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b)
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    24          
tcrit =    +/-   2.796939505      

Hence,

Reject Ho when t is not between -2.797 and 2.797. [ANSWER]

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c)

              
Getting the test statistic, as              
              
X = sample mean =    38690          
uo = hypothesized mean =    31140          
n = sample size =    25          
s = standard deviation =    12240          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.084150327 [ANSWER, TEST STATISTIC]

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d)

As 3.084 is not between the critical values, we reject Ho. Hence, it contradicts the report,

1. Reject Ho.          
2. Contradicts.
              

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