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

Set Up Hypothesis
Null, H0: U=27150
Alternate, H1: U!=27150
Test Statistic
Population Mean(U)=27150
Sample X(Mean)=29500
Standard Deviation(S.D)=11150
Number (n)=30
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =29500-27150/(11150/Sqrt(29))
to =1.154
| to | =1.154
Critical Value
The Value of |t a| with n-1 = 29 d.f is 2.756
We got |to| =1.154 & | t a | =2.756
Make Decision
Hence Value of |to | < | t a | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 1.1544 ) = 0.2578
Hence Value of P0.01 < 0.2578,Here We Do not Reject Ho

ANS:
H0: U=27150 , H1: U!=27150
REJECT Ho, if t is not between -2.756, 2.756
to =1.154
Do not Reject Ho
Contradict the Report