The test statistic t = t_(n-1) = 5.558457132
is greater than the critical value of t at 25 d.f which is Critical t value at 25 d.f. = 2.787436.
Hence we reject the null hypothesis and conclude that the average income of Mexican migrants to the U.S is not equal to $26,580.
Therefore the information from the sample disagrees with the United Nations report.
We use the follow these steps to arrive at the answer.
Null hypothesis : μ = $26,580
Alternate hypothesis : μ ≠ $26,580
Test : Since sample standard deviation is given, we use the Student's t-test
Level of Significance : 0.01, Two-tailed test
Degrees of freedom (d.f): n-1 d.f = 26-1 = 25
Calculation of test statistic:
The formula for test statistic is
t_(n-1)=(x ̅-μ)/(S/√n)
t_(n-1) = (38,900- 26,580) / (11,054/√26)
t_(n-1) = 12050
/ 2167.867758
t_(n-1) = 5.558457132
Critical t value at 25 d.f. = 2.787436
