Question

A united nations report shows the mean family income for mexican migrants to the united states is $26,580 per year. a floc (farm labor organizing committee) evaluation of 26 mexican family units reveals a mean to be $38,900 with a sample standard deviation of $11,054. does this information disagree with the united nations report? apply the 0.01 significance level.

Answer 1

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