Question

A United Nations report shows the mean family income for Mexican migrants to the United States is $28,120 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 27 Mexican family units reveals a mean to be $39,750 with a sample standard deviation of $12,765. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

(a)	State the null hypothesis and the alternate hypothesis.

H0: μ =
H1: μ ≠

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

Reject H0 if t is not between ? and ?

(c)	Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

(d)	Does this information disagree with the United Nations report? Apply the 0.01 significance level.

(Do not reject or reject) Ho. This data (does not contradict or contradicts) the report.

Answer 1

Solution:

Given:

A United Nations report shows the mean family income for Mexican migrants to the United States is $28,120 per year.

Sample size = n = 27

Sample mean =

Sample Standard Deviation = s = $12,765

significance level = 0.01

We have to test if this information disagree with the United Nations report.

Part a) State the null hypothesis and the alternate hypothesis

Since hypothesis statement is non-directional , this is two tailed test.

thus

H₀: μ = $28,120

H₁: μ ≠  $28,120

Part b) State the decision rule for 0.01 significance level

df = n - 1 = 27 - 1 = 26

two tail area = 0.01

t critical value = 2.779

since this is two tailed test, t critical values are: ( -2.779 , 2.779 )

Reject H₀ if t is not between -2.779 and 2.779.

Part c) Compute the value of the test statistic.

Part d) Does this information disagree with the United Nations report? Apply the 0.01 significance level

Since > t critical value = 2.779., we reject null hypothesis H0.

Thus at 0.01 significance level ,  this data does not support the United Nations report of mean family income for Mexican migrants to the United States is $28,120 per year.

Thus we get:

Reject Ho. This data contradicts the report.