Question

A United Nations report shows the mean family income for Mexican migrants to the US is $27,000 per year. A Farm Labor Organizing Committee sample of 25 Mexican families reveals a mean of $30,000, with a sample standard deviation of $10,000. Use this evidence to determine if the United Nations report is incorrect. Use the .01 level of significance. Begin by Stating the Appropriate Null Hypothesis.

Calculate the relevant test statistic.

Should the null hypothesis be rejected?

Is this evidence that the United Nations report is incorrect? Explain.

Answer 1

Solution:

Given:  A United Nations report shows the mean family income for Mexican migrants to the US is $27,000 per year.

that is:

Sample size = n = 25

Sample mean =

Sample standard deviation = s = $10,000.

We have to use this evidence to determine if the United Nations report is incorrect.

level of significance = 0.01

Part 1) State H0 and H1:

( Since hypothesis statement is non-directional , this is two tailed test, thus H1 is not equal to type )

Part 2) Calculate the relevant test statistic.

Part 3) Should the null hypothesis be rejected?

Find critical value:

df =n - 1= 25 -1 = 24

Two tail area = level of significance = 0.01

t critical values: ( -2.797 , 2.797)

Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value = 2.797, otherwise we fail to reject H0

Since absolute t test statistic value = t critical value = 2.797, we fail to reject H0

Thus the null hypothesis should not be rejected.

Part 4) Is this evidence that the United Nations report is incorrect? Explain.

Since null hypothesis is not rejected, that means a United Nations report shows the mean family income for Mexican migrants to the US is $27,000 per year is true or correct.

Thus there is no evidence that the United Nations report is incorrect.