Question

A United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of $10,000. Is this information consistent with the United Nations report

Answer 1

We conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.

Explanation:

We are given that a United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year.

A FLOC evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of $10,000.

Let
`\mu` = true mean family income for Mexican migrants.

So, Null Hypothesis,
`H_0` :
`\mu` = $27,000 {means that the mean family income for Mexican migrants to the United States is $27,000 per year}

Alternate Hypothesis,
`H_A` :
`\mu`
`\\eq` $27,000 {means that the mean family income for Mexican migrants to the United States is different from $27,000 per year}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean family income = $30,000

s = sample standard deviation = $10,000

n = sample of Mexican family = 25

So, the test statistics =
`(30,000-27,000)/((10,000)/(√(25) ) )` ~
`t_2_4`

= 1.50

The value of t test statistics is 1.50.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical values of -2.064 and 2.064 at 24 degree of freedom for two-tailed test.

Since our test statistic lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.