Question 1201376: 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. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population mean is assumed to be 27,000 per year.
sample of 25 mexicans shows the sample mean to be equal to 20,000 with a sample standard deviation of 10,000.
the standard error is equal to the sample standard deviation divided by the sample size = 10,000 / sqrt(25) = 10,000 / 5 = 2000.
you would use the t-score for the test because your standard deviation is from the sample and not from the population.
because you are looking at the mean of a sample, the standard error is used rather than the standard deviation.
standard error = standard deviation / sqrt(sample size) = 2000 / sqrt(25) = 2000 / 5 = 400.
the t-score formula is t = (x - m) / s
t is the t-score
x is the sample meaan
m is the population mean
s is the standard error.
t = (x - m) / becomes t = (30000 - 27000) / 400 = 7.5
the critical t-score with 24 degrees of freedom (number of degrees of freedom equals sample size minus 1) is equal to 2.796939498.
somce the test t-score is greater than the critical t-score, the results are significant and the conclusiomn is that the mean income is greater than 27,000.
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