Question 1033711: A United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 26 Mexican family units reveals a mean to be $30,500 with a sample standard deviation of $10,500. 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
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population mean is 30,500.
sample mean is 28,540.
sample standard deviation is 10,500.
since you don't have the population standard deviation, you need to do a t-score rather than a z-score.
the formula for the standard error is the same.
standard error = standard deviation / square root of sample size.
you get a standard error of 10,500 / sqrt(26) = 2059.22.
with a sample size of 26, your degrees of freedom are 25.
you look in the t-score table to find the t-score for a .01 level of significance for a two sided distribution.
you will find that the t-score is 2.787.
that means that anything with a t-score between -2.787 and +2.787 is within limits and the difference between the sample mean and the population mean is probably due to chance variations in the sample means.
next you have to calculate the t-score of your sample data.
the t-score is calculated as follows:
first subtract the population mean from your sample mean.
you will get 30500 - 28540 = 1960.
then divide that difference by the standard error.
you will get 1960 / 2059.22 = .95.
that's your t-score.
since your t-score is between -2.787 and +2.787, your sample mean is well within the confidence limits.
this means that the difference between your sample mean and the population mean is more then likely due to chance variations in the sample mean rather than any other explanation.
because of this, you cannot reject the null hypothesis that the mean family income is 28,540.
the t-score table i used is shown below:
http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
the limit is 2.787
it's in the third column from the right and on the row with 25 degrees of freedom.
the data you require is as follows:
h0 mean = 28540
h1 mean = 30500
t-score = .95
t-score is between the limits of plus or minus 2.787.
h0 cannot be rejected based on the data.
the null hypothesis is that the population mean is 28540.
the alternate hypothesis is that the population mean is not 28540.
the result is that your data is inconclusive and you can't state that the population mean is not 28540 based on the data you collected.
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