A United Nations report shows the mean family income for Mexican migrants to the
ID: 3132331 • Letter: A
Question
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,450 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 23 Mexican family units reveals a mean to be $37,190 with a sample standard deviation of $10,700. 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: = H1: 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.
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u = 26450
Ha: u =/ 26450 [ANSWER]
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b)
As we can see, this is a two tailed test.
Thus, getting the critical t,
df = n - 1 = 22
tcrit = +/- 2.818756061
Hence, we reject Ho when t is not between -2.819 and 2.819 [ANSWER]
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c)
Getting the test statistic, as
X = sample mean = 37190
uo = hypothesized mean = 26450
n = sample size = 23
s = standard deviation = 10700
Thus, t = (X - uo) * sqrt(n) / s = 4.813759865 [ANSWER]
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d)
As |t| > 2.819, then we reject Ho.
Hence, THIS DISAGREES WITH THE UNITED NATIONS REPORT.
There is significant evidence that the true mean is different from the United Nations report at 0.01 level. [CONCLUSION]
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