Respuesta :
Answer:
(a) H₀: µ = $27,150 vs. Hₐ: µ ≠$27,150.
(b) Reject H₀ if [tex]t_{cal.}[/tex] is not between -2.756 and 2.756.
(c) The value of the test statistic [tex]t_{cal.}[/tex] is, 1.154.
(d) The information does not disagrees with the United Nations report.
Step-by-step explanation:
A single mean test is applied to test whether the population mean family income for Mexican migrants to the United States is different from $27,150 per year.
(a)
The hypothesis is:
H₀: The mean family income for Mexican migrants to the United States is $27,150 per year, i.e. µ = $27,150.
Hₐ: The mean family income for Mexican migrants to the United States is $27,150 per year, i.e. µ ≠$27,150.
(b)
The decision rule is:
If the test statistic value, [tex]t_{cal.}[/tex] lies outside the interval[tex](t_{(1-\alpha/2), (n-1)}<t<t_{\alpha/2, (n-1)})[/tex] then the null hypothesis will be rejected.
Compute the critical values for α = 0.01 and degrees of freedom, (n -1) = 29 as follows:
[tex]t_{(1-\alpha/2), (n-1)}=-2.756[/tex]
[tex]t_{\alpha/2, (n-1)}=2.756[/tex]
Thus, the rejection region is:
Reject H₀ if [tex]t_{cal.}[/tex] is not between -2.756 and 2.756.
(c)
The information provided is:
[tex]\bar x=\$29500\\s=\$11150\\n=30\\\alpha =0.01[/tex]
Since the population standard deviation is not given we will use a t-test.
The t-statistic is given by,
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{29500-27150}{11150/\sqrt{30}}=1.154[/tex]
Thus, the value of the test statistic [tex]t_{cal.}[/tex] is, 1.154.
(d)
The calculated t-statistic is, t = 1.154.
The test statistic value lies in the range (-2.756, 2.756).
Thus, the null hypothesis will not be rejected at 1% level of significance.
Hence, concluding that the information does not disagrees with the United Nations report.
