2. The table below reports income comparison between genders. gender income gender income 1 Male 14.13 Female 11.79 2 Male 85.42 Female 68.21 5 7 3 Male 4 Male Male 6 Male Male 8 Male 61.07 Female 75.41 104.59 Female 148.92 28.94 Female 37.35 41.87 Female 27.27 32.79 Female 17.70 9 Male 10 Male 16.75 Female 38.95 45.12 Female 23.28 Female 22.56 36.30 11 Male 15.63 Female 10.84 12 Male 76.35 Assume that incomes are normally distributed. Let μ₂ be the income mean of Female population and μ₁ of Male population. (a) Test the Null hypothesis Hoμ₁ = μ₂ against the alternative H₁ μ₁<μ₂ at the significance level a = 5%. (b) Find ẞ and the power of the test for the hypothesis Ho H2 =0 vs H₁₂-μ₁ = 1. (c) Find the power function K(5) = P(Reject Ho | μ2 - µ₁ = d). (d) Plot the power curve.

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2. The table below reports income comparison between genders.
gender income gender income
1
Male
14.13 Female 11.79
2 Male
85.42 Female 68.21
5
7
3 Male
4 Male
Male
6 Male
Male
8 Male
61.07 Female 75.41
104.59 Female 148.92
28.94 Female 37.35
41.87 Female 27.27
32.79 Female 17.70
9 Male
10 Male
16.75 Female 38.95
45.12 Female
23.28 Female
22.56
36.30
11 Male
15.63 Female
10.84
12 Male
76.35
Assume that incomes are normally distributed. Let μ₂ be the income mean of Female
population and μ₁ of Male population.
(a) Test the Null hypothesis Hoμ₁ = μ₂ against the alternative H₁ μ₁<μ₂ at the
significance level a = 5%.
(b) Find ẞ and the power of the test for the hypothesis
Ho H2 =0 vs H₁₂-μ₁ = 1.
(c) Find the power function K(5) = P(Reject Ho | μ2 - µ₁ = d).
(d) Plot the power curve.
Transcribed Image Text:2. The table below reports income comparison between genders. gender income gender income 1 Male 14.13 Female 11.79 2 Male 85.42 Female 68.21 5 7 3 Male 4 Male Male 6 Male Male 8 Male 61.07 Female 75.41 104.59 Female 148.92 28.94 Female 37.35 41.87 Female 27.27 32.79 Female 17.70 9 Male 10 Male 16.75 Female 38.95 45.12 Female 23.28 Female 22.56 36.30 11 Male 15.63 Female 10.84 12 Male 76.35 Assume that incomes are normally distributed. Let μ₂ be the income mean of Female population and μ₁ of Male population. (a) Test the Null hypothesis Hoμ₁ = μ₂ against the alternative H₁ μ₁<μ₂ at the significance level a = 5%. (b) Find ẞ and the power of the test for the hypothesis Ho H2 =0 vs H₁₂-μ₁ = 1. (c) Find the power function K(5) = P(Reject Ho | μ2 - µ₁ = d). (d) Plot the power curve.
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