For Table 4, determine the following point estimates: 7. The mathematical expectation. 8. the variance. 9. the root mean square deviation 10. the correlation coefficient between X and Y. Table 4 is in the attached image. Thank you

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For Table 4, determine the following point estimates: 
7. The mathematical expectation.

8. the variance.

9. the root mean square deviation

10. the correlation coefficient between X and Y. 

 

Table 4 is in the attached image. 

 

Thank you 

X
y
Z
80
64
147
89
79
132
66
67
103
83
76
156
72
61
124
Transcribed Image Text:X y Z 80 64 147 89 79 132 66 67 103 83 76 156 72 61 124
X
y
Z
80
64
147
89
79
132
66
67
103
83
76
156
72
61
124
Transcribed Image Text:X y Z 80 64 147 89 79 132 66 67 103 83 76 156 72 61 124
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Follow-up Question

Thank you, that was really helpful. Could you please verify the few hypotheses below

α = 0.05
T(a/2, v = 2) = 4.3027
T(a/2, v = 3) = 3.1825
T(a/2, v = 4) = 2.7765
T(a/2, v = 6) = = 2.4469
T(a/2, v = 8) = 2.3060
F(a/2, 4, 4) = 9.6045
F(x/2,3,3) = 15.4392
F(a/2,3,4)= 9.9792
F(a/2, 1,4) = 7.708
F(a/2, 4, 3) = 9.12
G(a, 3, 4) = 0.7457
x² = x²,4)= 0.4844
x² = x²(1,4)= 11.1433
T(α,5) =
= 1.92
Transcribed Image Text:α = 0.05 T(a/2, v = 2) = 4.3027 T(a/2, v = 3) = 3.1825 T(a/2, v = 4) = 2.7765 T(a/2, v = 6) = = 2.4469 T(a/2, v = 8) = 2.3060 F(a/2, 4, 4) = 9.6045 F(x/2,3,3) = 15.4392 F(a/2,3,4)= 9.9792 F(a/2, 1,4) = 7.708 F(a/2, 4, 3) = 9.12 G(a, 3, 4) = 0.7457 x² = x²,4)= 0.4844 x² = x²(1,4)= 11.1433 T(α,5) = = 1.92
Verification of a hypothesis of equality of the mathematical expectation of two random quantities
Ho: mx = my; H1: mx = my
Verification of a hypothesis of equality of the mathematical expectation of two random quantities
Ho: mx = mz; H1: mx * mz
Verification of a hypothesis of equality of the mathematical expectation of two random quantities:
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H0: my = mz; H1: my amz
Testing a hypothesis whether x* is a gross error. Check the maximum and minimum values if they
are gross errors.
Testing a hypothesis whether y* is a gross error. Check the maximum and minimum values if they
are gross errors.
mamm
Testing a hypothesis whether z* is a gross error. Check the maximum and minimum values, if they
wwwwwwwwwwwwwwww
are gross errors
www.chim.www
Verification of the hypothesis of mutual correlation of two quantities: H0: pxy=0; H1: pxy = 0
Transcribed Image Text:Verification of a hypothesis of equality of the mathematical expectation of two random quantities Ho: mx = my; H1: mx = my Verification of a hypothesis of equality of the mathematical expectation of two random quantities Ho: mx = mz; H1: mx * mz Verification of a hypothesis of equality of the mathematical expectation of two random quantities: wwwwwwwww wwww.w.www.wwwwww.wwwwww H0: my = mz; H1: my amz Testing a hypothesis whether x* is a gross error. Check the maximum and minimum values if they are gross errors. Testing a hypothesis whether y* is a gross error. Check the maximum and minimum values if they are gross errors. mamm Testing a hypothesis whether z* is a gross error. Check the maximum and minimum values, if they wwwwwwwwwwwwwwww are gross errors www.chim.www Verification of the hypothesis of mutual correlation of two quantities: H0: pxy=0; H1: pxy = 0
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Follow-up Question

Following the values above could you please: 

5. Test a hypothesis that the mathematical expectation is equal to a given constant: 

?0: ?? = 77;  ?1: ?? ≠ 77 

6. Testing a hypothesis that the mathematical expectation is equal to a given constant 

?0: ?? = 64;  ?1: ?? ≠ 64 

7.Test a hypothesis that the mathematical expectation is equal to a given constant 

?0: ?? = 128;  ?1: ?? ≠ 128 

The table values are in the image below

α = 0.05
T(a/2, v = 2) = 4.3027
T(a/2, v = 3) = 3.1825
T(a/2, v = 4) = 2.7765
T(a/2, v = 6) = = 2.4469
T(a/2, v = 8) = 2.3060
F(a/2, 4, 4) = 9.6045
F(x/2,3,3) = 15.4392
F(a/2,3,4)= 9.9792
F(a/2, 1,4) = 7.708
F(a/2, 4, 3) = 9.12
G(a, 3, 4) = 0.7457
x² = x²,4)= 0.4844
x² = x²(1,4)= 11.1433
T(α,5) =
= 1.92
Transcribed Image Text:α = 0.05 T(a/2, v = 2) = 4.3027 T(a/2, v = 3) = 3.1825 T(a/2, v = 4) = 2.7765 T(a/2, v = 6) = = 2.4469 T(a/2, v = 8) = 2.3060 F(a/2, 4, 4) = 9.6045 F(x/2,3,3) = 15.4392 F(a/2,3,4)= 9.9792 F(a/2, 1,4) = 7.708 F(a/2, 4, 3) = 9.12 G(a, 3, 4) = 0.7457 x² = x²,4)= 0.4844 x² = x²(1,4)= 11.1433 T(α,5) = = 1.92
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