Pls help What is the scale factor?
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Answer:
(1) Null Hypothesis, :
Alternate Hypothesis, :
(2) Test statistics = -1.48
(3) At the 0.05 significance level, Fair field conclude that the population means are same.
Step-by-step explanation:
Let = mean annual family income for 12 people making inquiries at the first development
= mean annual family income for 24 people making inquiries at the second development
= standard deviation of annual family income for 12 people making inquiries at the first development
= standard deviation of annual family income for 24 people making inquiries at the second development
= sample of people of first development i.e. 12
= sample of people of second development i.e. 24
(1) Null Hypothesis, :
{population means are same}
Alternate Hypothesis, :
{population means are different}
<u>DECISION RULE ;</u>
- If the test statistics is less than the critical value of t from table at 5% significance level, then we will accept null hypothesis,
.
- If the test statistics is more than the critical value of t from table at 5% significance level, then we will reject null hypothesis,
(2) The test statistics is given by;
~
where, = Sample mean income of people at first development
= $153,000
= Sample mean income of people at second development = $171,000
= $42,000 and
= $30,000
=
= 34344.30
Test statistics = ~
= -1.48
(3) At 5% level of significance, t table gives critical value of 2.032 at 34 degree of freedom.Since our test statistics is less than the critical value of t so considering our decision rule, we will accept null hypothesis.
And conclude that population means are same.
The Taylor Series expansion of f(x) = sin(x) about a = π i given by
where the c's are contants.
That is
f(x) = c₀ + c₁(x-π) +c (x-π)² + c₃ (x-π)³ + ...,
₂
The first few derivatives of f(x) are
f' = c₁
f'' = 2c₂ = 2! c₂
f''' = 3.2c₃ = 3! c₃
f⁽⁴⁾ = 4.3.2c₄ = 4! c₄
and so on.
The pattern indicates that
The derivatives of f(x) are
f' = cos(x)
f'' = -sin(x)
f''' = -cos(x)
f⁽⁴⁾ = sin(x(
and so on
The pattern indicates that
f⁽ⁿ⁾(x) = cos(x), n=1,5,9, ...,
= -sin(x), n=2,6,10, ...,
= -cos(x), n=3,7,11, ...,
= sin(x), n=4,8,12, ...,
The radius of convergence is |x-π|<1 by the ratio test.
where the c's are contants.
That is
f(x) = c₀ + c₁(x-π) +c (x-π)² + c₃ (x-π)³ + ...,
₂
The first few derivatives of f(x) are
f' = c₁
f'' = 2c₂ = 2! c₂
f''' = 3.2c₃ = 3! c₃
f⁽⁴⁾ = 4.3.2c₄ = 4! c₄
and so on.
The pattern indicates that
The derivatives of f(x) are
f' = cos(x)
f'' = -sin(x)
f''' = -cos(x)
f⁽⁴⁾ = sin(x(
and so on
The pattern indicates that
f⁽ⁿ⁾(x) = cos(x), n=1,5,9, ...,
= -sin(x), n=2,6,10, ...,
= -cos(x), n=3,7,11, ...,
= sin(x), n=4,8,12, ...,
The radius of convergence is |x-π|<1 by the ratio test.