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Yuliya22 [10]
3 years ago
8

Use the given confidence interval limits to find the point estimate and the margin of error E.

Mathematics
1 answer:
nika2105 [10]3 years ago
4 0

Answer:

The point estimate = 0.507

Margin error of  a given confidence interval = 0.032

Step-by-step explanation:

The point estimate is calculated by using the sample statistics of a population.

Thus; point estimate can be expressed with the formula:

\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}

Given that : 0.475 < p < 0.539

\overline x = \dfrac{0.475+0.539}{2}

\overline x = \dfrac{1.014}{2}

\overline x = 0.507

The point estimate = 0.507

The margin of error  which shows  the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:

Margin error of  a given confidence interval = \mathtt{\dfrac{upper \ confidence \ limit - lower  \ confidence \ limit  }{2}}

Margin error of  a given confidence interval =  \dfrac{0.539-0.475}{2}

Margin error of  a given confidence interval = \dfrac{0.064}{2}

Margin error of  a given confidence interval = 0.032

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Applies to <em>addition </em>and <em>multiplication </em>only.

Grouping of numbers by parentheses in a different way does not affect their sum or product.

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Multiplication:  (a × b) × c = a × (b × c) = (a × c) × b

<u>Commutative Property Law</u>

Applies to addition and multiplication only.

Changing the order or position of two numbers does not change the end result.

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Multiplication:  a × b = b × a

<u>Distributive Property</u>

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Subtraction:   a(b - c) = ab - ac

<u>Identity Property of Addition</u>

Also known as the <em>identity property of zero</em>.  Adding 0 to any number does not change the number, i.e. the number keeps its identity.

a + 0 = a = 0 + a

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Also known as the <em>identity property of one</em>.  Multiplying any number by 1 does not change the number, i.e. the number keeps its identity.

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4 + 6 + 27   commutative property of addition

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4 × (¹/₄ × 5)   commutative property of multiplication

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