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DanielleElmas [232]
3 years ago
6

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

3]. The population standard deviation used for the analysis is known to be $14,300.
a. What is the point estimate of the mean salary for all college graduates in this town?
Point estimate
b. Determine the sample size used for the analysis.
Sample size
Mathematics
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

(38737+50463)/2 = 44600.

The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

M = \frac{50463-38737}{2} = 5863

Relating the margin of error with the sample size:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.9}{2} = 0.05

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.64.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

For this problem, we have that \sigma = 14300, M = 5863. So

M = z\frac{\sigma}{\sqrt{n}}

5863 = 1.645\frac{14300}{\sqrt{n}}

5863\sqrt{n} = 1.645*14300

\sqrt{n} = \frac{1.645*14300}{5863}

(\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2

n = 16

The sample size was of 16.

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What is vertically opposite angles?

  Angles that are vertically opposed to one another are always equal to one another. A vertical angle and the angle to which it is next are also supplementary angles; that is, they sum up to 180 degrees. As an illustration, if two lines connect to form an angle, say X=45°, then the angle's opposite angle is also 45°.

Here consider angle with 31° and 49° triangle is 1. We know that sum of all angles in triangle is add upto 180°. Then,

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Then unknown angle in triangle 1 ia 100°.

Now according to the vertically opposite angle theorem , opposite angles are equal to each other. Then ,

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1 year ago
Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I
lapo4ka [179]

Answer:

  • 48 years old.

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

  • (10y + x)/3 + 20 = 10x + y
  • (10y + x)/3 = 10x + y - 20
  • 10y + x = 3(10x + y - 20)
  • 10y + x = 30x + 3y - 60
  • 30x - x + 3y - 10y = 60
  • 29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

  • 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

  • 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

<h3>If x = 3</h3>

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<h3>If x = 4</h3>

  • 29*4 - 7y = 60
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So the age is 48.

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Answer:

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Step-by-step explanation:

The jar consist of blue, red and green marbles . The probability of each of them can be described as follows.

probability of blue marbles = 2/7

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probability of green marbles = 5/2k

The sum of the individual probability is equals to 1. Therefore,

2/7 + 3/k + 5/2k = 1

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11/2k =(7 - 2) /7

11/2k = 5/7

cross multiply

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divide both sides by 10

k = 77/10

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