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IrinaK [193]
3 years ago
12

A guidance counselor at a university career center is interested in studying the earning potential of certain college majors. He

claims that the proportion of graduates with degrees in engineering who earn more than $75,000 in their first year of work is not 15%. If the guidance counselor chooses a 5% significance level, what is/are the critical value(s) for the hypothesis test? 2010 20.05 20.025 1.960 20.01 2.326 20.005 2.576 1.282 1.645 Use the curve below to show your answer. Select the appropriate test by dragging the blue point to a right, left- or two tailed diagram. The shaded area represents the rejection region. Then, set the critical value(s) on the z-axis by moving the slider.
Mathematics
1 answer:
butalik [34]3 years ago
8 0

Answer:

For the critical value we know that the significance is 5% and the value for \alpha/2 = 0.025 so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:

Z_{\alpha/2}= \pm 1.96

Since we have a two tailed test,  the rejection zone would be: z or z>1.96

Step-by-step explanation:

Data given and notation

n represent the random sample taken

\hat p estimated proportion of interest

p_o=0.15 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of graduates with degrees in engineering who earn more than $75,000 in their first year of work is not 15%.:  

Null hypothesis:p=0.15  

Alternative hypothesis:p \neq 0.15  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

For the critical value we know that the significance is 5% and the value for \alpha/2 = 0.025 so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:

Z_{\alpha/2}= \pm 1.96

Since we have a two tailed test,  the rejection zone would be: Z or z>1.96

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avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see \boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.  

\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }

\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }

Both sides subtracted by 47°.

\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }

Thus \boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, \boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}

<u>Conclusion:</u>

  • m ∠a = 47°
  • m ∠b = 133°
  • m ∠c = 47°
  • m ∠d = 133°

<u>Notes:</u>

  • Supplementary angles are two angles when they add up to 180°. \boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }
  • Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. \boxed{ \ example: \angle{a} = \angle{c} \ }
<h3>Learn more</h3>
  1. About the measure of the central angle brainly.com/question/2115496
  2. Undefined terms needed to define angles  brainly.com/question/3717797
  3. Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

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The difference in these multipliers is ...

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Answer:

see explanation

Step-by-step explanation:

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m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = 2,4 ) and (x₂, y₂ ) = (5, 1)

m = \frac{1-4}{5-2}  = \frac{-3}{3} = - 1 ← negative slope

Repeat

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m = \frac{0-8}{-7+7} = \frac{-8}{0}

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Repeat with

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Repeat with

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