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Inga [223]
3 years ago
13

Fifteen years ago 57% of American families had money invested in the stock market. It is believed that this percentage has dropp

ed. To see if this is true, Morningstar recently sampled 200 American families and recorded in Excel each family’s Yes/No answer to the question "Do you have money invested in the stock market?". Based on these results, can Morningstar declare that the proportion of American families who have money invested in the stock market is now lower than .57 at α=.01? Use the excel output above to answer the following question.Find the critical value (typically two decimals if zcrit, three decimals if tcrit).
Mathematics
1 answer:
statuscvo [17]3 years ago
3 0

Answer:

z(critic) = -2.33

Step-by-step explanation:

In this case this is a population proportion test because the observations are simple random sampled and there is a fixed number of trials with only two possible options. Also, n is big enough.

Since this is a population test, the test statistic is z.

Also, this is a one tailed tast because the claim is that the population proportion is less than 0.57.

In this case, for a 0.01 significance level, z(critic) = -2.33

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Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
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Let <em>a</em>, <em>b</em>, and <em>c</em> be vectors each starting at the origin and terminating at the points (<em>x</em>, <em>x</em> + 1), (<em>x</em> + 2, <em>x</em> + 3), and (<em>x</em> + 3, 2<em>x</em> + 4), respectively.

Then the vectors <em>a</em> - <em>b</em>, <em>a</em> - <em>c</em>, and <em>b</em> - <em>c</em> are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0

We have

<em>a</em> - <em>b</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 2, <em>x</em> + 3) = (-2, -2)

<em>a</em> - <em>c</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-3, -<em>x</em> - 3)

<em>b</em> - <em>c</em> = (<em>x</em> + 2, <em>x</em> + 3) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-1, -<em>x</em> - 1)

Case 1: If (<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0, then

(-2, -2) • (-3, -<em>x</em> - 3) = (-2)×(-3) + (-2)×(-<em>x</em> - 3) = 2<em>x</em> + 12 = 0   ==>   <em>x</em> = -6

which would make <em>a</em> - <em>c</em> = (-3, 3) and <em>b</em> - <em>c</em> = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-2, -2) • (-1, -<em>x</em> - 1) = (-2)×(-1) + (-2)×(-<em>x</em> - 1) = 2<em>x</em> + 4 = 0   ==>   <em>x</em> = -2

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but the solutions to <em>x</em> here are non-real, so we throw out this case.

So there are two possible values of <em>x</em> that make a right triangle, <em>x</em> = -6 and <em>x</em> = -2.

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2 years ago
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The equation that shows how the total number of cups of ice used, y, depends on the number of glasses filled, x, is y = 0.8x + 80

<h3>Linear function</h3>

Filling the cooler is an illustration of a linear function

A linear function is represented as: y = mx + b

Where

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  • x and y are the variables

<h3>The equations</h3>

By comparison, we have the following parameters

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  • b = 80 ---- the initial amount of cup

So, the equation that represents this scenario is

y = 0.8x + 80

Read more about linear functions at:

brainly.com/question/14323743

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