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Fofino [41]
3 years ago
9

A Statistics exam is created by choosing for each question on the exam one possible version at random from a bank of possible ve

rsions of the question. There are 20 versions in the bank for each question. A specific question on the exam involves a one-sample test for the population mean with hypotheses
H0 : µ = 15
Ha : µ < 15

with all versions of the question involving a sample of size n = 35.

Seven versions of the question give the population standard deviation as σ = 3. Six versions give the sample standard deviation as s = 4.2. The remaining versions give the sample standard deviation as s = 5.7. Let σ be the critical value for the rejection region on this question. Calculate E[c].
Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

Answer: E (c *) = 13.77766

Step-by-step explanation:

the significance level of 0.05 is known

seeks to calculate the sample for the population medis using the hypothesis

H0: µ = 15

H0: µ 15

sample size n = 35

Degrees of freedom df = n-1 = 35-1 = 34

The critical value for z is -1.645

The critical value for t is -1.691

For \ sigma = 3,

Standard error = 3 /√ 35 = 0.5070926

When obtaining the results of the population standard deviation, we will use the z-score to estimate the critical value.

ex = 15-1645 * 0.5070926 = 14.16583

For s = 4.2,

Standard error = 4.2 / √ 35 = 0.7099296

When we do not know what the population standard deviation is, we can use the statistical t to obtain the critical value

c * = 15-1.691 * 0.7099296 = 13.79951

for s = 5.7,

Standard error = 5.7 / √ 3.5 = 0.9634759

c * = 15-1.691 * 0.9634759 = 13.37076

It is obtained that c * is the critical value for the rejection region in this question

P (c * = 14.16583) = 7/20

P (c * = 13.79951) = 6/20

P (c * = 13.37076) = 1-7 / 20-6 / 20

= 7/20

E (c *) = (7/20) * 14,16583 + (6/20) * 13.79951 + (7/20) * 13.37076

Outcome:

E (c *) = 13.77766

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3 years ago
A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?
Alexxx [7]

<u>Answer</u>:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of  larger square to smaller square is 9:1

<u>Step-by-step explanation:</u>

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side  of the small square is 2 units

so the are of the small square is 2^2 = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=>\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}

=>\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}

=>\sqrt{(3 +3)^2 +(-3 +3)^2}

=>\sqrt{(6)^2 +(0)^2}

=>\sqrt{36}

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

6^2

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0
3 years ago
Hi,so I've tried solving this problem for a while and I just don't get it,if you could give me some ideas I would appreciate it.
ziro4ka [17]

Answer:

187 cm²

Step-by-step explanation:

The bottom rectangle area is easy, it is 15*9 = 135 cm².

To find the area of the triangle, you only need the base width and its height (you don't need the hypotenuse). You can then use the formula: area triangle is base times half height.

The base width is 15-7 = 8 cm

The height is 22-9 = 13 cm

So the area of the triangle is 13*8/2 = 52 cm²

Together with the 135 of the rectangle that sums to 52+135 = 187 cm².

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What is triple of 1/2 oranges on a recipe?
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That's easy 327 <span>÷ 36 is  9.083</span>
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