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3 years ago

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A random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample sta

ndard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5.
(a) Is it appropriate to use a Student's t distribution? Explain. How many degrees of freedom do we use?
(b) What are the hypotheses?
(c) Compute the sample test statistic t.
(d) Estimate the P-value for the test.
(e) Do we reject or fail to reject H_0?
(f) Interpret the results.

1 answer:

nikklg [1K]3 years ago

6 0

Answer:

Step-by-step explanation:

Given that random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample standard deviation is 2.

95 % CI for mean 9.1744 to 10.8256

Since p >0.05 accept null hypothesis.

a) Yes because std dev sigma not known. df = 24

b)

H0: x bar = 9.5

Ha: x bar not equals 9.5

c) t-statistic 1.250

d) P = 0.2234

e) We fail to reject null hypothesis

f) There is no statistical evidence at 5% level to fail to reject H0.

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R+L=12
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-48L+36L=528-576
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4 years ago

match each system to the number the first equation can be multiplied by to eliminate the x-terms when adding the second equation

seraphim [82]

Part a: -2 is used to eliminate the x-terms when adding with the second equation.

Part b: $-\frac{1}{2}$ is used to eliminate the x-terms when adding with the second equation.

Part c: $\frac{1}{2}$ is used to eliminate the x-terms when adding with the second equation.

Part d: 2 is used to eliminate the x-terms when adding with the second equation.

Explanation:

Part a: The equations are $3 x-8 y=1$ and $6 x+5 y=12$

To eliminate the x-terms from both the equations, let us multiply -2 with the first equation and hence it becomes $-6x+16y=-2$

Adding the two equation, we get,

$-6x+16y+6 x+5 y=-2+12$

Simplifying, we get,

$21y=10$

Thus, the x-terms are eliminated when adding the equations.

Hence,-2 is used to eliminate the x-terms when adding with the second equation.

Part b: The equations are $-8 x+10 y=16$ and $-4 x-5 y=13$

To eliminate the x-terms from both the equations, let us multiply $-\frac{1}{2}$ with the first equation and hence it becomes $4 x-5 y=-8$

Adding the two equation, we get,

$4x-5y-4x-5y=-8+13$

Simplifying, we get,

$0=5$

Thus, the x-terms are eliminated when adding the equations.

Hence, $-\frac{1}{2}$ is used to eliminate the x-terms when adding with the second equation.

Part c: The equations are $10 x-4 y=-8$ and $-5 x+6 y=10$

To eliminate the x-terms from both the equations, let us multiply $\frac{1}{2}$ with the first equation and hence it becomes $5x-2y=-4$

Adding the two equation, we get,

$5x-2y-5x+6y=-4+10$

Simplifying, we get,

$4y=6$

Thus, the x-terms are eliminated when adding the equations.

Hence, $\frac{1}{2}$ is used to eliminate the x-terms when adding with the second equation.

Part d: The equations are $-2 x+6 y=3$ and $4 x+3 y=9$

To eliminate the x-terms from both the equations, let us multiply 2 with the first equation and hence it becomes $-4x+12y=6$

Adding the two equation, we get,

$-4x+12y+4x+3y=6+9$

Simplifying, we get,

$15y=15$

Thus, the x-terms are eliminated when adding the equations.

Hence, 2 is used to eliminate the x-terms when adding with the second equation.

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4 years ago

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If the children were to share the juice equally, how much would each child get? Show your work.

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Answer:

you are missing part of the question

Step-by-step explanation:

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3 years ago

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro

Neporo4naja [7]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

★ Perimeter of land = 400 m.

★ One of the diagonal = 160 m.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Area each of them [son and daughter] will get.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Let, ABCD be the rhombus shaped field and each side of the field be $x$

[ All sides of the rhombus are equal, therefore we will let the each side of the field be $x$ ]

Now,

• Perimeter = 400m

$\longrightarrow \tt AB+BC+CD+AD=400m$

$\longrightarrow \tt x + x + x + x=400$

$\longrightarrow \tt 4x=400$

$\longrightarrow \tt \: x = \dfrac{400}{4}$

$\longrightarrow \tt x= \red{100m}$

$\therefore$ Each side of the field = <u>100m</u><u>.</u>

Now, we have to find the area each [son and daughter] will get.

So, For $\triangle$ ABD,

Here,

• a = 100 [AB]

• b = 100 [AD]

• c = 160 [BD]

$\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }$

$\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}$

$\longrightarrow \tt S = \cancel{ \dfrac{360}{2}}$

$\longrightarrow \tt S = 180m$

Using <u>herons formula</u><u>,</u>

$\star \tt Area \: of \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star$

where

• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

<u>Putt</u><u>ing</u><u> the</u><u> values</u><u>,</u>

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(80)(80)(20) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180 \times 80 \times 80 \times 20 }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{9 \times 20 \times 20 \times 80 \times 80}$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{ {3}^{2} \times {20}^{2} \times {80}^{2} }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = 3 \times 20 \times 80$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \red{ 4800 \: {m}^{2} }$

Thus, area of $\triangle$ ABD = <u>4800 m²</u>

As both the triangles have same sides

So,

Area of $\triangle$ BCD = 4800 m²

<u>Therefore, area each of them [son and daughter] will get = 4800 m²</u>

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

${\underline{\rule{290pt}{2pt}}}$

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Answer:

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Step-by-step explanation:

Break each problem down into individual shapes.

For instance, A can be split into a 3 by 3 square and a 6 by 3 square.

Get the area by multiplying the length & height: A = L * H

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Shapes with unclear dimensions like C can be skipped and have their area revealed through process of elimination.

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