What is the result when 2x^3-9x^2+11x-6 is divided by x-3

The diameters of bearings used in an aircraft landing gear assembly have a standard deviation of ???? = 0.0020 cm. A random samp

vovikov84 [41]

Answer:

(a) We conclude after testing that mean diameter is 8.2500 cm.

(b) P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) 95% confidence interval on the mean diameter = [8.2525 , 8.2545]

Step-by-step explanation:

We are given with the population standard deviation, $\sigma$ = 0.0020 cm

Sample Mean, Xbar = 8.2535 cm and Sample size, n = 15

(a) Let Null Hypothesis, $H_0$ : Mean Diameter, $\mu$ = 8.2500 cm

Alternate Hypothesis, $H_1$ : Mean Diameter, $\mu$ $\neq$ 8.2500 cm{Given two sided}

So, Test Statistics for testing this hypothesis is given by;

$\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ follows Standard Normal distribution

After putting each value, Test Statistics = $\frac{8.2535-8.2500}{\frac{0.0020}{\sqrt{15} } }$ = 6.778

Now we are given with the level of significance of 5% and at this level of significance our z score has a value of 1.96 as it is two sided alternative.

<em>Since our test statistics does not lie in the rejection region{value smaller than 1.96} as 6.778>1.96 so we have sufficient evidence to accept null hypothesis and conclude that the mean diameter is 8.2500 cm.</em>

(b) P-value is the exact % where test statistics lie.

For calculating P-value , our test statistics has a value of 6.778

So, P(Z > 6.778) = Since in the Z table the highest value for test statistics is given as 4.4172 and our test statistics has value higher than this so we conclude that P - value is smaller than 2 x 0.0005% { Here 2 is multiplied with the % value of 4.4172 because of two sided alternative hypothesis}

Hence P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) For constructing Two-sided confidence interval we know that:

Probability(-1.96 < N(0,1) < 1.96) = 0.95 { This indicates that at 5% level of significance our Z score will lie between area of -1.96 to 1.96.

P(-1.96 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96\frac{\sigma}{\sqrt{n} }$ < $Xbar - \mu$ < $1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

P( $-Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $-\mu$ < $1.96\frac{\sigma}{\sqrt{n} }-Xbar$ ) = 0.95

P( $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $\mu$ < $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

So, 95% confidence interval for $\mu$ = [ $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ , $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ]

= [ $8.2535-1.96\frac{0.0020}{\sqrt{15} }$ , $8.2535+1.96\frac{0.0020}{\sqrt{15} }$ ]

= [8.2525 , 8.2545]

Here $\mu$ = mean diameter.

Therefore, 95% two-sided confidence interval on the mean diameter

= [8.2525 , 8.2545] .

6 0

3 years ago

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Tanya has a garden with a trench around it .The garden is a rectangle with length 2 1/2m and width 2 m.

Hunter-Best [27]

The area of the trench is 5 $\frac{1}{2}$ m²

Step-by-step explanation:

Tanya has a garden with a trench around it

The garden is a rectangle with length 2 $\frac{1}{2}$ m and width 2 m
The trench and garden together with length 3 $\frac{1}{2}$ m and width 3 m

We need to find the area of the trench

The area of the trench is the difference between the area of the garden with the trench and the area of the garden

The formula of the area of a rectangle is A = length × width

∵ The garden is a rectangle with length 2 $\frac{1}{2}$ m and width 2 m

∴ Length = 2 $\frac{1}{2}$ m

∴ Width = 2 m

Find the area of the garden

∴ A = 2 $\frac{1}{2}$ × 2 = 5 m²

∵ The trench and garden together with length 3 $\frac{1}{2}$ m and width 3 m

∴ Length = 3 $\frac{1}{2}$ m

∴ Width = 3 m

Find the area of the garden with the trench

∴ A = 3 $\frac{1}{2}$ × 3 = 10

The area of the trench = area of the garden with the trench - area of the garden

∴ The area of the trench = 10 $\frac{1}{2}$ - 5 = 5

The area of the trench is 5 $\frac{1}{2}$ m²

Learn more:

You can learn more about the area of rectangles in brainly.com/question/6564657

#LearnwithBrainly

6 0

3 years ago

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PLEASSSSSSEEEEEEEEE HELPPPPPPPPP !!!!!! Tyler begins funding a college education for his son. He saves $1000 the first year. Eac

vladimir2022 [97]

1050 each year he funds them

5 0

3 years ago

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A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height. What is the volume of the cylinder? E

Firdavs [7]

The answer is 49806.06.

6 0

3 years ago

What is the equation of the circle that has a center at (-3, 1) and a radius of 5? A) (x + 3)2 + (y - 1)2 = 5 B) (x - 3)2 + (y +

Gnoma [55]

Answer:

C

Step-by-step explanation:

The vertex form of the equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$ where (h,k) is the center of the circle and r is the radius. This means that for the circle with center (-3,1) and radius 5 substitute into the vertex form these values. Substitute h = -3, k= 1, and r = 5. The equation becomes $(x--3)^2 + (y-1)^2 = 5^2$ . This simplifies to $(x+3)^2 + (y-1)^2 = 25$ . The solution is C.

7 0

3 years ago