Answer:
a) The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).
b) The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).
c) A sample size of 12 is needed.
d) A sample size of 125 is needed.
Step-by-step explanation:
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.78}{\sqrt{15}} = 0.39[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.39 = 4.46
The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.39 = 5.24
The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).
(b) Compute a 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{0.78}{\sqrt{11}} = 0.55[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.56 - 0.55 = 4.01
The upper end of the interval is the sample mean added to M. So it is 4.56 + 0.55 = 5.11
The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).
(c) How large a sample size is necessary if the width of the 95% interval is to be 0.46?
95% CI means that [tex]z = 1.96[/tex]
A sample of n is needed, and n is found when M = 0.46. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.46 = 1.96\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.46\sqrt{n} = 1.96*0.78[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.78}{0.46})^2[/tex]
[tex]n = 11.05[/tex]
Rounding up
A sample size of 12 is needed.
(d) What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence?
99% CI means that [tex]z = 2.575[/tex]
A sample of n is needed, and n is found when M = 0.18. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.18 = 2.575\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.18\sqrt{n} = 2.575*0.78[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.78}{0.18})^2[/tex]
[tex]n = 124.5[/tex]
Rounding up
A sample size of 125 is needed.
6 ft = ____ yd
6 ft = 6 x 1 ft
= 6 x ____ yd
= ____ yd
Answer:
6 ft = 2 yd
6 ft = 6 x 1 ft
= 6 x 2 yd
= 12 yd
Find the volume of the triangular prism.
PLEASE HELP!
Answer:
53.76 cm³
Step-by-step explanation:
1/2(4.8)(3.2)(7)=53.76
The picture is quite blurry. I think it's 4.8 at the base, but can't see for sure.
4. A square has a perimeter of 28 units, an
ared of 49 units, and sides that are either
horizontal or vertical. The vertices are all
located in the same quadrant where the x
value is negative. What are the possible
coordinates of the square?
Answer:
7
Step-by-step explanation:
perimeter - 7+7+7+7=28
area - 7×7 = 49
it's a square so all sides are the same length.
area is length times width
perimeter is all sides added together.
the image of (-9,-4) after a reflection over the y-axis?
Answer:
The answer is (-4,9)
Step-by-step explanation:
When you reflect across y=-x the x and y coordinates switch places and change signs.
Angus has 5 pounds of apples. Justin has 3 pounds of apples. Who has more? How do you know?
Answer:
Angus has more apples.
Step-by-step explanation:
The apples are measured in pounds for both Angus and Justin. Angus has 5 pounds of apples, and Justin has 3 pounds of apples. 5 is greater than 3, so Angus has more apples.
Given g(x)=-2x+2, solve for x when g(x)=8
Answer:
x=±3. Explanation: g(x)=2x2−10 g(x)=8. ie 2x2−10=8 2x2=18 x2=9 x=±3.
Step-by-step explanation:
plz help I need help on math plz help the first one get bainys its actually for my lis sis
here is my picture
Answer:
Step-by-step explanation:
1. $5
2. 50 cents
3. 25 cents
4. 3 dollars
5. 70 cents
just subtract them
Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
Answer:
12.04
Step-by-step explanation:
Formula:
a² + b² = c²
8² + 9² = c²
64 + 81 = c²
145 = c²
c = 12.04
in ABC, what is the value of x?
Answer:
x = 16.2
Step-by-step explanation:
5/9 = 9/x
5x = 81
x = 16.2
Please answer this question!!! Thank you!
Answer:
your answer is b
Step-by-step explanation:
Mason spends $24 on hot dogs and buns for his graduation picnic. Hot dogs cost $3 per pack and buns cost $2 per packGraph the equation that models this situation, given that represents packs of hot dogs and y represents packs of buns
Answer: i don’t know
Step-by-step explanation: because I don’t know
helpppppppppppppppppp
Answer and Step-by-step explanation:
The independent variable is m, and the dependent variable is h.
This is because you can plug in any value for m, making m NOT have to depend on any other value to become m.
With h, it needs the result of m and its other values to become the result of h. H relies/depends on the values in the equation to become a value.
#teamtrees #PAW (Plant And Water)
Factor:
n^4- 3n^2 + 2
*example: n^2-n-2 factored would be: (n-2)(n+1)*
Step-by-step explanation:
[tex]( \: n - 1) \times (n + 1) \times \: ( {n }^{ 2 - 2)} [/tex]
Help me with this last one I don’t really get it
Answer:
Step-by-step explanation:
1. Bar graph.
2. fewer
3. more
Hope that helps!
In a right triangle, the hypotenuse has endpoints P(-3, 2) and Q(1, -3).
Answer:
the remaining points either be (-3,-3) or (1,2)
Help I’m doing 8th grade work
Answer:
I think B by I'm not sure
Step-by-step explanation:
I'm not good with this subject
Which set of measurements would not create a triangle?
A. 9 in., 8 in., 16 in.
B. 11 in., 12 in., 22 in.
C. 14 in., 6 in., 20 in.
D. 3 in., 8 in., 6 in.
what is the solution to the equation below -5/4 x + 2/5 equals -13 / 30
(08.01)
Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge,
strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find B'
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
Answer:
A
Step-by-step explanation:
njsusnhshbwhjkahbkans
help plssssssssssssssssssssssssssssssssssssssssssssssssssssssss
what is the volue of j?
Answer:
23 is the answer the J is acute but it has a vary so it is even smaller than 49 so it's like subtracting 26
Answer: j=27 degrees
49+j=76 because vertical angles are always congruent. Now that we know that, we can subtract 49 from 76 which equals 27 degrees and that's your answer!
Hope this helped you!
I can't seem to factor out this equation.
40x squared -46x +12
Which expression is equivalent to 6-8 x 65?
Answer:
12-16 X 130
Step-by-step explanation:
Lol its asking for an equivalent expression meaning the same thing soooo... I just multiplied each number by two: 6X2= 12) 8X2=16) 65X2= 130) so the expression will be 12-16 X 65.
ps.
If u get any other answers with a different one than mine it doesnt mean its incorrect because there are infinite equivalent answers for this expression
Translate the sentence into an inequality.
A number increased by 2 is greater than or equal to 19.
Answer:
X + 2 [tex]\geq \\[/tex] 19
Step-by-step explanation:
a number ur going to represent with a variable x and increased by 2 means + 2 so x + 2 and when it say greater than or equal to remember that it always opens to the lager number or x + 2 and has a line underneath to represent the or equal to.
Urgent!Math help!!! What’s the real answers?
Answer: you got the two right, the third is incorrect and the fourth is correct
Step-by-step explanation: I took the quiz hope I pulled some weights off your shoulders
-6(2x - 6) - 4x + 7 Simplify the algebraic expression.
Answer:
− 1 6 + 4 3
Step-by-−
−6 ( 2 − 6 ) − 4 + 7
− 1 2 + 3 6 − 4 + 7
− 1 2 + 3 6 − 4 + 7
− 1 2 + 4 3 − 4
− 1 2 + 4 3 − 4
− 1 6 + 4 3
step explanation:
Distribute
Add the numbers
Combine like terms
A square notepad has sides that are 14 centimeters long. What is the notepads perimeter?
Answer:
56 cm (22.4 in)
Step-by-step explanation:
14+14+14+14=56 or 14x4=56
2/7 of 49
fractions
Answer:
14
Step-by-step explanation
5.5 + n = 10 please help
Answer:
n = 4.5
Step-by-step explanation:
10 - 5.5 = n
Answer:
I feel like its 4.5
Step-by-step explanation:
Is 8/15 greater than 4/5 ? and is 2/3 greater than 5/8 ?
Answer:
yes 8/15 is greater and 2/3 is less than
Elis, Raine and Avery buy a boat for $33 000.
Elise pays $12 000, Raine pays $6000 and Avery pays the rest.
Six years later they sell the boat for $25 300.
They share the money in the same ration that they bought the boat.
How much money does Avery lose on the sale of the boat?
Amount Avery paid: 32,000-12,000-6,000 = 15,000
Divide portion she paid by total cost:
15,000/33,000
Simplify to 15/33
Multiply the amount the boat was sold for by her portion:
25,300 x 15/33 = 11,500
Subtract the amount she got from the amount she paid:
15,000 - 11,500 = 3,500
She lost $3,500
Answer:
yes
Step-by-step explanation:
yes!