Answer:
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
First group: Sample of 163, 13% has a second episode.
This means that:
[tex]p_1 = 0.13, s_1 = \sqrt{\frac{0.13*0.87}{163}} = 0.026[/tex]
Second group: Sample of 160, 14% has a second episode
This means that:
[tex]p_2 = 0.14, s_2 = \sqrt{\frac{0.14*0.86}{160}} = 0.027[/tex]
Distribution of the difference:
[tex]p = p_1 - p_2 = 0.13 - 0.14 = -0.01[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.026^2+0.027^2} = 0.0375[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Lower bound:
[tex]p - 1.645s = -0.01 - 1.645*0.0375 = -0.0717[/tex]
Upper bound:
[tex]p + 1.645s = -0.01 + 1.645*0.0375 = 0.0517[/tex]
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Two parallel lines are cut by a transversal. What is the measure of <1?
A 80
В. 180
C. 100
D. 90
Answer:
C - 100
Step-by-step explanation:
9514 1404 393
Answer:
C. 100°
Step-by-step explanation:
Consecutive (same-side) exterior angles are supplementary.
∠1 = 180° -∠7 = 180° -80°
∠1 = 100°
160% of what number 56?
Answer:
160% of 35 is 56.
Step-by-step explanation:
[tex]\frac{56}{y} :\frac{160}{100}[/tex]
y · 160 = 56 · 100
160y = 5600
160y ÷ 160 = 5600 ÷ 160
y = 35
Plz help ASAP plz help
Answer:
no solution for the answer
find the difference between 0.1 kg and 75g
Answer:
25 g
Step-by-step explanation:
0.1 kg can be written as 100 grams
& 75 g
while 1 kg is 1000 grams
so difference:-
(100- 75 ) grams
= 25 g
The difference between 0.1 kg and 75 g is 25 grams. To find the difference between 0.1 kg and 75g, you need to make sure both quantities have the same unit.
Since 1 kg is equal to 1000 g, you can convert 0.1 kg to grams:
0.1 kg = 0.1 * 1000 g = 100 g
Now, the two quantities are in the same unit:
0.1 kg - 75 g = 100 g - 75 g = 25 g
So, the difference between 0.1 kg and 75 g is 25 grams.
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what is the answer to 3(x-2)+15=-3(x-3)
i will give brainliest
Answer:
x = 0
Step-by-step explanation:
3(x - 2) + 15= -3(x - 3)
3x - 6 + 15 = -3x + 9
3x + 9 = -3x + 9
3x + 3x = 9 - 9
6x = 0
x = 0
Find the area of each figure. Round to the nearest tenth. Use 3.14 or 22/7
a. 18.8
b.9.4
c. 113
d. 28.3
Answer:
d. 28.3
Step-by-step explanation:
Given
Radius ( r) = 3 m
Area of the circle
= π r²
= 3.14 * 3* 3
= 28.26
= 28.3 ft²
Use formulas to find area
Answer:
120.08
Step-by-step explanation:
15.8 x 7.6
-> 120.08 [tex]m^2\\[/tex]
Use systems of linear equations solve x+2y=4
Must include;
Step to solve problem
Answer: y=2-2x
Step-by-step explanation:
A circle has a diameter of 10 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
15.7 cm²
31.4 cm²
78.5 cm²
314 cm²
Answer:
78.5 (please put brainliest)
Step-by-step explanation:
r = diameter / 2 = 5
area = π * r^2 = 25 * 3.14 = 78.5
Answer:
78.5 m^2
Step-by-step explanation:
Eight eagle stamps and two raccoon stamps cost $2.80. Three eagle stamps and four raccoon stamps cost $2.35. Find the cost of each kind of stamp
Show work please
Answer:
Cost of each eagle stamp = $0.25
Cost of each racoon stamp = $0.4
Step-by-step explanation:
Given:
Cost of 8 eagle stamp and 2 racoon stamp = $2.80
Cost of 3 eagle stamp and 4 racoon stamp = $2.35
Find:
Cost of each stamp
Computation:
Assume;
Cost of each eagle stamp = e
Cost of each racoon stamp = r
So,
8e + 2r = 2.80........... Eq 1
3e + 4r = 2.35 ........... Eq 2
Eq 1 x 2
16e + 4r = 5.6 .........Eq3
Eq 3 - Eq 2
13e = 3.25
e = 0.25
Cost of each eagle stamp = $0.25
8e + 2r = 2.80
8(0.25) + 2r = 2.80
2 + 2r = 2.80
r = 0.4
Cost of each racoon stamp = $0.4
5th grade math. correct answer will be marked brainliest
Answer:
4ft, 7 inches
Step-by-step explanation:
4 ft (48 inches), 7 inches
I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS
please help this is very important
this is a big part of my grade
Answer:
pretty sure the answer is electrons so D
Step-by-step explanation:
Electrons are particles that surround the nucleus of an atom like a cloud
Can someone please help?
Answer:
it's the top right box
Step-by-step explanation:
start from the first box and count how many units was added
The Unit Circle
What is the period for the graph of y = cos(∅)? (Sketch a graph to help determine the answer)
a. 180°
b. 90°
c. 360°
d. 270°
Please select the best answer from the choices provided
Answer:
C. 360°
Step-by-step explanation:
I calculated it logically
Answer:
Answer is C) 360°
Step-by-step explanation:
If the radius of a cylinder is 3 centimeters and the height of the cylinder is 4 centimeters, then the area of the lateral surface is 75.36 square centimeters. True False
Answer:
True
Step-by-step explanation:
The Answer is 75.36 cm
2 x (pi)3.14 = 6.28
6.28 x (r)3 = 18.84
18.84 x (h)4 = 75.36
The statement, "If the radius of a cylinder is 3 centimeters and the height of the cylinder is 4 centimeters, then the area of the lateral surface is 75.36 square centimeters." is true.
What is cylinder?"A cylinder is a three-dimensional geometrical structure which consists of two circular bases connected with a curved surface."
Formula to calculate the area of the lateral surface of a cylinder:For a cylinder with radius r and height h,
the curved / lateral surface area is,
A = 2 × π × r × h
Given: r = 3 cm, h = 4 cm
Using the formula for area of lateral surface of a cylinder:
⇒ A = 2 × π × 3 × 4
⇒ A = 24 × π
⇒ A = 24 × 3.14
⇒ A = 75.36 sq.cm.
Therefore, given statement is true.
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Please answer for branliest
What is 8% of 200?
4
16
25
Done
Answer:
16
Step-by-step explanation:
8% of 200 is 16
Answer: 16
Explanation: That's an i-Ready Diagnostic!! Heh...
What is the absolute value of a number?
Answer:
It is the distance from the zero on a number line. Also, it is never negative.
Step-by-step explanation:
No links please 15 Points
Answer:
C
Step-by-step explanation:
struggling with homework!!
Answer:
40
Step-by-step explanation:
if 20% were Caesar and 20 divided by 5 is 4, then every four salads sold is five percent.
Volume answer rn djdjd
Answer:
133.7π cm^3 or approximately 418.77430072 cm^3.
Step-by-step explanation:
For the cylinder half, use the formula: π*r^2*h, or pi times radius squared times height.
Since the diameter is 8, which means the radius is 4, and the height is 6, the volume of the cylinder would be 96π or 301.59289474...
For the cone on top, use the formula 1/3 (π*r^2*h), or one third pi times radius squared times height. Don't forget to calcuate the part in parentheses before dividing it by three.
Because the overall height was 13, you can subtract the 6 from the cylinder to get the cone's height. It has a height of 7 and a radius of 4 just like the cylinder. The volume of the cone is 112π/3 or 37.3π.
Now add both volumes together to get 133.7π cm^3 or approximately 418.77430072 cm^3.
What is the distance between (2, 5) and (2, -7)?
Question 1 options:
2
5
12
14
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
i need assistance please
Does anybody know the answer please.
Answer:
The sign of each y-coordinate changed.
Step-by-step explanation:
This was a reflection over the x-axis.
If you look at point F, it is (-5, -1) the corresponding point F' is (-5,1). Notice the numerical values of x and y are the same, but the sign of y flipped from negative to positive. The other four points all follow the same pattern.
Planes A and B intersect. Which describes the intersection of plane A and line m? Oline k B m Olinen À point X O point W X 3 k Y Z
The intersection of plane A and line m can be describes as line m .
What is reflectional symmetry?Let's a plane. Consider a design or shape on that plane. Now consider an axis.
If we think of that axis as a mirror, and on the opposite side of that axis create the image of the considered shape, then if the shape's image looks exactly as the shape itself, therrefore that shape is called to have a reflectional symmetry.
Given that Planes A and B intersect.
We can see the two walls as planes in geometry.
A plane can be thought of as a wall or a floor of a room also a flat surface that has no thickness.
When two planes intersect, their intersection is a line.
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Surface area of a solid figure can be found by multiplying the area of the base by the height of the figure.
True
O False
Answer:
Surface area of a solid figure can be found by multiplying the area of the base by the height of the figure.
it's false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
The triangles below are similar. Find the length and round to the nearest tenth if necessary.
Answer:
x=48
Step-by-step explanation:
You start with the values of 4 and 16. Figure out how many times 4 goes into 16, which is 4. (4*4=16)
Now, since 4 is multiplied by itself to reach the value of 16, 12 will also be multiplied by 4 to give you the value of x.
The set of life spans of an appliance is normally distributed with a mean y = 48 months and a standard deviation or
8 months. What is the z-score of an appliance that stopped working at 64 months?
Answer:
The set of life spans of an appliance is normally distributed with a mean µ= 48 months and a standard deviation σ= 8 months. ... Thanh finds that his grade on the test has a z-score of -2.5. ... are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668.
Step-by-step explanation:
=============================================================
Explanation:
The raw score is x = 64, and we want to find its corresponding z score.
The mean and standard deviation are mu = 48 and sigma = 8 respectively.
The z score is...
z = (x-mu)/sigma
z = (64-48)/8
z = 16/8
z = 2
A z score of 2 means we're 2 standard deviations above the mean.
As the formula above implies, we find the difference from the raw score (x) to the mean (mu). Then we divide over sigma to find out how many sigma steps we have to take to go from mu to x.
A negative z score would indicate the raw score is below the mean.
Which equation in rectangular form describes the parametric equations x=2-3 cos t and y=1+4 sin t?
Answer:
The parametric equations represents an ellipse by the rectangular equation [tex]\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1[/tex].
Step-by-step explanation:
We proceed to use the following trigonometric identity to derive an expression in rectangular form:
[tex]\cos^{2} t + \sin^{2} t = 1[/tex] (1)
Where:
[tex]\cos t = \frac{2-x}{3}[/tex] and [tex]\sin t = \frac{y-1}{4}[/tex]
Then, we expand the expression as follows:
[tex]\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1[/tex] (2)
The parametric equations represents an ellipse by the rectangular equation [tex]\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1[/tex].
Evaluate the following expression if x= 2.14
3.35x + 25 - 2x
Answer:
The final answer is 27.889 (Feel free to round it)
Step-by-step explanation:
3.35 x 2.14 = 7.169
7.169 + 25 = 32.169
2 x 2.14 = 4.28
32.169 - 4.28 = 27.889
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!