Answer:
A sample size of 1068 is required.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
CBS wishes to have 95% confidence and a margin of error in its estimate of ±0.03. What sample size is required?
We need a sample size of n, and is found when M = 0.03.
We dont have an estimate for the true proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.03})^2[/tex]
[tex]n = 1067.1[/tex]
Rounding up,
A sample size of 1068 is required.
The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 768 boys and 745 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting.
Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use μboys − μgirls. Round your test statistic to two decimal places and your P-value to four decimal places.)
Answer:
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
The value of p is 0 .00233. The result is significant at p < 0.10.
Step-by-step explanation:
1) Let the null and alternate hypothesis be
H0: μboys − μgirls > 0
against the claim
Ha: μboys − μgirls ≤ 0
2) The significance level is set at 0.01
3) The critical region is z ≤ ± 1.28
4) The test statistic
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
Here p1= 397/768= 0.5169 and p2= 331/745=0.4429
pc = 397+331/768+745
pc= 0.4811
qc= 1-pc= 1-0.4811=0.5188
5) Calculations
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
z= 0.5169-0.4429/√ 0.4811*0.5188( 1/768+ 1/745)
z= 2.82
6) Conclusion
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
7)
The value of p is 0 .00233. The result is significant at p < 0.10.
Let f(x) = x-9
Find (f o f)(x) and its domain
(f o f)(x) =
Answer:
Step-by-step explanation:
Write the equation of the line that passes through the point (-1,-5) and has a slope of -2?
Answer: -7 is the answer.
Step-by-step explanation:
y2 - y1 = m (x2 - x1)
y - (-5) = -2 {x - (-1)} [Taking y2 as y and x2 as x]
y + 5 = -2 (x + 1)
y + 5 = -2x -2
y + 2x = -2 - 5
2x + y = -7
Explain what a ratio is in your own words.
(I need this, please. I will mark brainliest ; — ; no one has been frikin helping me)
The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Step-by-step explanation:
Hope it helps
Answer:
a ratio is a proportion indicating coorelation between two different things
GIVING 25 PTS I REALLY NEED HELP ON THIS LAST QUESTION AND IM TIMED ILL GIVE BRAINLIEST TO WHOS RIGHT
Answer: A, 314 square inches
Step-by-step explanation:
The equation for the area of a circle is A = 3.14 x r²
3.14 x 10² ≈ 314
Which is the value of this expression when P= -2
and q=-1
((p^2)(q^-3))^-2•((p^-3)(q^5))^-2
-4
-1/16
1/16
4
Answer:
B -1/16
Step-by-step explanation:
There are 192 cubes. The length is 6 and the width is 4. What is the height?
Answer:
Height = 8
Step-by-step explanation:
Volume = Length x width x height
192 = 6 x 4 x H
192 = 24 x H
192/24 = H
8 = H
Height = 8
Pls help I don’t know hot to multiply the last part 8 2
Answer:
8^2 = 64
Step-by-step explanation:
Hi! Okay, let's get started!
[tex]8^{2}[/tex] is what you need help with right?
So, that equals to 8 x 8.
8 x 8 = 64, so it would be 64
Hope that helps!
-Aphrodite :)
a bag contains 1 red beads,2 yellow beads,2 green beads and 1 blue beads
a bead is chosen at random
a)what is probability that it is green ?
b)what probability that it is green or yellow
Answer:
a) 2/6 b) 4/6
Step-by-step explanation:
You add the amount of beads: 1+2+2+1= 6
And take the amount of green beads and put it over the total amount so 2/6
For b you do the same but add the green and yellow beads and put that over the total amount 4/6
Answer:
Step-by-step explanation:
a) 2/6 = 1/3
b) green or yellow = (2/6 x 1/5) + (2/6 x 1/5) = 1/15 x 1/15 = 1/225
im not sure if my answers are correct
5th grade math. correct answer will be marked brainliest
Answer:
Step-by-step explanation:
1[tex]\frac{1}{2}[/tex] * [tex]\frac{1}{3}[/tex] = [tex]\frac{3}{2}[/tex]*[tex]\frac{1}{3}[/tex] cross cancel then you have [tex]\frac{1}{2}[/tex] :)
Answer:
He will use 1 1/6 teaspoons
You can change mixed numbers by changing it into an improper fraction.
Step-by-step explanation:
help me! I have a retake on this and my last answer I put was A and D and I got it wrong!
9514 1404 393
Answer:
A, E
Step-by-step explanation:
You are correct that the appropriate relationship is ...
g = 0.4t . . . . choice A
You are also correct that an equivalent relationship is ...
t = 2.5g . . . . choice D
However, when we say gallons are proportional to seconds, we usually expect that to be written ...
g = kt . . . . for some value of k
__
We note that another equivalent is ...
g = 2/5t . . . . choice E
The appropriate choices are probably A and E. Choice D might be argued to be correct, but you could very well lose that argument to someone who prefers a "g = " form of the relationship.
HELPPPPPPP PLSSSSSSSS
Answer:
D'(5,2)
E'(13,-5)
F'(15,3)
Volume of a square prism with faces of 3/8
Answer:
27/512 in.^3
Step-by-step explanation:
volume = side^3
V = (3/8 in.)^3
V = 27/512 in.^3
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 35
Step-by-step explanation:
The sum of interior angles of a triangle is 180°.
40 + 2a + 2a = 180
4a + 40 = 180
4a = 140
a = 35
33°
(3m + 3)
ent OR Vertical_
Angle Relationship: Complementary OR Supplementary
Answer:
complementary
Step-by-step explanation:
because the angles add up to 90°
please please help me I will mark brainlist !!
Answer:
9. B. 32 millimeters
10. C. 7 inches
11. C. 56.24 millimeters
13. B. 14.13 square feet
Step-by-step explanation:
9. Radius of a circle or any circular shape = ½ of its diameter
Diameter of the disk = 64 millimeters
Radius of the disk = ½(64) = 32 millimeters
10. Width of the cooler = 6 in.
Length = 8 in.
Volume = 336 in.³
Height = ?
Formula for volume of a rectangular prism = L*W*H
Plug in the values
336 = 8*6*H
336 = 48*H
Divide both sides by 48
336/48 = H
H = 7 inches
11. A dime has a circular shape
The circumference of the dime = circumference of a circle = πd
Where,
d = 17.91 millimeters
π = 3.14
Plug in the values
C = 3.14 × 17.91 = 56.2374
≈ 56.24 millimeters (nearest hundredth)
12. Area of the top of the desk = area of semicircle = ½ × πr²
Where,
r = ½(6) = 3 ft
π = 3.14
Plug in the values
Area = ½ × 3.14 × 3² = ½ × 3.14 × 9
Area = 14.13 square feet
what is the GCF of 24 and 20 is?
Step-by-step explanation:
4. because it's the highest number your can evenly divide both numbers by
find m angle F
A . 60
B. 30
C. 10
D. 15
Answer:
D i hope heulful
Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
measure of angle F = [tex]sin^{-1} (9/18) = 30[/tex]
seventeen and nine hundred five thousandths in decimal form
Answer:
17.905
#CarryOnlearning
Let's play Cooking Diary! Together we'll rock the culinary world! https://social-cd.mytonagames.com/4gx9R8
What effect does armature reaction have on the torque speed characteristic of a DC shunt motor?
Answer:
Step-by-step explanation:
The armature reaction in the motor affects the torque speed characteristics of the motor. Due to the armature reaction in the motor the shape of the torque speed characteristics will changes. The relation between torque and speed of the motor is given below.
…… (1)
where
Terminal voltage of the motor
Flux in the motor
Torque induced in the motor
Armature resistance
If a motor has armature reaction, as the load increases the flux weakening effect reduces the flux in the field winding. From equation (1), as the flux reduces, the speed of the motor increases at a given load over the speed it would run at without armature reaction.
Rachel received a monthly raise of $105.25. If this represented a 5.5% increase, what is her monthly salary after the raise?
A. $1,913.64
B. $1,964.13
С. $2,018.89
D. $2.089.18
Answer:
C
Step-by-step explanation:
105,25:5,5*105.5=2018,89
Which line shown appears to have a Y-intercept of 3?
A. I
B. II
C. III
D. IV
E. none of the above
7) Una epidemia mató los 3/7 de las vacas de un granero y de las que le quedaron vendió 1/2. Si todavía le quedaron 24 vacas, ¿Cuántas vacas tenía al principio, ¿cuántas murieron y cuántas vendió?
Answer:
Habían inicialmente 84 vacas. Murieron 36 vacas. 24 vacas fueron vendidas.
Step-by-step explanation:
Sea [tex]x[/tex] la cantidad inicial de vacas. De acuerdo con el enunciado, murieron tres séptimos de la cantidad inicial y la mitad de ese remanente fue vendida, quedando 24 vacas. Matemáticamente, tenemos las siguientes operaciones:
Cantidad inicial de vacas
[tex]x = \frac{24}{\left(1-\frac{3}{7} \right)\cdot \left(1-\frac{1}{2} \right)}[/tex]
[tex]x = 84[/tex]
Habían inicialmente 84 vacas.
Cantidad de vacas muertas
[tex]y = \frac{3}{7}\cdot x[/tex]
[tex]y = 36[/tex]
Murieron 36 vacas.
Cantidad de vacas vendidas
[tex]z = \left(1-\frac{3}{7} \right)\cdot \frac{1}{2}\cdot x[/tex]
[tex]z = 24[/tex]
24 vacas fueron vendidas.
sin 30Degrees = square of 3/2 and cos 30degrees =1/2 true or false
Answer:
False
Step-by-step explanation:
Trying it in a calculator says otherwise meaning it's false
Graph the function f(x)= -³√x+2.
Answer:
Step-by-step explanation:
How do you convert a fraction or decimal to a percent?
Answer:
a
Step-by-step explanation:
Answer:
To convert a decimal to a percent, multiply it by 100 (move the decimal place two digits to the right) and add the "%" sign.
A fraction must be converted into a decimal first by dividing the denominator into the numerator, then converting that answer to a percent like above.
Find the 14th term of the geometric sequence 2,6,18, ...
Answer:
Step-by-step explanation:
The answer to this question link is here
https://socratic.org/answers/623991
The geometric sequence is starting with 2 and multiplying by 3 every time. We can get the rule of this sequence by...
If 2 is [tex]a_{1}[/tex], 6 is [tex]a_{2}[/tex], 18 is [tex]a_{3}[/tex], etc...then, [tex]a_{n}[/tex]=2(3)^(n - 1)For the 14th term, plus in 14 for n, and it will look like this:
= 2(3)^(14 -1)
= 2(3)^(13)
= 3188646
1.Write an inequality comparing the rational numbers -3/4 and -2 .
2. Using complete sentences, explain what your inequality means about the position of the two numbers on the number line.
Answer:
[tex]-2<x<-\dfrac{3}{4}[/tex] Or [tex]x\in (-2,-\dfrac{3}{4})[/tex]
Step-by-step explanation:
The numbers are [tex]-\dfrac{3}{4}[/tex] and [tex]-2[/tex].
We need an inequality that gives us the numbers between the above numbers.
The inequality will be
[tex]-2<x<-\dfrac{3}{4}[/tex]
Or
[tex]x\in (-2,-\dfrac{3}{4})[/tex]
This means that [tex]x[/tex] is a number that is in between the rational numbers [tex]-\dfrac{3}{4}[/tex] and [tex]-2[/tex]. Also, [tex]x[/tex] is greater than [tex]-2[/tex] and less than [tex]-\dfrac{3}{4}[/tex]
The positions in the number line are shown in the figure where the numbers are marked by arrow.
The train clock run fast and gain 4 minutes every 3 days. How many minutes and seconds will it have gained at the end of 2 days.
Answer:
2 minutes, 40 seconds
Step-by-step explanation:
set up a proportion and cross-multiply:
4/3 = x/2
3x = 8
x = 2 2/3 which is 2 minutes, 40 seconds