Answer:
B. 0.024
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
1999:
Of 100, 20 were in the bottom thid. So
[tex]p_B = \frac{20}{100} = 0.2[/tex]
[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
Of 100, 10 were in the bottom third, so:
[tex]p_A = \frac{10}{100} = 0.1[/tex]
[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.
Can also be rewritten as:
[tex]H_0: p_B - p_A = 0[/tex]
[tex]H_1: p_B - p_A > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample:
[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]
[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.976.
1 - 0.976 = 0.024, so the p-value is given by option B.
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Find the slope of the graphed line.
ASAP
y = mx+b
y = 1/3x+4
Sincerely,
William
help! provide the missing statement and reasons for the following proof:
Theorem: opposite sides of parallelograms are congruent
Given: Parallelogram ABCD with diagonal AC
Prove: AB ≅ CD and AD ≅ BC
Answer:
So I figured it would be easier if I sent the pics instead. Hope it helps
(-8, -7); y = - 3x + 2
write an equation for The Line in slope Intercept form
Answer:
y=-3x^2+2x+201
Step-by-step explanation:
What is the slope of the line that passes through the pair of points?
(-7,8), (-4, 20)
0 -4
0.25
0.33
Answer:
4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(20-8)/(-4-(-7))
m=12/(-4+7)
m=12/3
m=4
A red die is tossed and a green die is tossed.what is the probability that a red die shows an even number or the green die shows an even number? Make sure your answer is reduced
Answer: 75%
Step-by-step explanation:
Since there are 3 even numbers on each die and 3 odd, each dice has a 50% chance of showing an even number.
An easier way to think about this might be what are the chances that both dice show odd, because that is the only scenario where neither show an even number.
To do this, simply multiply the chances together:
[tex]0.5 * 0.5 = .25[/tex]
Therefore, there is a 25% chance that both die will be odd, meaning there is a 75% chance that one or both of the dice show an even number
kiyo bought a pizza for 12.75 and four medium drinks to Pauli’s pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink costs $3.
The total cost, if one drink costs $3 is $27.75
Let the cost of a pizza be xLet the cost of a drink be yIf kiyo bought a pizza for 12.75 and four medium drinks to Pauli’s pizza, this expressed as x + 4y
Since a pizza costs $12.75, hence x = $12.75
The function becomes 12.75 + 5y
f(y) = 12.75 + 5y
To get the total cost if one drink costs $3, hence;
f(3) = 12.75 + 5(3)
f(3) = 12.75 + 15
f(3) = 27.75
Hene the total cost, if one drink costs $3 is $27.75
Learn more on function here: https://brainly.com/question/9418047
PLSSS HELP THIS IS HARD ANYONE
Answer:
270 degrees counterclockwise rotation/ the last answer
Step-by-step explanation:
reflection over the y axis wouldn't work bc the shape would still be a horizontal rectangle
dilation would change the size of the shape
and translation wouldn't map it correctly bc it would still be turned the wrong way
Answer:
270 degrees counterclockwise rotation
Step-by-step explanation:
you can use the formulas, but if you don't know them you can always draw
270 degrees counterclockwise = 90 degrees clockwise
(x,y) -> (y,-x)
A'(1,-2) -> A(-2,-1)
B'(3,-2) -> B(-2,-3)
C'(3,-5) -> C(-5,-3)
D'(1,-5) -> D(-5,-1)
Solve for a, round your answer to the nearest hundredth:-3(a + 9) - 5(a - 5) = 8
Answer:
22
Step-by-step explanation:
3(a+9)-5(a-5)=8
3a+27-5a+25=8
3a-5a+27+25=8
-2a+52=8
-2a=8-52
-2a=-44
a=-44/-2
a=+22
Whats 12 3/8 - 9 1/8
Answer:
3[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Answer:
13/4
Step-by-step explanation:1238−918
Convert 1238
to an improper fraction.
Tap for more steps...
998−918
Convert 918
to an improper fraction.
Tap for more steps...
998−738
Combine the numerators over the common denominator.
99−738
Subtract 73
from 99
.
268
Cancel the common factor of 26
and 8
.
Tap for more steps...
134
x - 3y = 17
x = 2y + 13
What are the steps for solving these?
Answer:
(x, y) = (5, -4)
Step-by-step explanation:
The second equation gives you an expression for x that can be substituted into the first equation.
(2y +13) -3y = 17 . . substitute for x in the first equation
-y = 4 . . . . . . . . . . . subtract 13 and simplify
y = -4
x = 2(-4) +13 = 5 . . . use the second equation to find the value of x
The solution is (x, y) = (5, -4).
_____
Additional comment
When faced with a system of linear equations, the first step is to look at them and observe where the variable terms are, and any relationships between coefficients. Several options are generally open to you for solving the equations. Methods generally taught first are ...
substitutioneliminationSubstitution is handy when one of the variables or variable terms can be written (easily) in terms of the other variable. Elimination is handy when some simple multiple of one of the equations can be added to the other equation to cancel one of the variable terms (eliminate it).
Other available methods include matrix methods, Cramer's rule, and graphing. Working knowledge of all of these methods will help you identify the one that will be easiest to use in any given situation.
The availability of calculators able to use these methods greatly simplifies the task of finding a solution. It is simply a matter of entering the equations in the appropriate form.
One of my favorites is the graphing calculator, which only requires you type in the given equations and click on the solution point to find its coordinates.
15 points in 4 quarters
Is this u asking a question or just saying 15 points in 4 quarters?
Help Me Please!
A repairman charges an inspection fee plus $20 per hour. A customer
with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair.
How many hours are worked when a customer pays $90 without a coupon?
Answer:
$108.50 for the 30% off an 1 hour and 35 min without the coupon 155 x 0.3 = 46.5. 155-46.5=108.50
The final price of a pair of socks is $6.40. It is on sale for 20% off. What is
the original price of the socks?
Answer: original price= $8
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 8 × 20/100
Discount = 8 x 0.2
You save = $1.60
Final Price = Original Price - Discount
Final Price = 8 - 1.6
Final Price = $6.40
someone answer this asap pls lots of points
Answer:
0.34
Step-by-step explanation:
64^1/2=34
10^-2=0.01
34*0.01=0.34
If the mean of 16‚20‚25 and p is 20.Find the value of p.
Is this right?
If not what is the answer
Answer:
yes it is correct
Step-by-step explanation:
How do you write an equation of a line so that it is parallel or perpendicular to a given point??
The equation of a line so that it is perpendicular to a given point will be
y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)
The equation of a line so that it is perpendicular to a given point will be
y-y0=m (x - xo)
The standard equation of the line is better written in point-slope form expressed as:
y-y0=m(x - xo)
where: m is the slope of the given line (x0, y0) is any point of the giuven line.
m is the slope of the given line
(x0, y0) is any point on the given line
If the given slope of the line is m, the slope of the line perpendicular will be expressed as -1/m
The equation of a line so that it is perpendicular to a given point will be
y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)
what is the total number of edges on a rectangular prism
Answer:
12 edges
Step-by-step explanation:
A rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.
Answer:
12
Step-by-step explanation:
You have to multiply 7 by 19. Which equation uses the Distributive Property to take this problem apan
A. 7(10 + 9) = 70 + 16
CB B. 7(10 + 9) = 70 + 9
c. 7(10 + 9) = 70 +63
D. 7(10 + 9) = 17 +63
I need help with a photo and y’all can choose whatever like for number 7
Step-by-step explanation:
The one point where the lines intersect is one solution. If both points are on the same line it is one solution. If the lines do not intersect it is no solution.
HELPPP
I NEED TO CHECK OFF ALL THE FUNCTIONS PLEASE HELP ME
Answer:
I'm not sure but I think it's everything outside of circular, graphic and reflective. I'm only unsure with the last one but since it's 4 point I would assume it's 4 answers.
Find all missing angles.
Answer:
1= 41
2=85
3= 95
4=85
5= 36
6= 49
7= 188
Step-by-step explanation:
I think that's the answer
In the figure below, m∠1 = x and m∠2 = x - 4. Which statement could be used to prove that x = 47?
A) m∠1 = m∠2
B) m∠2 = 47
C) m∠1 + m∠2 = 90
D) m∠1 + m∠2 = 180
The answer is C) m∠1 + m∠2 = 90
Explanation: So ∠1 is x and ∠2 is x-4
Basically you know than ∠3 is 90° ... And a straight line is 180° .. So technically we can just find out 180-90 is 90(the other angle 1 + 2).
To get 90° we'll add ∠1 and ∠2 in other ways, like technical thinking-
So you already know adding ∠1 and ∠2 is 90°. So ∠1 + ∠2 = 90°
In other words you can say m∠1 + m∠2 = 90
please solve quickly
Step-by-step explanation:
first you need to find the height
V = L×W×H
the volume your given is 880mm³
length is 22mm
width is 8mm
height is unknown
furthermore
V=L×W×H
880mm³= 22mm×8mm×H
880mm³= 176mm²×H
880mm³/176mm²=176mm²/176mm²×H
5mm=H
H=5mm
Surface Area= S.Atherefore S.A=2(L×W+ W×H +L×H)
=2(22mm×8mm+8mm×5mm+22mm×5mm)
=2(176mm²+40mm²+ 110mm²)
=352mm²+80mm²+220mm²
=652mm²
Question locate in image show working
Find the area of the square
Answer:
144
Step-by-step explanation:
225-81 because with pythagorean thorem both sides should equal the C value or the bigger square.
how to turn x+7y=20 into y=mx+b
Answer:
y = -1/7x +20/7
Step-by-step explanation:
Solve for y.
7y = -x +20 . . . . . subtract x from both sides to get the y-term by itself
y = -1/7x +20/7 . . . . divide both sides by the coefficient of x
In this form, you can see ...
m = -1/7b = 20/7 = 2 6/7Answer:
y=-1/7x+20/7
Step-by-step explanation:
So they are asking us to put x+7y=20 into slop-intercept form (y=mx+b).
They're pretty much just asking us to solve for y.
x+7y=20
7x=20-x (Subtract x from both sides)
y=20-x/7 (Divide 7 on both sides to isolate y)
y=20/7-1/7x
y=-1/7x+20/7
So..
m=-1/7
b=20/7
Hope this helps :)
6t – 6t
Please answer this :)
That would probably be zero for the answer, because if a number or an equation subtracts the same number or equation it will cancel itself out. Thus giving us zero.
Hope this help :D.
What is the equation for the line in slope-intercept form
Answer:
y=-2x-4
Step-by-step explanation:
What is 540 into standard form
Answer:
5.40 x [tex]10^{2}[/tex]
Step-by-step explanation:
hoped that helped:P
