Answer:
The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between 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.
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.
35 students from large sections. The mean and sample standard deviation of grades on the common final exam for the students from large sections were 72.8 and 7.4;
This means that:
[tex]\mu_L = 72.8, s_L = \frac{7.4}{\sqrt{35}} = 1.25[/tex]
35 students from small sections. For the students from small sections, the mean and standard deviation were 75.3 and 6.8.
This means that:
[tex]\mu_S = 75.3, s_S = \frac{6.8}{\sqrt{35}} = 1.15[/tex]
Distribution of the difference in the mean common final exam scores between students in the two types of sections:
Has mean and standard error given by:
[tex]\mu = \mu_L - \mu_S = 72.8 - 75.3 = -2.5[/tex]
[tex]s = \sqrt{s_L^2+s_S^2} = \sqrt{1.25^2 + 1.15^2} = 1.7[/tex]
Confidence interval:
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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs = 1.645*1.7 = 2.8[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is -2.5 - 2.8 = -5.3
The upper end of the interval is the sample mean added to M. So it is -2.5 + 2.8 = 0.3
The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).
Sam drew this 40° angle on his paper. What size angle should he draw to make a pair of complementary angles?
Answer:
52
Step-by-step explanation:
40(x)=52
Answer:
50°
Complentary angles are two angles that sum up to 90°
So 50+40=90
Please help me ASAP please
Answer:
Equation: 45 - 21 = s
The second answer is 24.
You can check by adding 24 + 21 which is 45.
the length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas is 45 in^2. find the lengths of the sides of the two squares
Answer:
2025 is the answer
Step-by-step explanation:
What is the area of the green triangle?
Answer:
The answer is 65
Step-by-step explanation:
Formula for triangle: b x h x 1/2
base= 13cm height= 10cm
13 x 10 x 1/2 =65
The area of the green triangle is 65.
A sweater costs $25. The store marks up the price by 85%. What is the selling price of the sweater?
If 12 pens are packed equally into 2 boxes, how many pens will each box hold?
Answer:
6
Step-by-step explanation:
12/2=6
Hope it helps......
The triangle and square have equal perimeters. What is the perimeter of the triangle?
A. 18
B. 4
C. 12
D. 32
E. 16
F. 24
Answer:
E. 16
Step-by-step explanation:
Perimeter of the triangle = 4x+4x+(x+7)
Perimeter of square = 4(x+3)
We know that the perimeters are equal so we can form an equation to solve for x:
9x+7 = 4x + 12
Now we can subtract 4x from both sides to move the xs to the left side, and the same with the 7 so we have the variable on one side and the constant on the other:
9x+7-7-4x=12+4x-4x-7
5x = 5
Now we divide both sides by 5 to get:
5x/5 = 5/5
x = 1
Now we can use this value to figure out the perimeter of the triangle:
P = 9x + 7
x=1, substitute into equation:
P = 9(1) + 7
P = 16
Hope this helped!
If y=qx5 and if q=10 then what is y?
100 points if you tell me what is range
Answer:
Difference in large and small numbers, higher or smaller value.
Answer:
The range is the difference between the largest and smallest numbers. If you are talking in math.
Example 1: 1, 2, 5, 6, 7
so the smallest number is 1 and the largest number is 7 so 7-1=6
The range is 6.
Example 2: 16, 19, 10, 17, 42
now we have a data set that is not in order. First step is to order them:
10, 16, 17, 19, 42
Next take the smallest and largest number and subtract them: 42-10=32
The range is 32.
Step-by-step explanation:
Have a nice day!
and can I maybe have brainliest? Thanks!
Noah raised $54, which is 60% of his fundraising goal to support the animal shelter.
Write an equation to represent the situation.
What is Noah's fundraising goal? Show or explain how you found it.
Answer:
make shur your using fractions
54 60
x 100 cross multiply
54(100) 60(x)
5400 60x
divided both by 60
5400/60 60/60
90 1
= $90
then you go
54 60
90 100
and use a caculater to see if your answer is coorect
you just fowllow the steps to see if you get 90
Step-by-step explanation:
please help me! yah thats all i just need help
Answer:
WT=63
Step-by-step explanation:
[tex] \frac{56}{5 \times x + 3} = \frac{40}{4 \times x - 3} \\ x = 12[/tex]
So
[tex]5 \times x + 3 = 5 \times 12 + 3 = 63[/tex]
The label on the can of soup covers
about 354.2 square centimeters. What is the
height of the can
Radius : 4.7 cm
HELPP
Answer:
h = 12 cm
Step-by-step explanation:
Given that,
The area of the can of a soup, A = 354.2 cm²
Radius of the can, r = 4.7 cm
We need to find the height of the can. The formula for the volume of a cylinder is given by :
[tex]A=2\pi rh\\\\ 354.2=2\times 3.14\times 4.7h\\\\h=\dfrac{354.2}{2\times 3.14\times 4.7}\\\\h=12\ cm[/tex]
So, the height of the can is equal to 12 cm.
7000 litres of water is pumped out of a tank in 42 minutes. How many litres could be pumped out in one hour at the same rate?
Answer:
8600 litre×235 will be there in the tanks
Simplify the expression:
6x ^ 2 + 7x - 3x ^ 2 - 2x
Answer:
3x²+5x
Step-by-step explanation:
Solve for x.
2 In (3x)=-4
Do not round any intermediate computations, and round your answer to nearest hundredth
Solve for x.
5+3(4x - 1) = 14
Enter your answer in the box.
X=
Answer:
5+12x-3 = 14
12x = 14 -5+3
12x = 12
x = 1
Answer:
X=1. I did mental math. I am sure.
Nathaniel created the circle graph below
to show the percentage of his free time he
will engage in different activities on Sunday.
Free Time
Drawing Reading
25%
Exercising
30%
Watching
Television
25%
If Nathaniel has 9 hours of free time on
Sunday, which shows the amount of time
he will spend reading?
A 1 hour 8 minutes
B 1 hour 35 minutes
C 1 hour 21 minutes
D 1 hour 48 minutes
Answer:
The real answer is 1 hour and 8 minutes
Step-by-step explanation:
You add all the percentages you have then you get 80% so you mince that by a hundred witch is 20% so now you need to find out what is 20% of 9 wich is 1.8 making the answer 1 hour and 8 miutes c:
Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. An article reported on an experiment involving 84 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.2 and the sample mean for the treatment group was 3.2; both sample standard deviations were 2.3.
a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this α, and a sample mean difference of 2.1 also suggests practical significance).
b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.
Answer:
a) We reject H₀ We find difference between the mean of the two groups
b) we accept H₀ : There is no statistical difference ( in the scale of pain) when the difference in samples means is 1
Step-by-step explanation:
Group 1: Only with educational material
Sample size n₁ = 42
Sample mean x₁ = 3,2
Sample standard deviation s₁ = 2,3
Group 2: With exercises with the treatment of individuals
Sample size n₂ = 42
Sample mean x₂ = 5,2
Sample standard deviation s₂ = 2,3
Test Hypothesis
Null Hypothesis H₀ x₂ - x₁ = 0 or x₁ = x₂
Alternative Hypothesis Hₐ x₂ - x ₁ > 0 or x₂ > x₁
Significance level α = 0,01
Sample sizes are n₁ = n₂ > 30
We use z-test
for α = 0,01 z(c) ≈ 2,32
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √ (2,3)²/42 + (2,3)²/42
z(s) = ( 5,2 - 3,2 )/ √0,2519
z(s) = 2 / 0,5
z(s) = 4
Comparing z(s) and z(c)
z(s) > z(c)
z(s) is in the rejection region. We reject H₀ the true average pain level for the control condition exceeds that for the treatment condition.
b) Does the true average pain level for the control condition exceed that for the treatment condition by more than 1.
In this case
z( s) = x₂ - x₁ / 0,5
z(s) = 1 /0,5
z(s) = 2
Comparing z(s) and z(c) now
z(s) < z(c) 2 < 2,32
And z(s) is in the acceptance region ( for the same significance level) and we should accept H₀ equivalent to say that the two groups statistical have the same mean
what its 1010 + 800 pls help
Answer:
1,810 hope this helps ;)
Answer:
1810
Step-by-step explanation:
lol, did I get trolled?
Find the area of similar figure.XTRA POINTS!!!! PLUS BRAILIEST!!!!!!
NO LINKS OR WEBSITES!!!!! YOU WILL GET REPORTED!!!!!
Answer:
[tex]6 in^{2}[/tex]
Step-by-step explanation:
Ratio d area= ( Ratio d side length)²
[tex]\frac{a}{24}=(\frac{3}{6})^{2}[/tex]
[tex]a=\frac{24*9}{36} =6[/tex]
So your answer is 6 you are correct!!
[tex]----------------[/tex]
hope it helps...
have a great day!!
What is the factored form of x^2-x-20
Answer:
(x+4)(x-5)
Step-by-step explanation:
x²-x-20
But ax² + bx +c
product = ac = 1 × -20 = -20
sum = b = -1
Factors are: -5,4( numbers if you multiply you get -20 and sum to get -1)
Therefore:
x²-5x+4x-20
x(x-5)+4(x-5)
(x+4)(x-5)
Step-by-step explanation:
x^2-5x+4x-20
x(x-5)+4(x-5)
(x-5)(x+4)
Find the missing values
Answer Is 5/3 20/12 3 1/3 / 2 8 1/3 / 5
Natasha was thinking of a number. Natasha doubles it and adds 6.5 to get an answer of 79.4. Form an equation with
x
from the information.
Answer:
Let the correct number be x.
therefore,
x - 6.5 = 79.4
Melody paid for a scarf with a ten dollar bill her change was two dollar three quarters and two dimes how much was the scarf
Answer:
Step-by-step explanation:
10 -2.95 = 7.05
the scarf cost $ 7.05
Answer:
4456646
Step-by-step explanation:
its that bc we add
HELP HELP HELP IM BEGGIN YU
Answer:
Option C
Step-by-step explanation:
If two triangles are congruent then their corresponding sides and angles are congruent.
[tex]---------------[/tex]
hope it helps you..
have a great day!!
Answer:
option c is correct answer of this question
hope it helps
What is 3÷3/4? (Btw you guys are so helpfil literally tysm
Answer:
Answer is 0.25.
Step-by-step explanation:
3/3=1
1/4=0.25
Have a nice day!
and can I maybe have brainliest? Thanks!
WOW This is my 150th answer!!!
I need help on Section 5- Topic 10 Algebra Nation, Algebra 1 Practice book. If anyone could give me answers to the questions, I will be extremely thankful!
Step-by-step explanation:
Just post a pic of the page
Which equation shows that the Pythagorean identity is true for ø = 270º?
Select the equation that is in the form sin^2ø+cos^2ø=1
Answer: (a)
Step-by-step explanation:
Given
angle is [tex]270^{\circ}[/tex]
Sine and cosine at this angle is
[tex]\Rightarrow \sin 270^{\circ}=-1\\\Rightarrow \cos 270^{\circ}=0[/tex]
Put the values in the identity [tex]\sin ^2\phi +\cos^2 \phi=1[/tex]
[tex]\Rightarrow (-1)^2+(0)^2=1[/tex]
The same thing is depicted by option (a)
The equation sin²ø + cos²ø = 1 is written as (-1)² + 0² = 1. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The equation is given below.
sin²ø + cos²ø = 1
We know that the ø = 270°. Then we have
sin 270° = -1
cos 270° = 0
Then the equation will be
(-1)² + 0² = 1
Then the correct option is A.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ5
What can you conclude about alternate interior angles?
Plz be specific..Will give BRAINLIEST!!!
Answer:
We can conclude that if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Please mark as brainliest.
A cryptography expert is deciphering a computer code. To do this, the expert needs to
minimize the product of a positive rational number and a negative rational number, given
that the positive number is exactly 7 greater than the negative number. What final
product is the expert looking for?
What’s the answer?
9514 1404 393
Answer:
-49/4
Step-by-step explanation:
The product of a positive number and a negative number will be negative. Its value will be minimized (most negative) when the magnitudes of the two numbers are the same. That is, the numbers that are 7 apart are symmetrically located about 0, so each has a magnitude of 7/2.
The product being sought is (7/2)(-7/2) = -49/4.
Answer: -49/4
Step-by-step explanation:
First set up two equations; a primary and a secondary equation.
Primary: P=xy
Secondary: x=7+y
Substitute the secondary equation into the primary equation: P=(7+y)(y), then simply: 7y+y^.
Next find the derivative of the simplified equation: 7+2y, then find the zeros: y = -7/2
Finally substitute y value into the secondary equation and solve for x:
x = 7 - 7/2
= 14/2 - 7/2
= 7/2
Multiply the two values together: -7/2 * 7/2 = -49/4