Answer:
The point estimate for the true difference between the population means is of -2.62 years.
The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.
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.
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 of normal variables:
When we subtract normal variables, the mean is the subtraction of the mean, while the standard deviation is the square root of the sum of variances.
A sample of 138 cars owned by students had an average age of 5.13 years. The population standard deviation for cars owned by students is 3.45 years.
This means that:
[tex]\mu_{s} = 5.13, \sigma_{s} = 3.45, n = 138, s_s = \frac{3.45}{\sqrt{138}} = 0.2937[/tex]
A sample of 111 cars owned by faculty had an average age of 7.75 years. The population standard deviation for cars owned by faculty is 2.08 years.
This means that [tex]\mu_{f} = 7.75, \sigma_{f} = 2.08, n = 111, s_f = \frac{2.08}{\sqrt{111}} = 0.2658[/tex]
Difference between the true mean ages for cars owned by students and faculty.
s - f
Mean:
[tex]\mu = \mu_s - \mu_f = 5.13 - 7.75 = -2.62[/tex]
This is the point estimate for the true difference between the population means.
Standard deviation:
[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2937^2+0.2658^2} = 0.3961[/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 - 0.95}{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 = zs = 1.96*0.3961 = 0.78[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is -2.62 - 0.78 = -3.4
The upper end of the interval is the sample mean added to M. So it is -2.62 + 0.78 = -1.84
The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.
1) A line passes through the points (7,4) and (-5, - 2). Which of the
following equations BEST defines this line?
Answer:
.5x = y
Step-by-step explanation:
You can find mx by comparing two points on a graph
A bag with 6 marbles has 2 blue marbles, 1 red marble, and 3 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is
blue?
Write your answer as a fraction in simplest form.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
There are 6 marbles total. Divide the number of blue marbles by the total amount of marbles.
[tex]\frac{2}{6}[/tex]
Simplify
[tex]\frac{1}{3}[/tex]
pls help 10 ptsssssssssssss
Please help with this question ASAP! Thanks!
Answer:
The equivalent expression is [tex]8.25\cdot y -14[/tex].
Step-by-step explanation:
Let [tex]4\cdot (1.75\cdot y -3.5)+1.25\cdot y[/tex], we proceed to simplify the expression by like terms and other algebraic operations:
1) [tex]4\cdot (1.75\cdot y -3.5)+1.25\cdot y[/tex] Given
2) [tex][1.75\cdot y +(-3.5)]\cdot 4 + 1.25\cdot y[/tex] Commutative property/Definition of subtraction.
3) [tex](1.75\cdot 4) \cdot y +(-3.5)\cdot 4 + 1.25\cdot y[/tex] Distributive and associative properties.
4) [tex]7\cdot y +(-14)+1.25\cdot y[/tex] Definition of multiplication/[tex]a\cdot (-b) = - a\cdot b[/tex]
5) [tex](7+1.25)\cdot y -14[/tex] Commutative and distributive properties/Definition of subtraction.
6) [tex]8.25\cdot y -14[/tex] Definition of addition/Result
The equivalent expression is [tex]8.25\cdot y -14[/tex].
help asap
IS
Find the value of x. Round to the
nearest tenth.
35
х
12
X=
= [ ?]
Answer:
x ≈ 17.14
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )
x × tan35° = 12 ( divide both sides by tan35° )
x = [tex]\frac{12}{tan35}[/tex] ≈ 17.14 ( to the nearest tenth )
Please help thank you
Answer:
[tex] \frac{4}{9} [/tex]
You spin the spinner once what is p(greater than 4 or less then 5)
Answer:
can someone look at my answer
Step-by-step explanation:
Find the sum of -3x^2-4x+3−3x 2−4x+3 and 2x^2-x+32x 2 −x+3.
Answer:
28x^2-10x+9
Step-by-step explanation:
28x^2-10x+9
please help i need to pass
Find the measurements of the numbered angles in each kite.
Answer:
∠1 = 90°
∠2 = 26°
Step-by-step explanation:
I need some help!! I wil try to give brainliest!!!
Find the Mean, Median, Mode and Range of the following data. 17, 11, 12, 8, 16,6
Answer:
Mean: 11.822.
Mode: 17,11,12,8,16,6.
Median: 12.
Step-by-step explanation:
Hope this helps! The mode is the number that occurs most in the set and since they all show up once the mode is all of them.
what is the equation of the line that passes through the points (-4,-5) and (-2,-6)
Answer:
The equation is: y=-0.5x-7
Step-by-step explanation:
Find the measure of angle A
Answer:
Step-by-step explanation:
AB and DC are parallel, so ∠B and ∠C are supplementary angles.
∠B = 180°-∠C = 79°
AD and BC are congruent. ∠A = ∠B = 79°
Jenelle draws one card from a standard deck of 52 cards.
Determine the probability of drawing either a jack or a ten? Write your answer as a reduced fraction=
Determine the probability of drawing either a jack or a diamond? Write your answer as a reduced fraction=
13
+
4
−
1
52
=
16
52
=
4
13
≈
0.3077
Explanation:
In a standard deck of cards, there are 52 cards. They are broken down into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each. Each suit has 13 ordinal cards (A, 2 through 10, Jack, Queen, King).
Here we're asked to draw a card at random and find the probability of drawing either a diamond or a 7.
With probability, we look at the fraction of ways we can achieve some condition (the numerator) over the number of ways we can do something (the denominator).
Our denominator here is 52 - the number of cards from which we can pull 1.
Our numerator is both all the diamonds, 13 cards, and all the sevens, 4 cards, but we need to subtract 1 to account for the double counting of the 7 of diamonds.
The probability of drawing a jack or ten from a deck of cards is 2/13.
The probability of drawing a jack or a diamond is 15/52.
How to calculate probability?
Fact: A deck of cards has 52 cards and in it:
13 cards of diamond13 cards of heart13 cards of clubs13 cards of spadeAnother classification:
4 cards each of A,2,3,4,5,6,7,8,9,10,king,queen and jack And those 4 cards consist of a diamond, heart, club and spade card.Now coming to the question:
We have 4 jack card and 4 10 cards, therefore total cards =8Probability: Desired outcomes/total outcome
=8/52
=2/13
We have 13 diamond cards( in which 2 jack cards are already included) and another 2 jack cards.therefore, total cards desired=13+2=15
Probability:15/52
To solve more such problems refer:https://brainly.com/question/5858025
#SPJ2
Find the value of x
B
as a traingle is 180 degrees
Solve the system.
x + y - 3z = -20
-3y + 2z = 5
z = 4
Answer:
x= -9
y= 1
Step-by-step explanation:
-3y+2z=5
(put the value of z in the equation)
-3y+2(4)=5
-3y+8=5
8-5=3y
3=3y
y=3/3
therefore y= 1
x+y-3z=-20
(put the value of y and z in the equation)
x+1-3(4)=-20
x+1-12=-20
x+1= -20+12
x= -8-1
therefore x= -9
I hope it will help.
What comes next in the pattern?12,16,20
A. 10
B. 22
C. 23
D. 24
What's equivalent to 5x + 10 and none Equivalent to 5x + 10
Answer:
2(5x+6)-9
Step-by-step explanation:
That's the answer to the problem
Musichelp me out please
Answer:
right arrow
Step-by-step explanation:
100 Pts! PLS HELP ASAP!!!
Find the lateral area of this cone.
Leave your answer in terms of 7.
15cm
178 cm
LA = [ ? ]cm2
Answer:
I’m pretty sure it’s basexHeight
Step-by-step explanation:
But other than that... i don’t know
Please don’t report me... I’m sorry for the :( answer
Answer:
15x8= 120 Squared is 10.95445115010332
Step-by-step explanation:
Order the sides of each triangle from shortest to longest
A rectangle has an area of 1008
square feet. Its width is six feet less
than twice the length. Find the
measures of the length and width of
the rectangle.
9514 1404 393
Answer:
length: 24 ftwidth: 42 ftStep-by-step explanation:
The area is the product of length and width. If L represents the length, then the width is (2L -6), and the area is ...
L(2L -6) = 1008
L² -3L -504 = 0 . . . . . divide by 2, put in standard form
(L -24)(L +21) = 0 . . . . factor
L = 24 . . . . makes the first factor zero
W = 2L -6 = 2(24) -6 = 42
The length of the rectangle is 24 feet; the width is 42 feet.
During the Falcons game, Julio Jones ran a straight route 40 yards up the sideline before turning around and catching a pass from Matt Ryan. Defender, Malcolm Butler, who started 20 yards across the field from Jones, saw the play setup and ran horizontally toward the receiver. What was the distance the defender had to run to get to the spot where Jones caught the ball? (PLS DONT GIVE WEBSITE PLS JUST ANSWER)
Answer:
its 20 because he ran 20 from jones
10 points if you solve this!!!
Answer:
x = 128
Step-by-step explanation:
Right angles are 90 degrees. 90 + 90 + 52 = 232. 360 (angles in a quadrilateral) - 232 = 128.
Answer:
ans is 128
Step-by-step explanation:
90+90+52+x=360(all sides of triangle is 360)
180+52+x=360
232+x=360
x=360_232
x=128
Find the area of a rectangle with length of p+3 and width of 3p-2
Answer:
Area of rectangle = length × breadth
= ( p+3) (3p - 2)
= 3p² -2p + 9p -6
= 3p² + 7p -6
Question 1 of 22
Klay's lunch cost $6. This is $2 less than Ella's lunch cost. How much did
Ella's lunch cost? Select the correct solution method, using x to represent the
cost of Ella's lunch.
A.
NIX
= 6. Multiply both sides by 2. Ella's lunch cost $12.
B. 2x = 6. Divide both sides by 2. Ella's lunch cost $3.
C. x + 2 = 6. Subtract 2 from both sides. Ella's lunch cost $4.
O D. X-2 = 6. Add 2 to both sides. Ella's lunch cost $8.
Answer:
D
Step-by-step explanation:
Because it says Klay lunch cost is $2 less than Ella's.
==> Ella's - $2 = Klay's
==> x-2=6
plus both side by 2
so the answer is $8
Find the measure of angle 1.
Answer:
Hi! I would LOVEEE to help you...But, there is no picyure or anything to see angle 1.
Step-by-step explanation:
A easy question please help.
Answer:
D
Step-by-step explanation:
I have no idea how to explain this, but I'll try my best. Let me know if you want further clarification.
When you're slicing parallel to the base, it would mean "in line" with the base if that makes sense. If we were to draw a line on where we would slice it, and another repersenting the base, neither line would ever touch.
So looking through each possible answer, if we were to slice each shape parallel to the base, only D would produce a circle.
Again, sorry about this sloppy explaination.
Answer:
d
Step-by-step explanation:
the bottom is a circle
an adult and 5 children rent skates. it cost $4 per adult for skates and a total of $16.
Answer:
$2.40 per child
Step-by-step explanation:
Subtract.
16 - 4 = 12
Divide.
12/5= 2.4
Very simple mental math. Please try to learn this 4th-5th grade math, you will definitely use this in real life, and it's not a pain to learn.