In a hatch chemical process, two catalysts arc being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a sample of 10 batches was obtained using catalyst 2. The 12 batches for which catalyst 1 was used gave an average yield of 85 with a sample standard deviation of 4, and the second sample gave an average of 81 and a sample standard deviation of 5. Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances
Answer:
The 90% confidence interval, C.I = (0.693, 0.7307)
Step-by-step explanation:
Catalysts 1 and catalyst 2 have the following statistical data;
Catalyst 1
The number of batches in the sample, n₁ = 12
The average yield by the 12 batches of catalyst 1, [tex]\overline x_1[/tex] = 85
The sample standard deviation, s₁ = 4
Catalyst 2
The number of batches in the sample, n₂ = 10
The average yield, [tex]\overline x_2[/tex] = 81
The standard deviation, s₂ = 5
F-test = s₂²/s₁² = 5²/4² = 1.5625
The degrees of freedom, df = n₁ + n₂ - 2
∴ df = 12 + 10 - 2 = 20
The critical-t at 90% confidence level = 1.725
The F-test < The critical-t, we pool the variance
The 90% confidence interval with the assumption of equal variance is given as follows;
[tex]The \ 90\% \ confidence \ interval= \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times (s_p) \times \sqrt{\dfrac{1^{2}}{n_{1}}+\dfrac{1^{2}}{n_{2}}}[/tex]
[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]
Therefore;
[tex]s_p[/tex] = √((12 - 1)×4² + (10 - 1)×5²)/(12 + 10 - 2)) ≈ 4.48
Therefore, we get;
[tex]C.I. = \left (85- 81 \right )\pm 1.725 \times 4.48 \times \sqrt{\dfrac{1}{12}+\dfrac{1}{10}}[/tex]
The 90% confidence interval, C.I = 0.693 < μ₁ - μ₂ < 7.307 = (0.693, 0.7307).
Simplify:
a+b
a-b
= [?]
a=5 and b=3
The value of the given expression will be 4.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is as follows
[tex]=\dfrac{a+b}{a-b}[/tex]
a = 5 and b=3
[tex]=\dfrac{5+3}{5-3}=\dfrac{8}{2}=4[/tex]
Therefore the value of the given expression will be 4.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ2
Need help asp being timed
Answer:
a(x) = √x+3
Step-by-step explanation:
i graphed it on desmos
state whether 0 is a rational number
8. Let U= {x:x e P and x< 12} be the
universal set and A = {1, 3, 5, 6, 7},
B= {4, 6, 7,9}.
Find: i) A' ii) B' iii) An B'
Answer:
b is a answer I think so hmmm
pleas help me alot of points
Answer:
12
Step-by-step explanation:
its a square all sides of the square are the same so 48 divided by 4 is 12
5 points is not a lot of points
Malik, who is 5 feet tall, stands 15 feet from a mirror. In
the mirror, he can see the reflection of the top of a tree,
which he measures to be 92 feet away from the mirror. round your answer to the nearest hundredth
The box plots show the weights in pounds of the dogs in two different animal shelters
Weights of Dogs in Shelter A
6
8
10
12
14
16
18
20
22
24
26
28
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A between 10 and 28 pounds in shelter B
benveen 8 and 17 pounds in shelter A between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A between 20 and 28 pounds in shelter B
Answer:
between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B
Step-by-step explanation:
One half of the dogs in each shelter points at the the upper 50% of the dog weight. This point is marked by the median value up to the maximum weight value.
The median value is the point marked inside the box on a boxplot and the maximum value is the upper end or the endpoint of the whisker.
For SHELTER A:
Median = 21
Maximum = 30
Hence, For shelter A, it is the interval between 21 and 30
For shelter B:
Median = 18
Maximum = 28
Hence, it is the interval between 18 and 28
Answer:
it's c
Step-by-step explanation:
:)
A car dealership has $3,570 to spend on newspaper ads. If each ad costs $70, how many ads can the dealership buy?
Answer:
51
Step-by-step explanation:
Hello! Would appreciate help!!
Find the value of x. Round to the
nearest tenth.
Answer:
17.14
Step-by-step explanation:
tan 35 = 12/x
x = 12/ tan 35
= 17.14
Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and the rest on t-shirts. Write an inequality that represents the relationship between the amount of money Debbie has and how much she can spend on t-shirts.
Answer:
22+8x less then or equal to 60
Step-by-step explanation:
Debbie has at most $60 to spend
Then it will be <=60
Now she has to spend 22 dollars on jeans so 22 will be add to the initial amount for sure.
And
Let x be the number of t-shirts
Then the cost of x t-shirts will be 8x
Putting this in to inequality will be:
The inequality to find the maximum number of t-shirts is:
7
Which equation can be used to describe the relationship between x and y shown in the graph
below?
3x + 2
D-3x - 6
D
3-6
D3X2
Melly wants to simplify the expression 323/5
Answer:
64 3/5
Step-by-step explanation:
If you spin the spinner once, determine the probability and the likelihood of spinning with colors red, orange, blue or green, red blue orange or green, not red
Answer:
Step-by-step explanation: There are 12 colours on a spinner,
Probability of red,orange, blue or green = 1/12×4 =4/12
=1/3
Probability of red,blue, orange or green= 1/12×4=1/3
Probability of not red= 1-1/12
=11/12
Please solve these, I thank you my friends
Write and solve an equation to find the value of x
Answer:
180 - (52 + 28) = x and then x = 100.
Step-by-step explanation:
A triangle's angles must ALWAYS add up to 180. No matter what. So, the problem gives us 2 of the three angles already, 52 and 28. 52 + 28 is 80. As I mentioned before, a triangle's angles must always add up to 180, so to find x, you must subtract 80 from 180, getting 100. Therefore, x is 100 degrees.
The equation we used to find that is: 180 - (52 + 28) = x.
52 and 28 are the two angles we know, and subtracting their sum from 180 gives us the missing angle.
1. What is the absolute value of -45?
Answer:
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
G'day m8!
The area of a circle, in terms of π , is 72 π m2. Find the value of the radius. Give your answer as a simplified surd.
Answer:
R=3rad2
Step-by-step explanation:
Area of circle: pi r^2
72pi=pir^2
r^2=72
r=6rad2
find the volume! please :) ( links = blocked )
Write the name of the property which says a + (b + c) = (a + b) + c
Answer:
This is the associative property of addition, which states that you can add or multiply regardless of how the numbers are grouped.
In ΔTUV, the measure of ∠V=90°, TV = 28, UT = 53, and VU = 45. What ratio represents the cosecant of ∠U?
Answer:
53/28 is the answer on delta math
Step-by-step explanation:
Ryan goes for a run for 29 minutes. He knows that each mile he runs
takes 6 minutes. To the nearest tenth, how many miles did Ryan run?
(turn your answer into a mixed number...simplify it...then type it as a decimal)
Answer:
4 and 5/29
Step-by-step explanation:
2/3 y = 1/4 y ___?
A) 3/8
B) 5/12
C) 11/12
D) 2 2/3
Answer:
Heyaa!! Im Pinky!! And Im Here To Inform You That Your Answer Is...
Step-by-step explanation:
!!!! A. 3/8 !!!!
My calculations:
Given
2/3 y = 1/4
Multiply Each Sides by 3!
2y = 3 × 1/4= 3/4
Then we can Divide both sides by 2!
y= 3/4 ÷ 2 = 3/4 × 1/2 = 3/8!!
Have An Amazingly Good Day!!! (or night!)
~Pinky~
Carter's last ten shot put distances, in meters,are shown in the list 20.24, 20.11, 19.95, 19.99, 20.02, 19.88, 19.97, 20.21, 20.07 move words to the blanks to describe the measure of variability for this data set
Answer:
mad symmetric without
Step-by-step explanation:
Somone help me with this
Answer:
112
Step-by-step explanation:
V= lwh /3
= 7·6·8 /3
=112
Which shape contains exactly two pairs of parallel lines?
Trapezoid
Rectangle
Equilateral triangle
Acute triangle
Answer:
Rectangle is the correct answer hope it helps you have a great day keep smiling be happy stay safe ☺️
A rectangle is a special type of parallelogram. Any parallelogram has two pairs of opposite parallel sides. A rectangle is a parallelogram where all four angles are the same, and all four angles are 90 degrees.
Keep in mind that not all parallelograms are rectangles, but any rectangle is always a parallelogram.
In slight contrast, a trapezoid has exactly one pair of parallel lines, while the other pair of opposite sides are not parallel. Triangles of any kind can be ruled out because they don't have any parallel sides at all.
hi can someone pls help me, it’s confusing
Answer:
options C -x^2/3z
Step-by-step explanation:
this is the correct answer after we cancelled them
Answer:
C
Step-by-step explanation:
This requires you to know the law of quotient for exponents. For this I recommend separating everything with the same variable into its own fraction to make it easier so you have (-2x^4/6x^2), (y^2/y^2), (z/z^2). Then to simplify you divide the coefficients and signs like normal but for the exponents, you subtract the exponent of the numerator from the denominator. This gives
(-x^2 / 3), (1), and ( 1/z), which you can multiple together to get c.
Hope this helps. Ask if you need me to clarify something.
Find the surface area of the ball shown. Use 3.14 for pie.
Radius is 17cm
The ball has a surface area of about ? Cm^2
Answer:
[tex] \displaystyle S _{ \text{sphere}} =3629.84 {cm}^{2} [/tex]
Step-by-step explanation:
we are given a ball
remember that,a ball is a Sphere
thus,
[tex] \displaystyle S _{ \text{sphere}} = 4\pi {r}^{2} [/tex]
given that, redious is 17 cm
substitute:
[tex] \displaystyle S _{ \text{sphere}} = 4 \times \pi \times {17}^{2} [/tex]
simplify square:
[tex] \displaystyle S _{ \text{sphere}} = 4 \times \pi \times 289[/tex]
substitute the approximate value of π:
[tex] \displaystyle S _{ \text{sphere}} = 4 \times 3.14 \times 289[/tex]
simplify multiplication:
[tex] \displaystyle S _{ \text{sphere}} =3629.84[/tex]
hence, the surface area of the sphere is 3629.84 cm²
Andrea tiene 40 dulces y los reparte entre sus seis amigos Cuántos dulces Le tocará a cada uno
Answer:
This is an english server.
Step-by-step explanation:
Respuesta :
siete porque 40/6 darian 6 y como sobran 4 le reparterian 1 a cada 1 por eso darian a a siete
Espero que te sirba
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
0.96
What is the equivalent fraction?
Answer:
96% percent and fraction is 24/25
Answer: Down below
Step-by-step explanation:
64 % = 16 / 25
21 / 50 = 0. 42
9 / 25 = 36 %
2 / 5 = 40 %
/ = divide okay
What is a reasonable domain and range for the function in #13 If the frame must be at least 1 inch and no more than 3 inches wide
Answer:
[tex]Domain: \{1 \le x \le 3\}[/tex]
Step-by-step explanation:
Given
See attachment for options
Required
Determine the domain and the range
From the question, we understand that:
[tex]x \ge 1[/tex] --- at least 1 inch
[tex]x \le 3[/tex] --- not more than 3 inches
So, the domain is:
[tex]x \ge 1[/tex] and [tex]x \le 3[/tex]
Rewrite as:
[tex]1 \le x[/tex] and [tex]x \le 3[/tex]
Combine both:
[tex]1 \le x \le 3[/tex]
Hence, the domain is:
[tex]Domain: \{1 \le x \le 3\}[/tex]
There is no available to determine the range.
A general rule is that, substitute the limits of the domain (i.e. 1 and 3) in the function formula, the result is the range of the dataset.
For instance:
[tex]A(x) = 5x[/tex]
We have:
[tex]A(1) = 5*1=5[/tex]
[tex]A(3) = 5*3=15[/tex]
The range will be:
[tex]Range: \{5 \le A(x) \le 15\}[/tex]