Answer:
The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.
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 two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of variances.
Ohio had an average of 52, standard deviation of 7.22, sample of 40.
This means that [tex]\mu_O = 52, s_O = \frac{7.22}{\sqrt{40}} = 1.1416[/tex]
Pennsylvania had an average of 33, standard deviation of 10.11, sample of 33.
This means that [tex]\mu_P = 33, s_P = \frac{10.11}{\sqrt{33}} = 1.76[/tex]
Distribution of the difference:
[tex]\mu = \mu_O - \mu_P = 52 - 33 = 19[/tex]
[tex]s = \sqrt{s_O^2 + s_P^2} = \sqrt{1.1416^2 + 1.76^2} = 2.1[/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 - 0.999}{2} = 0.0005[/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 - 0.0005 = 0.9995[/tex], so Z = 3.29.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 3.29*2.1 = 6.91[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 19 - 6.91 = 12.09 hours per week
The upper end of the interval is the sample mean added to M. So it is 19 + 6.91 = 25.91 hours per week.
The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.
Please help I'll mark you as brainiest
The answer is going to be B
10% of $200,000 = $20,000
A cylinder soup has a radius of 1,6 in and is 5/7 in. tall what is the volume
Answer:
[tex]V=0.0623\ inch^3[/tex]
Step-by-step explanation:
Given that,
The radius of cylinder, r = 1/6 inch
The height of the cylinder, h = 5/7 inch
We need to find the volume of the cylinder. The formula for the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\=3.14\times (\dfrac{1}{6})^2\times \dfrac{5}{7}\\\\V=0.0623\ inch^3[/tex]
So, the volume of the cylinder is equal to [tex]0.0623\ inch^3[/tex].
A parallelogram has an area of 324 square feet and a base of 13.5 ft. how long is the height of the parallelogram? please help me!!
Which if the shaded regions below represents 3/5 of the whole circle
Answer:B
Step-by-step explanation: i have the same test
One fourth of the 120 students took wood shop. How many students did not take wood shop?
Answer:
90 students.
Step-by-step explanation:
Given 1/4 of the 120 students took woodshop, just take the 3/4 that didn't take it:
[tex]\frac{3}{4}(120)[/tex]
Find common factors between 4 and 120 to simplify, so 4.
[tex]\frac{3}{1} (30)[/tex]
Now multiple across to get 90.
Divide £104 in the ratio 3:5
Answer:
39:65
Step-by-step explanation:
104/(3+5) = 104/8 = 13 13(3):13(5) = 39:65
Pls help me, is for my gf
Answer:
tell ur gf good luck because what this is
also no hablo español
Answer:
x-bar, the average between all the values, x1+x2+x3/3
An item has a listed price of $45. If the sales tax rate is 3%, how much is the sales tax (in dollars)?
Answer:
1.35
Step-by-step explanation:
45 x .03
A right triangular prism is shown.
6 in.
11 in.
8 in.
What is the volume in cubic inches of the prism? Enter only the number.
The volume in cubic inches of the prism is 528 cubic inches.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the Cuboid.
The volume is calculated as:-
V = L x W x H
V = 6 x 11 x 8
V = 528 cubic inches
Therefore the volume in cubic inches of the prism is 528 cubic inches.
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Find the surface of the triangular prism
17m 17m 15m 16m 10m
Need help finding the answer
9514 1404 393
Answer:
x = 5
FD = 22
Step-by-step explanation:
The products of the segment lengths on the same chord are the same.
8×15 = 12×(3x -5)
10 = 3x -5 . . . . . . . divide by 12 (we use this value to find FD)
15 = 3x
5 = x
__
FD = (3x -5) +12 = 10 +12
FD = 22
Another area and perimeter question!!!
Pls helppppp
Answer:
D. 62 inches
Step-by-step explanation:
the object is symmetrical across z, so the lengths on the other side will be the same as x and y
the perimeter would just be 2x + 2y = 2(12) + 2(19) = 62 inches
5/9 times 8 GUYS PLS HELP ME
Answer: 4.44
HOPE THIS HELPS
Calculate the quotient below. Enter your answer in lowest terms, using the
slash mark (/) for the fraction bar.
Answer: 8/11
Step-by-step explanation:
A rectangular safe can hold 7,296 cubic inches. Gold bars that are 4 inches by 8 inches by 2 inches fit to completely fill
the safe. What is the volume of each gold bar?
(A) 14in
(B) 24in
(C) 128in
(D) 64in
Answer:
I think it's 64 in
I hope it's helps you
John gets his first job working at an ice cream shop because he loves ice cream. He gets paid $9 per hour. Create a table to demonstrate how much money John will make from 0 - 6 hours. Let x equal the number of hours worked, and let y equal the amount of money that he will make. Then, create a graph with your results.
Answer:
1hr: $9
2hr: $18
3hr: $27
4hr: $36
5hr: $45
6hr: $54
Step-by-step explanation:
You can use Desmos, the graphing calculator (online tool)
find the missing side using the pythagorean theorem
Answer:
26.55
Step-by-step explanation:
[tex]a^2 + b^2 = c^2\\b^2 = c^2 - a^2[/tex]
use the b^2 equation
------------------------
b^2 = 31 squared - 16 squared.
b^2 = 705
b=[tex]\sqrt{705}[/tex]
b=26.5518361
Determining the sale price of a home is an important task for city assessors, as it helps the city project future tax revenue. Regression models using the physical characteristics of a home to predict the sale price is standard practice for many assessors. A random sample of 724 homes sold in Ames, Iowa, between 2006 and 2010 was obtained to build such a model for the city of Ames. The assessor considered the following variables in their initial model:
Variable Description
LotArea Lot size (in thousands of square feet)
LivingArea Living space (in thousands of square feet)
Bedrooms Number of bedrooms
Rooms Number of rooms
Fireplaces Number of fireplaces
Bath Number of bathrooms
Age Age of the home (in years)
Price Sale price of the home (in thousands of dollars)
Below is the output obtained from the statistical software.
Estimate Std Error t value Pr(>|t|)
(Intercept) 100.55 6.167 16.31 < 0.0001
LotArea 0.99 0.144 6.86 < 0.0001
LivingArea 112.97 5.600 20.17 <0 .0001
Bedrooms −16.35 2.366 −6.91 < 0.0001
Rooms −0.51 1.667 −0.30 0.7613
Fireplaces 12.80 2.206 5.80 < 0.0001
Bat −13.60 3.459 −3.93 < 0.0001
Age−0.96 0.054 −17.86 < 0.0001
Number of Observations Residual Std Error R2 Adjusted R2
724 33.69 0.7686 0.7663
What is the response variable?
a. lot area
b. living area
c. age
d. sale price
What proportion of the variation in sale price does this multiple regression model explain?
a. .3369
b. .7686
c. .7663
d. 0.2314
The number of books (b) in a preschool classroom is proportional to the number of children (c) enrolled.
If the preschool has three books in a classroom for each child enrolled, which equation represents the total number of books in the classroom?
A. b=3c
B. b=3+c
C. b= 1 over 3c
D. b=3-c
Evaluate 12 ÷ 2 × 6.
Answer:
[tex]36[/tex]
Step-by-step explanation:
1) Simplify 12 ÷ 2 to 6.
[tex]6 \times 6[/tex]
2) Simplify.
[tex]36[/tex]
therefor, the answer is 36.
Which is more likely: rolling a total of 8 when two dice are rolled or rolling a total of 8 when 3 dice are rolled? Discuss your solution by explaining it.
Answer:
Rolling a sum of 8 from two dice is more likely
Step-by-step explanation:
To obtain which is more likely, we could obtain the individual probabilities of both events.
TWO DICE :
Sample space for 2 die rolls = total possible outcomes = 6² = 36
Number of favorable outcomes = sum of 8 from 2 rolls = 5
Probability = number of favorable outcomes / total possible outcomes
P(sum of 8) = 5 / 36 = 0.1388
THREE DICE :
Total possible outcomes = 6³ = 216
Number of favorable outcomes = 21
P(sum of 8) = 21 / 216 = 0.097222
0.1388 > 0.097222
Please help this is due today.
Answer:
[tex]b = 90[/tex]
[tex]c=80[/tex]
[tex]d =100[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find b, c and d
First, we solve for b using:
[tex]b + 10 + b - 10 = 180[/tex] --- base angles of a parallelogram
Collect like terms
[tex]b + b =180+10-10[/tex]
[tex]2b = 180[/tex]
Solve for b
[tex]b = 180/2[/tex]
[tex]b = 90[/tex]
Then, we have:
[tex]d =b + 10[/tex]
[tex]c = b - 10[/tex] --- opposite angles
So, we have:
[tex]d =90 + 10[/tex]
[tex]d =100[/tex]
[tex]c = 90 - 10[/tex]
[tex]c=80[/tex]
3) (Infer) What would happen if two kinds of animals living in the same habitat had the same niche?
4) Why might an animal need to move to a different habitat?
I report people who add links in there answer or use safari
Have a good day! :)
what is 9/-2 as an equivalent fraction
Answer:
18/-4 as equivalent fraction there are many others
please help me to find this out i really really need help.
The diagram shows a triangular prism ABCDEF with a horizontal base ABEF.
Give your answer correct to 3 significant figures.
Answer:
38.7°
Step-by-step explanation:
Let the angle we're looking for be called x.
Consider ΔADF (which consists of sides AD, FD and FA, and which contains the angle x.
tan(angle)=opposite/adjacent
tan(x)=FD/FA
x=tan⁻¹(12/15)=38.6598082541°≈38.7°
Therefore, the length of the angle be [tex]x=38.65[/tex] degree.
What is the trigonometry?
Trigonometry states that the trigo mean 'triangle', and metry means métron is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
Let the length of the angle be [tex]x[/tex].
Consider Δ[tex]ADF[/tex]
which consists of sides [tex]AD, FD[/tex] and [tex]FA[/tex], and which contains the angle [tex]x[/tex].
So,
tan(x)=Perpendicular / Base
i.e.,
[tex]tan(x)=\frac{FD}{FA}\\\\tan(x)=\frac{FD}{FA}\\\\x=tan^{-1}(\frac{12}{15})\\\\x=38.65[/tex]
Hence, the length of the angle be [tex]x=38.65[/tex] degree.
To know more about the trigonometry
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Which of these statements is true about heat? A. Heat always flows from cooler to warmer substances. B. Heat doesn’t flow between substances. C. Heat always flows from warmer to cooler substances. D. Heat flows when both substances have the same temperature.
Answer:
C. Heat always flow from warmer to cooler substances.
Find the area of each figure. Use 3.14 for pi
WILL GIVE BRAINLIEST AND 40 POINTS TO CORRECT ANSWER (URGENT)
chef daniels places her favorite recipes in a bag for 4 pasta dishes, 5 casseroles, 3 types of chili, and 8 desserts. If Chef Daniel chooses two recipes at random (but replaces the first one before drawing the second), what is the probability that the first recipe she selects is a casserole and the second recipe she selects is a dessert?
Answer:
Hi
Step-by-step explanation:
I have the same question, did you figure it out?
Consider the function g(x) = StartLayout Enlarged left-brace first row negative 9, x less-than 11 second row 7, x greater-than-or-equal-to 11 EndLayout.
What is Limit of g (x) as x approaches 11, if it exists?
–9
–1
7
DNE
The limit as g(x) approaches 11 doesn't exist.
[tex]\lim_{x \to 11} g(x) = DNE[/tex]
It looks like you are working with the following piecewise defined function:
[tex]g(x)=\left \{ {{-9;x<11} \atop {7;x\geq11}} \right.[/tex]
There is a rule in calculus that tells us that for a limit to exist, both lateral limits must be the same as x approaches a given value. This is:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)[/tex]
if and only if this is true, then:
[tex]\lim_{x \to a^{-}} f(x)=\lim_{x \to a^{+}} f(x)=\lim_{x \to a} f(x)[/tex]
if that condition isn't met, then the limit doesn't exist.
So let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{-}} g(x) = -9[/tex]
This means that as x approaches 11 from the left, the function will return a value close to -9
Now, let's calculate the lateral limits for this function:
[tex]\lim_{x \to 11^{+}} g(x) = 7[/tex]
This means that as x approaches 11 from the right, the function will return a value close to 7
You can better visualize this in the graph of the function which I attached to this answer.
Notice that both lateral limits are different, from the left you got a -9 and from the right you got a 7. Therefore, according to the rule I wrote above, the limit does not exist.
For more information on this topic, you can go to the following link:
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Answer:
D) DNE
Step-by-step explanation:
edge 2021
A researcher is investigating the relationship between the length, in centimeters, and weight, in grams, of pineapples. The researcher will select a random sample of 15 pineapples from grocery stores in a region and construct a 95% confidence interval for the slope of the population regression line, where length is the explanatory variable and weight is the response variable. When computing a confidence interval for the slope of the population regression line, which of the following is not a condition that must be checked?
A. The true relationship between length and weight is linear.
B. The standard deviation for weight does not vary with length.
C. The values of weight are approximately normally distributed at each value of length.
D. The sum of the residuals is zero.
E. The observations are independent.
Answer:
D. The sum of the residuals is zero.
Step-by-step explanation:
The relation between length and weight of pineapples is observed. The observation should be independent and the values must be normally distributed in order to find the confidence interval for slope of population regression line.
