Answer:
Question a:
c) 1.645
Question b:
a) (-0.11, 3.11)
Step-by-step explanation:
Before answering the question, 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 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.
A random sample of 36 gaming console A users had an average age of 34.2 years, with a standard deviation of 3.9 years.
This means that [tex]\mu_A = 34.2, s_A = \frac{3.9}{\sqrt{36}} = 0.65[/tex]
A random sample of 30 gaming console B users had an average age of 32.7 years, with a standard deviation of 4 years.
This means that [tex]\mu_B = 32.7, s_B = \frac{4}{\sqrt{30}} = 0.73[/tex]
Distribution of the difference in population means:
[tex]\mu = \mu_A - \mu_B = 34.2 - 32.7 = 1.5[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.65^2+0.73^2} = 0.9774[/tex]
a) What is the critical value for this hypothesis test?
We test if the means are different, which means that we have a two-tailed test.
We have the standard deviations for the population, which means that we have a Z test.
Since it is a two-tailed Z-test, the critical value is Z with a p-value of 1 - (0.1/2) = 1 - 0.05 = 0.95, so, looking at the z-table, Z = 1.645, which is option C.
b) What is the 90% confidence interval for the difference in population means?
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[/tex]
[tex]M = 1.645*0.9774 = 1.61[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 1.61 = -0.11
The upper end of the interval is the sample mean added to M. So it is 1.5 + 1.61 = 3.11
The correct answer is given by option A.
Find the value of x
Answer:
Yes the bots answer was deleted!
Anyways x = 29 because 29 + 151 = 180
Hope that helps!
I’m need the answer pls
Answer:
B. 16 students
Step-by-step explanation:
Just count all of the dots.
Hope this helps
Brainliest would be appreciated
Answer:b
Step-by-step explanation: well 7+5+3+1= 16
One solution to a quadratic function, g, is given 9-square root 2i which statement is true
Answer:
the answer is : D I got it right
Option (D) the other solution to the function g is 9 + √2i option (D) is correct.
What is a quadratic function?Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
We have:
One solution to a quadratic function, g, is:
9 - √2i
As we know complex solutions are always in the pair.
So the other solution will be 9 + √2i
Thus, option (D) the other solution to the function g is 9 + √2i option (D) is correct.
Learn more about quadratic function here:
brainly.com/question/2263981
#SPJ5
A ________ is the collection of data from every member of the population.
A.
census
B.
placebo
C.
sample
D.
statistic
Answer:A census
Step-by-step explanation:
Census is the collection of data from every member of a population. Parameter: A numerical measurement describing some characteristic of a population.
Milton purchases a 5-gallon aquarium for his bedroom. To fill the aquarium with water, he uses a container with a capacity of 1 quart.How many times will Milton fill and empty the container before the
aquarium is full?
Answer:
5-gallon = 20 quarts
4 quarts is a gallon 4 x 5 = 20 quarts
Digger the Dog Logan's dog, Digger, was constantly digging his way under the fence, escaping from the back yard, and following Logan to school. Digger was also in big trouble with Logan's mom who enjoyed leisure time away from her law firm by taking care of her flower garden. They decided they would have to keep digger tied up while they were away during the day. After a long discussion about how much of the back yard Digger should be allowed to destroy, they agreed that at least two-thirds of the yard should be safe for planting flowers and other plants. Logan tied Digger to the corner of the shed, at point A, with a 25-foot rope. Will this satisfy his mom?
Answer:
Is there a picture attached to this or how big the whole yard is?
Step-by-step explanation:
help please thank you
Answer:
1.8cm²
Step-by-step explanation:
The shape shown is a rhombus with a height of 1.2 cm and a base length of 1.5 cm.
The area of a rhombus can simply be calculated by multiplying the base length by the height
So area = 1.2 * 1.5
1.2 * 1.5 = 1.8
Hence the area of the rhombus is 1.8cm²
Answer:
0.9 cm²
Step-by-step explanation:
PlS help lots of points
1. How many blocks does each pyramid have?
a. several thousand
b. several million
c. several billion
Answer:
B. Several Million
Step-by-step explanation:
Each of the estimated 2.3 million blocks of stone weighs about 2267.96 Kg (about 2.3 tons) each The Great Pyramid of Giza is located at the border of Cairo in Egypt. It is believed that the pyramid was built over a time period of between 10-60 years by Pharaoh Khufu at around 2550 B.C. together with his successors including Khafre and Menkaure.
If a speedboat can travel 34 nautical miles in 2 hours, how far can it travel in 3 hours? Round your answer to the nearest tenth.
Answer:
(34 / 2) * 3 = 51 nautical miles
Step-by-step explanation:
(34/2) => Finds miles per hour
* 3 => Finds total miles traveled in 3 hours
Answer:
51
Step-by-step explanation:
1 hour= 17 nautical miles
2 hour= 34 nautical miles
3 hour= 51 nautical miles
Robin has a rectangular picture frame that is 8 1/2 by 11 inches. What is the
approximate perimeter of the picture frame in centimeters?
Answer: 99.06cm
Step-by-step explanation:
Note that 1 inch = 2.54cm
Therefore, we'll convert the sides of the frame in inches to cm. This will be:
8 1/2 inch = 8.5 × 2.54cm = 21.59cm
11inches = 11 × 2.54cm = 27.94cm
Therefore, the perimeter of a rectangle will be:
= 2(length + width)
= 2(27.94 + 21.59)
= 2(49.53)
= 99.06cm
3. A palm free is 12m in height.
A coconut tree is 16m in height.
What is the combined height of the
trees?
Answer:
12+16= 28m
28m is the combined height of the trees .
Hope this helps !
Degree and Radian Measures
Convert the given radian measures to a degree measure.
2 /pi (π)
a. 360°
b. -360°
c. -180°
d. 180°
Pleases select the best answer from the choices provided
Answer:
A. 360°
Step-by-step explanation:
I calculated it logically
A rectangle has the length of (3x + 4) cm with a width of (2x - 2) cm. What is the perimeter of the rectangle?
Answer:
Step-by-step explanation:
Can someone please help?
Answer:
The one all the way to the right
Step-by-step explanation:
30 ÷ X = 6
30 ÷ 5 = 6
fraction equivalent to 3/8 with denominator of 72
Answer:
27/72 IS MY best guest
Step-by-step explanation:
Please answer the question correctly with factual information for brainliest.
Answer:
5 or D
Step-by-step explanation:
The volume of a cube is equal to a side length to the power of three. Hence the term "cubed". so x^3=125
x=cbrt(125)
x=5
Double check:
(5*5)*5=25*5=125
Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n rectangles. Calculate the approximation for each of the given function and interval below. (You may use calculator and keep the final numerical answer in decimals for this question) (a) (3 pts) R5, f(x) = x 2 + x on the interval [−1, 1]
Answer:
[tex]R_5=1.12[/tex]
Step-by-step explanation:
We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:
[tex]f(x)=x^2+x[/tex]
On the interval [-1, 1] using five equal rectangles.
Find the width of each rectangle:
[tex]\displaystyle \Delta x=\frac{1-(-1)}{5}=\frac{2}{5}[/tex]
List the x-coordinates starting with -1 and ending with 1 with increments of 2/5:
-1, -3/5, -1/5, 1/5, 3/5, 1.
Since we are find the right-hand approximation, we use the five coordinates on the right.
Evaluate the function for each value. This is shown in the table below.
Each area of each rectangle is its area (the y-value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function f(x) over the interval [-1, 1] using five equal rectangles is:
[tex]\displaystyle R_5=\frac{2}{5}\left(-0.24+-0.16+0.24+0.96+2)= 1.12[/tex]
daniel’s print shop purchased a new printer for 35,000 each year it depreciates at a rate of 5% how much will the printer be worth in 8 years
Answer:
$23,219.72
Step-by-step explanation:
ab^x
a: initial value
b: value remaining after depreciation per year (in percentage)
x: number of years that have passed
35000(0.95)^8= 23219.7151
Round to the nearest hundredth value:
About $23219.72
HELP HELP HELP HELP ✨
answer:
30
step by step:
8+13+5+4=30
20 POINTS PLEASE HELP
Which of the following expressions is true? A. 2^4 • 2^3 = 212 B. 3^3 • 3^6 > 3^8 C. 4^2 • 4^2 > 4^4 D. 5^5 • 5^2 = 5^10
Answer:
Step-by-step explanation:
Exponents of the same base add
A. 2^4 • 2^3 = 212
2^7 = 128 ≠ 212
B. 3^3 • 3^6 > 3^8
3^9 > 3^8
C. 4^2 • 4^2 > 4^4
4^4 = 4^4
D. 5^5 • 5^2 = 5^10
5^7 ≠ 5^10
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
a) [0.00590, 0.0251].
b) [0.00690, 0.0551].
c) [0.0890, 0.0551].
d) [0.00690, 0.0351].
e) [0.00890, 0.0651].
Answer:
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of 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 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.
First group: Sample of 163, 13% has a second episode.
This means that:
[tex]p_1 = 0.13, s_1 = \sqrt{\frac{0.13*0.87}{163}} = 0.026[/tex]
Second group: Sample of 160, 14% has a second episode
This means that:
[tex]p_2 = 0.14, s_2 = \sqrt{\frac{0.14*0.86}{160}} = 0.027[/tex]
Distribution of the difference:
[tex]p = p_1 - p_2 = 0.13 - 0.14 = -0.01[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.026^2+0.027^2} = 0.0375[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Lower bound:
[tex]p - 1.645s = -0.01 - 1.645*0.0375 = -0.0717[/tex]
Upper bound:
[tex]p + 1.645s = -0.01 + 1.645*0.0375 = 0.0517[/tex]
90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).
Please solve this question
Answer:
it would be y=0
Step-by-step explanation:
because y+6y+9y=0
you basically add 6y+y=7y because the y that's by its self counts as 1
then you 7y+9y=16y
then it would be 16y=0
hope this helps out believe it's right
Apen is being built that is 10 feet long and 20 feet wide. How much fencing material will be needed
Answer:
40 square feet of material
Step-by-step explanation:
Find the volume of the cylinder.
Round to the nearest tenth.
r = 5 cm
5 cm
V = [?] cm3
Enter the number that goes in the green box.
Enter
Answer:
392.7
Step-by-step explanation:
The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2} h[/tex]
It is given that the radius of the cylinder is 5 cm and the height of the cylinder is 5 cm also.
So, The volume of the cylinder = [tex]\pi r^{2} h[/tex]
= 3.14 x 5^2 x 5
= 3.14 x 125
= 392.7 cubics cm
Thus, The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm.
Learn more about volume;
https://brainly.com/question/1578538
The price of a cell phone is usually $240 Ella mom buys one of these cell phones when the discount is 25 how much did Ella mom save?
Answer:
$60
Step-by-step explanation:
$240 = 100%
Discount = 25%
100% - 25% = 75%
75% as a decimal is 0.75
Multiply:
240(0.75) = 180
You could also do 3/4 of 240 because 0.75 is 3/4
To find out how much she saved, let's subtract the sale price from the original price:
240 - 180 = 60
Ella's mom saved $60 from the discount
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
6 friends share 10 pizzas equally plz help
Answer:
6/10 of the pizza.
If 2 gallons of paint cover 665 square feet, how much paint is needed to cover 2660 square feet?
Answer:
8 gallons
Step-by-step explanation:
2 gallons cover 665ft^2
2660/665 = 4
therefore 4 times more paint is needed
so 8 gallons
Khan Question :) Please do help no links pls
Answer:
sqrt(41)
Step-by-step explanation:
Using pythagoras theorem
The average temperature at the South Pole is - 47° F. The average temperature on the Equator is 86° F. How much warmer is the
average temperature on the Equator than at the South Pole?
Answer:
133° F
Step-by-step explanation:
So from -47 to 0 is 47. Add that on to 86.
That comes out to 133
Hope this helps
Brainliest would be appreciated
Answer:
133
Step-by-step explanation:
