Answer:
a) The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.
b) The null hypothesis is [tex]H_0: \pi_1 - \pi_2 = 0[/tex] and the alternate hypothesis is [tex]H_1: \pi_1 - \pi_2 \neq 0[/tex].
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Females:
49% from a sample of 600. So
[tex]\pi_1 = 0.49, s_{\pi_1} = \sqrt{\frac{0.49*0.51}{600}} = 0.0204[/tex]
Males:
41% from a sample of 500. So
[tex]\pi_2 = 0.41, s_{\pi_2} = \sqrt{\frac{0.41*0.59}{500}} = 0.022[/tex]
Test if there is a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade.
From here, question b can already be answered.
At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0. So
[tex]H_0: \pi_1 - \pi_2 = 0[/tex]
At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So
[tex]H_1: \pi_1 - \pi_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = \pi_1 - \pi_2 = 0.49 - 0.41 = 0.08[/tex]
[tex]s = \sqrt{s_{\pi_1}^2 + s_{\pi_2}^2} = \sqrt{0.0204^2 + 0.022^2} = 0.03[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.08 - 0}{0.03}[/tex]
[tex]z = 2.67[/tex]
Question a:
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.08, which is P(|Z| > 2.670, which is 2 multiplied by the p-value of Z = -2.67.
Looking at the z-table, Z = -2.67 has a p-value of 0.0038.
2*0.0038 = 0.0076
The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.
Find the volume of this cylinder.
Round to the nearest tenth.
16cm
4 cm
[?] cm3
The volume of the given cylinder with a diameter of 4 cm and the height of the cylinder is 16cm is 201.062 cm².
What is the volume of a right circular cylinder?The right circular cylinder is the cylinder in which the line joining the centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The volume of the given cylinder is,
Volume of the cylinder = (π/4) × (4cm)² × 16cm
= 201.062 cm²
Hence, the volume of the given cylinder is 201.062 cm².
Learn more about the Volume of the Cylinder:
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A local pizza parlor is selling two different shapes of cheese pizza for the same price. You can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches. Which choice gives you more pizza
Answer:
It is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
Step-by-step explanation:
Since a local pizza parlor is selling two different shapes of cheese pizza for the same price, and you can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches, to determine which choice gives you more pizza the following calculations must be carried out, knowing that the area of a square is equal to pi multiplied by the radius squared, and that the area of a square is equal to its side squared:
Round pizza:
Radius = Half the diameter
3.14 x 6 ^ 2 = X
3.14 x 36 = X
113.04 = X
Square pizzas:
(7x7) x 2 = X
49 x 2 = X
98 = X
Therefore, it is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
which comprison is correct?
a. 3/2 < 1/3
b. 3/8 > 1/6
c. 11/6 < 3/4
d. 3/5 = 5/8
Answer:
The second one
Step-by-step explanation:
USE THE BUTTERFLY TECHINQUE
3/8 O 1/6
18 3/8 O 1/6 8
18 > 8
3/8 > 1/6
Answer:
B is correct
3/8> 1/6 = 3 · 3/8 · 3 > 1 · 4/6 · 4 = 9/24 > 4/24 = 9 > 4 = Yes
Solve for y
4y = 32
Please answer!
Answer:
y = 8
Step-by-step explanation:
4t=32
Divide each side by 4
4y/4 = 32/4
y = 8
Answer: y = 8
Step-by-step explanation:
Firstly, you divide 4 ÷ 4y = 1y or more known as "y" then you do the same thing for the 32 (32 ÷ 4 = 8)
Finally, you write y = 8 and that is your final answer!
I hope this helps! Good luck with future homework and exams! <3
P.S Here's a fun fact! ~~
Hot water will turn into ice faster than cold water!
find the solution for x if |6x+8|=32
Answer:
X = 4
Step-by-step explanation:
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 4
the solution is X = 4.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 4
hence, the solution is x=4.
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Nuts Berry Farm sells nuts for $60 for 4 pounds. Today, and just for today only, Nuts Berry Farm is giving a 30% discount to all those who will buy nuts today. Enter how much, in dollars, is a pound of nuts today after the discount.
Parker is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with three equal-sized sections labeled Walk, Run, Stop, and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
Answer:60
Step-by-step explanation:
4*3*5
What is 5 / 7 ÷ ½ ?
step by step pls
Answer:
1 3/7
Step-by-step explanation:
5 / 7 ÷ ½
Copy dot flip
5/7 * 2/1
10 /7
Changing from an improper fraction
7/7 + 3/7
1 3/7
Choose all the expressions that show this statement is true.
Answer:
F. or C.
Step-by-step explanation:
please help me with this last one
Q = 91°
Step-by-step explanation:
Note how the angles correspond to each of the shapes:
J ---> S
G ---> R
H ---> Q
I ----> P
Since J = 55°, we can see that S is also 55°. With H = 91°, this means that Q is also 91°
Can someone help me please?
9514 1404 393
Answer:
[tex]\textsf{B.}\ \ 6x-1+\dfrac{-11x+8}{x^2+3}[/tex]
Step-by-step explanation:
See the attachment for the working out of the long division.
Subtract the sum of -6 and -2 from -18. *
Answer:
-26
Step-by-step explanation:
Because -6+ -2= -8
-18- 8= -26
FINALSSSSSS
I need help on this ASAP!!!!
Answer:
geometry?
Step-by-step explanation:
SHEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEESH
Any help would be greatly appreciated!
Answer:
the answer for that question is sqrt(49)
Find the median and mean of the data set below:
5, 7, 3, 36, 7, 23
Ed
Answer: mean is 13.5 and median is 7
Step-by-step explanation:
to get median you do (7+7)/2 and get 7 and for the mean you just add all of the numbers and divide by how many numbers there are. Basically it is 81/6 to get 13.5
Answer:
Median = 7
Mean = 13.5
Step-by-step explanation:
To find the median, put them in increasing order:
3, 5, 7, 7, 23, 36
cross out the values on the ends until you meet in the middle:
/, 5, 7, 7, 23, /
/, /, 7, 7, /, /
Find the average of the two middle numbers: (7+7)/2 = 7
Median = 7
For the mean, add all numbers and divide by the amount of numbers you have:
3 + 5 + 7 + 7 + 23 + 36 / 6
=81/6
= 13.5
A basketball player made 135 of the 225
foul shots he took in 4
games.
How many shots will he make in his next game if he attempts 30 foul shots?
135/225=3/5
3/5 times 6 on both sides=18/30
so he will make 18 shots
the area of a carpeted closet is 20 square feet . if the width of the closet is 3/2 feet , what is the width ?
Answer:
Length = 40/3 or 13.33 feet
Step-by-step explanation:
Given the following data;
Area of carpet = 20 feet
Width = 3/2 feet
To find the length of the carpet
Assuming that the shape of a carpeted closet is rectangular.
Area of rectangle = length * width
20 = length * 3/2
Multiplying both sides by 2/3
2/3 * 20 = length * 3/2 * 2/3
40/3 = length
Length = 40/3 or 13.33 feet
-1/2+(3/4x419) =
A. 1/9
B. 5/6
C. -1/5
D. -1/6
9514 1404 393
Answer:
D. -1/6
Step-by-step explanation:
Your calculator can tell you the answer to this.
[tex]-\dfrac{1}{2}+\left(\dfrac{3}{4}\cdot\dfrac{4}{9}\right)=-1/2+\dfrac{4\cdot3}{4\cdot9}=-\dfrac{1}{2}+\dfrac{3}{9}\\\\=-\dfrac{1}{2}+\dfrac{1}{3}=-\dfrac{3}{6}+\dfrac{2}{6}=\boxed{-\dfrac{1}{6}}[/tex]
A cylinder has a radius of 8 cm and a height of 4 cm what is the approximate value of the surface area of the cylinder
Area of cylinder = curved area + 2 x base circle
Circles = 2 x π(8)² = 128π cm²
Curved area = circumference of circle x height of cylinder
Circumference of circle = 2πr = 2π(8) = 16π cm
Curved area = 16π x 4 = 64π cm²
Total surface area = 128π + 64π = 192π cm² = 603.19cm² (5sf)
Please I need it now
A rational number is terminating decimal, if its denominator has
no prime factor other than:
A. 2 and 3 B. 3 and 5 C. 2 and 5 D. 2 and 7
Answer:
it's C. 2 and 5...
Step-by-step explanation:
If the denominator of rational number contains no prime factors other then 2 or 5 or both, then this rational number can be expressed as terminating decimal. So the correct answer is option is C
2x^+7x - 15= 0 If r and s are two solutions of the equation above and r > s which of the following is the value of r-s?
Answer:
6.5
Step-by-step explanation:
You failed to include the choices
Suppose that you have the option to buy an itern with either cash or credit?Under which condition would you use credit?
A if you don't want to pay interest
B if you want to build a good credit history
C if you like carrying a lot of cash on you
Answer:
Step-by-step explanation:
B. You build credit by using credit cards so b is the answer.
What are the repeating digits in the smallest group of repeating digits in the decimal equivalent of the fraction shown below?
1111/999
Answer:
1.112
Step-by-step explanation:
First, divide 1111 by 999 to find the decimal equivalent. 1111 divided by 999 equals 1.112112112
Second, look at the digits to see the smallest sequence of digits that repeat. The digits that repeat are 1 1 and 2
can I have brainlyest
Find the equation of the line that passes through the points (-2, - 5) and (3. – 8).
Answer:
Equation of line that passes through the points is; y= -13x - 31
Step-by-step explanation:
Given coordinates;
(- 2, - 5) and (3. - 8)
Find:
Equation of the line
Computation:
Equation of line that passes through the points is;
y = mx + c
So,
in (- 2, - 5)
-5 = m(-2) + c
-5 = -2m + c ...................Eq1
in (3, - 8)
- 8 = m(3) + c
-8 = 3m + c .....................Eq2
From eq2 + eq1
m = -13
-5 = -2m + c
-5 = -2(-13) + c
-5 = 26 + c
c = -31
So,
y = mx + c
y = (-13)x + (-31)
Equation of line that passes through the points is; y= -13x - 31
the graph of f(x)=x^2 will be translated 5 up and 2 units to the right .which function describe the graph produced by the translation
help please!!!!!!!!!!!!!!!!
Answer:
D
The X Axis is the time, the Y Axis is the amount of pages being read.
help asap will mark branniest thx
Answer:
[tex](\pi)r ^{2} h \div 3[/tex]
Volume = 3.14 × 5² ×6 ÷ 3
volume = 157 cm³ B
A class spends 1 hour 15 minutes on
English Language each school day. If
the total time spent in school each day
is 5 hour. What fraction of the time is
spent on English Language
Answer:
1/4
this is fraction of time spent on English language...
68 - 4 × (6 - 4)4
pls help o-o
Answer:
Here you go!, hope it helped. 68-32x
Answer:
36 is the answer I think :D
A TV has a listed price of $864.98 before tax. If the sales tax rate is 9.75%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Step-by-step explanation:
you would do 864.98 times 109.75% it would be estimated to 949 dollars