Answer:
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
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 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 the variances.
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance.
This means that:
[tex]p_D = \frac{10}{42} = 0.2381, s_D = \sqrt{\frac{0.2381*(1-0.2381)}{42}} = 0.0657[/tex]
In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance.
This means that:
[tex]p_R = \frac{12}{58} = 0.2069, s_R = \sqrt{\frac{0.2069*(1-0.2069)}{58}} = 0.0532[/tex]
Distribution of the difference:
[tex]p = p_D - p_R = 0.2381 - 0.2069 = 0.0312[/tex]
[tex]s = \sqrt{0.0657^2+0.0532^2} = 0.0845[/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 - 0.9}{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*0.0845 = 0.139[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.0312 - 0.139 = -0.1078
The upper end of the interval is the sample mean added to M. So it is 0.0312 + 0.139 = 0.1702
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
Joseph and Ryan have 84 cards to sign. Joseph sins 1/4 of the cards. While Ryan signs 3/7. How many cards are left to be signed?
SIDE NOTE: PLEASE BE FAST!!
Answer:
27 cards left to be signed
Answer:
27 cards
Step-by-step explanation:
first we need to find what 1/4 of 84 is which will be 21 then we need to find what 3/7 of 84 is which will be 36 now we add the two getting 57 and then subtract 57 from 84 leaving us with 27 cards left. hope this helps.
Nathan Drives a motorcycle that travels 166.5 miles on a 4.5 gallon tank. What is the unit rate in miles per gallon.
Answer:
37 miles per gallon
Step-by-step explanation:
Ratios:
[tex]\frac{166.5}{4.5} =\frac{x}{1} \\\\4.5x=166.5\\x=37[/tex]
Can someone please help me please
Answer:
5
Step-by-step explanation:
Tom sells the hot dogs for £3.15 each
Answer:
Then what???
Step-by-step explanation:
If 5 shirts and 5 sweaters cost $205, and 6 shirts and 9 sweaters cost $294, what is the cost of one shirt and what is the
cost of one sweater?
Answer:
one shirt 25.00 one sweater 16.00
Step-by-step explanation:
$\text{one shirt: }\$25,\text{ one sweater: }\$16$
Let x be the cost of one shirt and y be the cost of one sweater; then
5x+5y6x+9y=205=294
The augmented matrix for this system of equations is
[5659205294]
Using Gaussian elimination, divide row one by 5 to get
[161941294]
Multiply row one by −6 and add the result to row two to get
[10134148]
Divide row two by 3 to get
[10114116]
After back substitution, y=16 and x=25.
The cost of one shirt is $25 and cost of sweater is $16.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the cost of one shirt and y be the cost of sweater.
5 shirts and 5 sweaters cost $205
5x+5y=205...(1)
6 shirts and 9 sweaters cost $294
6x+9y=294...(2)
Multiply equation (1) with 6 and equation (2) with 5.
30x+30y=1230..(3)
30x+45y=1470...(4)
Subtract 3 and 4
30y-45y=1230-1470
-15y = -240
Divide both sides by 15
y=240/15
y=16
Now plug in y value in any of the equation
5x+16(5)=205
5x + 80 = 205
5x = 125
Divide both sides by 5
x=25
Hence, the cost of one shirt is $25 and cost of sweater is $16.
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look at pic 10 pts will mark brainilest pls
Answer: it look like you have to do 20*10=200 and 8*4=32 the 4 where I got it from is 10-6=4 so 200+32=232 this is what I think, sorry if it wrong.
Step-by-step explanation: Hope this help :D
What is the lateral surface area of this cylinder?
A-452.16 sq. yds
B-226.08 sq. yds
C-678.24 sq. yds
D-904.32 sq. yds
Answer:
A. 452.16 yd²
Step-by-step explanation:
Lateral surface of the cylinder = 2πrh
Where,
r = 6 yd
h = 12 yd
π = 3.14
Plug in the values
Lateral Surface Area of the cylinder = 2*3.14*6*12
Area = 452.16 yd²
How many solutions exist for the system of equations below?
Answer Choices:
none
one
two
infinitely many
Answer:
None
Step-by-step explanation:
No solutions exist for the system of equations because the system is illogical: 3x+y=3x+y, but 18≠16.
Johanna flips a coin, and then she spins a spinner with 4 equal sections colored yellow, green, red, and purple.
Answer:
What's the question though?
pls help me giving brainless.
fever thermometer: decimeter
needle: decimeter
interstate highway:kilometer
fingernail: probably a centimeter
river: kilometer
tree trunk: meter
hope this helps.
PLZ help will mark the brainliest!!!!
Answer:
The answer is 0
Step-by-step explanation:
2x+15=x+15
-15 -x
x=0
Help please lost on this question
Answer:
First one is 6
Second one is 4
Step-by-step explanation:
Right on egg
Pls Help! Put a proper answer! And do not put a link or I will report you!
Two times the sum of a number, x, and 9 is at most four times the number. Write and solve an inequality to find the value of the number.
Answer:
2(x+9)≤4x
Step-by-step explanation:
2x+18≤4x
-18 -18
2x≤4x-18
-4x -4x
-2x≤18
/-2 /-2
x≥9
17 A plank of wood is 3.6 metres long. 85 cm is sawn off.
How long is the remaining plank?
help please if yo help she will marry you
Answer:
2.75
Step-by-step explanation:
So lets work this out:
First, we will need to convert 85 cm to meters. That would be 0.85 meters.
Now we can take 0.85 meters and subtract it from 3.6. This equals 2.75.
A plank of wood is 3.6 meters long. 85 cm is sawn off. How long is the remaining plank? 2.75 meters
Also no thank you I am a lady
1. Many of the continuous random variables that occur in real life are approximately normally distributed. How do you think this helps in studying real life variables?
2. Do you realize and understand the advantage of being able to convert values of an arbitrary normally distributed random variable to the corresponding values of the standard normal variable? If yes, list all the possible advantages of being able to do this. If not what do you plan to do to understand why the standard normal random variable is widely used for computations involving normal distributions?
Plss answer me direct type no link
Answer:
Step-by-step explanation:
jenny has $55 in her checking account, he bought 7 equally priced dvds and paid with a check. her new account balance is -$22. how much was each dvd?
Answer:
Jenny spent $11 on each dvd she bought.
Step-by-step explanation:
First and foremost, add 55 and 22 since her account balance is now at -$22 since that shows she spent even more.
55+22= 77
Next step divide 7 into 77 since that's how many dvds jenny bought.
77÷7= 11
The answer is $11. Jenny spent $11 on each dvd she bought.
Hope this helps
The circumference of a circle is 604 cm. What is the diameter of the circle?
Step-by-step explanation:
The Circumference is:
[tex]c = 2\pi \: r[/tex]
Radius r is:
[tex]r = \frac{d}{2} [/tex]
So,
[tex]c = \pi \: d \\ d = \frac{c}{\pi} \\ d = \frac{604}{\pi} \: cm[/tex]
IF PASSPORT is written as RCUURQTV, then how will BOOKLET be coded?
Answer: DQQMNGV
Step-by-step explanation: Each letter is shifted two letters to the right on a letter strip (a -> b -> c), so BOOKLET would be DQQMNGV.
Hope this helps!
Craig filled 1/3 of a bag with black beans and 2/6 of the same bag with red beans what fraction of the bag did Craig fill with beans
Answer:
4/6
Step-by-step explanation:
Make 1/3 into 6 as its denominator.
1 x 2 = 2
3 x 2 = 6
Black beans fill up 2/6 of the bag.
Red beans fill up 2/6 of the bag.
Find out what is the fraction both bags fill up altogether.
2/6 + 2/6 = 4/6
Two of Mr. Evan's Earth science classes have 23 students each. Box plots for recent test scores for these two classes are
displayed
Third Period
The Statement A which says that the mean of the two data sets are equal is the correct statement.
What is box plot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
According to the given problem,
We can notice from the two box plots that the mean for both the box plots is less than 80 but greater than 75.
Hence, we can conclude that the mean of the two data sets are equal.
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The number of bacteria in a petri dish triples every month, if the dish started with 25 bacteria, how many will there be an 8 months?
Answer:
600
Step-by-step explanation:
25x3 (per month) therefore it would be 75 times 8
Answer:
164025
Step-by-step explanation:
Anyone know how to answer this question
Solve the system of equations x + 2y = 8 and - 2x - 3y = - 7 by combining the equations.
Answer:
X+2Y = 8
-2X-3Y = -7
(X-2X+2Y-3Y)=8-7
-X-Y=1
is -0.4 a rational number?
Can someone help me plsssss I’ve been struggling
Answer: YES
REASON: Since a rectangle is made of two right triangles then a rectangle inscribed in a circle must have its diagonal as the diameter of the circle.
The Jacksons pay a monthly mortgage payment of $938. They also pay a semi-annual property tax bill of $3,298 and an annual homeowner’s insurance of $840. The property tax and insurance are paid monthly into an escrow account to their lender. What is their monthly payment including all three bills? Round to the penny.
9514 1404 393
Answer:
$1,557.67
Step-by-step explanation:
The monthly amount of the semi-annual tax bill is ...
$3,298/6 = 549.67
The monthly amount of the annual insurance bill is ...
$840/12 = $70
Then the total of the amount paid to the lender is ...
$938 +549.67 +70 = $1,557.67 . . . monthly payment
What is all the partial products for 3.4 x 1.2
Answer:
4.09
Step-by-step explanation:
Hope it helps. That is the answer
The partial product of 3.4 x 1.2 is (3 + 0.4) x (1 + 0.2).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3.4 x 1.2
3.4 is equal to 3 + 0.4.
1.2 is equal to 1 + 0.2.
Now,
(3 + 0.4) x (1 + 0.2)
= 3 + 0.6 + 0.4 + 0.08
= 3 + 1 + 0.08
= 4 + 0.08
= 4.08
Thus,
3.4 x 1.2 is equal to (3 + 0.4) x (1 + 0.2).
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A soft drink costs $1.65 and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase?
Answer: 3 refills
Step-by-step explanation:
$1.65 + 0.95 + 0.95 + 0.95 = $4.50
Help me find the answer please
Answer:
60
Step-by-step explanation:
m∠1=(55+65)/2=60
Pls help me no links I am serious
Answer:
March
Step-by-step explanation:
It’s March because in February there were 45 or so students, but then in March it went all the way up to 120. So, 120 - 45 = 75, which is the most amount of students increasing in a month.
I hope this helped and it wasn’t so confusing!!
