Answer:
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
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 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 simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.
This means that:
[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]
An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.
This means that:
[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]
Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Mean:
[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]
Standard deviation:
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/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]
So
[tex]M = 1.645*2.6 = 4.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7
The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
The ratio of hot dogs to hamburgers on a barbeque table is 6:4. If there are 36 hot dogs on the table then how many hamburgers must be there?
Answer: 24
Step-by-step explanation:
6 hot dogs for every 4 hamburgers
6*6 = 36
36 hot dogs for every ? hamburgers
since 6*6 equals 36, do 4*6
4*6 = 24
so 24 hamburgers
I can’t guarantee that this is right but I think it is
hopefully it’s helpful
Amanda is 160 cm tall. She is 10 cm taller than her younger sister Carl a. Which of the following equations can be used to find x? X + 10 = 160 X + 160 = 10 X - 10 = 160 x = 10 + 160
Answer:
A. x + 10 = 160
Step-by-step explanation:
This is the correct choice since, we already know the height of Amanda and it gives us the difference between her sister and her height. We can formulate an expression.
x + 10 = 160
Solve.
160 - 10 = 150
x = 150
Thus, Carla is 150 centimeters tall.
please answer this question
itss 11
Step-by-step explanation:
no worries about it is the same time for me
2
Find the lateral area and the surface area of the cone. Keep answer in exact form.
12 ft
16 ft
lateral area
surface area -
Answer:
I think:
192 lateral area
56 surface area
If Im wroung Im very sorry
2) r = 4/4 cm
Calculate the diameter of the circle
Answer:
radius is 4/4 cm meaning its 1 cm, and since diameter is twice the radius its 2cm.
Step-by-step explanation:
5. Match each description with the correct equation below. Then solve the equation.
a) When 4.26 is added to a number, the sum is 17.04.
b) The product of 4.26 and a number is 17.04.
c) When a number is doubled and 4.26 is subtracted, the result is 17.04.
4.26n = 17.04 2n − 4.26 = 17.04 n + 4.26 = 17.04
Answer:
.
Step-by-step explanation:
There are twice as many students on Mr. Sneed's team as on Mr. Johnson's team. Together, they want to raise 360$ to buy uniforms. According to the size of their team, how much money should each team raise?
Answer:
go on MATH.WAY. it'll give you the answer and explanation
Step-by-step explanation:
it took 5 hours to mow 6 yards. at the rate, how many yards can be mowed in 20 hours
Answer:
24 yards
Step-by-step explanation:
Given: 5 hours to mow 6 yards.
To find: At the same rate, how many yards can be mowed in 20 hours?
Solution: There are lots of different ways of solving this but I will show you setting up fractions to know how much 5 hours are for 6 yards let "x" be the variable
Step 1: Multiply all terms by the same value to eliminate fraction denominators
[tex]\frac{6}{5} = \frac{x}{20} \\\\20*\frac{6}{5} = 20 * \frac{x}{20}[/tex]
Step 2: Cancel multiplied terms that are in the denominator
[tex]20*\frac{6}{5} = 20 * \frac{x}{20}\\\\20 * \frac{6}{5} = x[/tex]
Step 3: Multiply the numbers
[tex]20 * \frac{6}{5} = x\\\\24 = x[/tex]
Step 4: Move the variable to the left
[tex]24 = x\\\\x = 24[/tex]
Therefore, 24 yards can be mowed in 20 hours.
20 PTS! WILL MARK BRAINLIEST
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 157 square units, and the area of the cross-section of the cylinder is 50π square units. Based on this information, which argument can be made?
The volume of the square prism is one third the volume of the cylinder.
The volume of the square prism is half the volume of the cylinder.
The volume of the square prism is equal to the volume of the cylinder.
The volume of the square prism is twice the volume of the cylinder.
Answer:
The volume of the square prism is equal to the volume of the cylinder.
Step-by-step explanation:
As per the information depicted the volume of the square prism is equal all to the volume of the cylinder. Hence option C is correct.
What is the square prism?A square prism is thee dimensional cuboid with a base and the top has an equal square while the remaining four faces have a rectangle and the opposite side angles of the square prism are congruent and parallel to each other.
As a square prism have the least two lengths that are equal to each other. Hence the volume of the square prism is equal to the volume of the cylinder as they have the same height and area of cross-section.
Find out more information about the square prism.
brainly.com/question/4315703
HELP ME PLEASEEEEEEEEEEEEEEEE
Answer:
522 m^2
Step-by-step explanation:
I've circles the numbers that you actually need to solve this problem.
First, find the area of the bigger rectangle by multiplying the length and width.
24*21=504
Then find the area of the smaller rectangle the same way
3*6=18
then add them to get the total area
504+18=522
522 m^2
What is the volume of this triangular prism in cm^3? Image is in the png link. Ples help. :(
Jason baked 7 pans of brownies. He gave ¼ of the brownies to his two sisters. How many pans of brownies did he give to his sisters? *
Step-by-step explanation:
7×1/4 = 1.75
1.75 ÷ 2 = 0.875 pans each
4. Solve the logarithmic equation for X:
log(x) -log(4) = 3
Answer:
X=7
Step-by-step explanation:
Please Help. Lateena solved the equation below. Is her solution correct? Explain why or why not?
I've attached the picture for the problem.
Answer:
Not correct
Step-by-step explanation:
Given:
x² - 6x - 7 = 0
The following equation can be solved correctly by factoring Thus,
x² - x + 7x - 7 = 0
x(x - 1) +7(x - 1) = 0
(x - 1)(x + 7) = 0
(x - 1) = 0
x - 1 = 0
x - 1 + 1 = 0 + 1
x = 1
Or
(x + 7) = 0
x + 7 = 0
x + 7 - 7 = 0 - 7
x = -7
Therefore, the solution would be x = 1 or x = -7
Lateena solution is therefore NOT CORRECT because she used a wrong method.
A child pool is 3.8 feet wide 5.5 feet long and 1.2 fee deep, what is the volume of the pool?
Answer:
25.08
Step-by-step explanation:
Answer:
25.08 cubic feet
Step-by-step explanation:
v = l * w * h
v = 5.5 * 3.8 * 1.2
v = 25.08 cubic feet
Consider the salt shaker shown.
5 cm
cm
What is the volume of the salt shaker, including the top? Round your answer to the nearest hundredth.
Volume of Salt Shaker =
Answer:
Volume of salt shaker = 42.4 cm³ (Approx.)
Step-by-step explanation:
Given:
Height of salt shaker = 5 cm
Diameter of salt shaker = 3 cm
Find:
Volume of salt shaker
Computation:
Radius of salt shaker = Diameter of salt shaker / 2
Radius of salt shaker = 3 / 2
Radius of salt shaker = 1.5 cm
Volume of salt shaker = Volume of cylinder + Volume of Hemisphere
Volume of salt shaker = πr²h + (2/3)πr³
Volume of salt shaker = (3.14)(1.5)²(5) + (2/3)(3.14)(1.5)³
Volume of salt shaker = (3.14)(2.25)(5) + (0.667)(3.14)(3.375)
Volume of salt shaker = 35.325 + 7.068
Volume of salt shaker = 42.4 cm³ (Approx.)
There are 53 beads on Ashley's necklace. 19 of the beads are pink and the rest are purple. What is the ratio of the number of purple beads to the total number of beads?
34: ?
Answer:
34 beads are purple so for every 19 pink there are 34 purple hope this helps
Which of the following numbers is not a perfect square?
49 124 169 361
Answer: 124
Step-by-step explanation: 7^2=49; 13^2=169; 19^2=361. Only 124 cannot be expressed as a square of an integer.
Answer:
124
Step-by-step explanation:
3. What is the measure of angle F? A 120° D G B A. 60 degrees. B. 90 degrees. C. 120 degrees. D. 180 degrees.
Answer:
120°
Step-by-step explanation:
The angles that has 120° is the same as angle E.
Angle E = 120°
Angle D = 180° - 120° = 60°
60° + Angle F = 180°
Angle F = 180° - 60°
Angle F = 120°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
This dot plot is not symmetric, and the data set has two
extreme values.
.
2
3
8
What is the best measure of center for this dot plot?
O A. The mean absolute deviation (MAD)
B. The interquartile range (IQR)
C. The median
D. The mean
Answer:
C: The median
Step-by-step explanation:
Lauren went to a store to buy some clothes. The shirts were selling at a 20% discount. A pair of pants cost $5 less than 3 times the original cost of a shirt.
If she spent $36 in all, what was the original cost of a shirt?
Answer:
OMG
Step-by-step explanation:
I had the same question
Answer:
$10.79
Step-by-step explanation:
x = original cost of one t shirt
We can build this equation
x - (20/100) x + 3x- 5 = 36
-1/5x + 4x = 41
-x + 20x = 205
19x = 205
x = $10.79
What is the greatest common factor (GCF) of 24 and 40?
Question:
What is the greatest common factor (GCF) of 24 and 40?
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
40=2×2×2×5
24=2×2×2×3 then we take the common 2×2×2=8
Solve for the value of a
Answer:
a= 90 i think
hope this helped
½ cup of sugar, and I only have a ¼ cup scoop and a ⅛ cup scoop. I need at least two different ways I can get ½ cup
2 ways to get to 1/2
Way 1:
Use the 1/4 scoop 2 times
1/4 + 1/4 =2/4
2/4 simplified is 1/2
Way 2:
Use the 1/8 scoop 4 titmes
1/8+1/8+1/8+1/8=4/8
4/8 simplified is 1/2
Hope this helps!
The area of a rectangular shaped pool is 64 squared meters. The width is 9 meters. Write and solve an equation to determine the length of the pool. Show work.
Answer:
7.11
Step-by-step explanation: Area=lengthxwdth
64=lengthx9
64/9=length
7.11=length
Maria had $22.45 to spend on groceries. After buying 3 bags of chips, she had $10.60 left. If each bag of chips costs the same amount, what is the price of one bag of chips
Answer:
$3.95
Step-by-step explanation:
Take the amount she has to spend and subtract the amount left ($10.60) and that will leave you with $11.85. So this is how much was spent on the 3 bags of chips. To find how much each bag cost, divide $11.85/3 bags = $3.95 per bag.
Explain how to graph the following including asymptotes and key features. f(x)=3^x+2
Answer:
y=2
Step-by-step explanation:
I need the answers for this question please
its triangle and 7.3 and 23.7 hope this helps
Can someone help me please
Answer:
4) 60 ft.²
5) 96 cm.²
6) 96
7) 126
8) 72
9) 32
10) 90
11) 216
(Formula for the area of a rectangle: length x width)
(Remember to follow PEMDAS when calculating the problems.)
the amount of gas used by a household is shown in the table. what is the slope of the data from the table
Answer. i cant answer this without a pic of the slope
Step-by-step explanation: