11. You conduct a random
sample of 250 of UCLA's entering freshmen and get an average GPA of
a. Find a 95% confidence interval for the average GPA of all of UCLA's entering freshmen.
b. UCLA claims the average GPA for entering freshmen is 4.05. Does your confidence interval
support this claim? Explain your reasoning
Answers
Answer:
a) The 95% confidence interval for the average GPA of all of UCLA's entering freshmen is (4.11, 4.31).
b) 4.05 is not part of the confidence interval, which means that it does not support this claim.
Step-by-step explanation:
Question a:
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 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.75}{\sqrt{250}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.21 - 0.1 = 4.11
The upper end of the interval is the sample mean added to M. So it is 4.21 + 0.1 = 4.31
The 95% confidence interval for the average GPA of all of UCLA's entering freshmen is (4.11, 4.31).
b. UCLA claims the average GPA for entering freshmen is 4.05. Does your confidence interval support this claim?
4.05 is not part of the confidence interval, which means that it does not support this claim.
Related Questions
6z3+2z2-9
What is the constant
Answers
Answer:
.; i don't know the constant but i know that the degree is 3 Step-by-step explanation:
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
I need the answer step by step
Answers
Answer:
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Step-by-step explanation:
From Algebra we know that a second order polynomial is a perfect square if and only if [tex](x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]. From statement, we must fulfill the following identity:
[tex]a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]
By Associative and Commutative properties, we can reorganize the expression as follows:
[tex]a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}[/tex] (1)
Then, we have the following system of equations:
[tex]x = a[/tex] (2)
[tex](b^{2}-1) = 2\cdot x\cdot y[/tex] (3)
[tex]y = c[/tex] (4)
By (2) and (4) in (3), we have the following expression:
[tex](b^{2} - 1) = 2\cdot a \cdot c[/tex]
[tex]b^{2} = 1 + 2\cdot a \cdot c[/tex]
[tex]b = \sqrt{1 + 2\cdot a\cdot c}[/tex]
From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, [tex]a, b, c > 1[/tex]. If [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are prime numbers, then [tex]2\cdot a\cdot c[/tex] must be an even composite number, which means that [tex]a[/tex] and [tex]c[/tex] can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.
In addition, [tex]b[/tex] must be a natural number, which means that:
[tex]1 + 2\cdot a\cdot c \ge 4[/tex]
[tex]2\cdot a \cdot c \ge 3[/tex]
[tex]a\cdot c \ge \frac{3}{2}[/tex]
But the lowest possible product made by two prime numbers is [tex]2^{2} = 4[/tex]. Hence, [tex]a\cdot c \ge 4[/tex].
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Example: [tex]a = 2[/tex], [tex]c = 2[/tex]
[tex]b = \sqrt{1 + 2\cdot (2)\cdot (2)}[/tex]
[tex]b = 3[/tex]
if the length is 9 cm,breadth is 10 cm and volume of cuboid is 1800cm cube ,,find the height and total surface area of cuboid,
Answers
Answer:
the height is 20 cm.
tsa is 940 cm square
Step-by-step explanation:
volume of cuboid = l*b*h
1800 = 9*10*h
h= 20 cm
TSA = 2(L*B+ B*H + L*H)
= 2(9*10 + 10*20 + 9*20)
=940 cm square
The height of the cuboid will be 20 cm
The total surface area of cuboid will be 940 cm²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of cuboid = 9 cm
The breadth of cuboid = 10 cm
And, The volume of cuboid = 1800 cm³
Now,
We know that;
Volume of cuboid = Length × Breadth × Height
⇒ 1800 = 9 × 10 × h
⇒ 1800 / 90 = h
⇒ h = 20 cm
And, The total surface area of cuboid = 2lw + 2lh + 2hw
Substitute all the values, we get;
⇒ The total surface area of cuboid = 2 (9 × 10 + 9 × 20 + 20 × 10)
= 2 (90 + 180 + 200)
= 2 × 470
= 940 cm²
Learn more about the multiply visit:
brainly.com/question/14176303
#SPJ2
Which statement is most likely to be true for this distribution?
1
A. The mean is less than the median.
B. The mean is greater than the median.
O C. The mean is the same as the median.
Answers
Find the measure of the angle, round to the nearest tenth: Sin X = .7547
Answers
X = INVERSE-SIN(.7547)
X = 49.0 degrees
Elliot read a report from a previous year saying that 6%, percent of adults in his city biked to work. He wants to test whether this has changed, so he is going to take a random sample of adults in his city and see what percent of them bike to work. Let p represent the proportion of adults in Elliot's city that bike to work.
Required:
What is an appropriate set of hypotheses for his significance test?
Answers
Answer:
The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]
Step-by-step explanation:
Elliot read a report from a previous year saying that 6%, percent of adults in his city biked to work. He wants to test whether this proportion has changed.
At the null hypothesis we test if the proportion is still the same, that is, of 6%. So
[tex]H_0: p = 0.06[/tex]
At the alternate hypothesis, we test if the proportion has changed, that is, it is different of 6%. So
[tex]H_1: p \neq 0.06[/tex]
What is an appropriate set of hypotheses for his significance test?
The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]
CORRECT (SELECTED)
z=\dfrac{0.1-0.06}{\sqrt{\dfrac{0.06(0.94)}{240}}}z=
240
0.06(0.94)
0.1−0.06
Four hundred randomly selected working adults in a certain state, including those who worked at home, were asked the distance from their home to their workplace. The average distance was x-bar equal to 8.84 miles. Assume that the standard deviation of the population of all working adults in that state is 2.70 miles. Construct a 99% confidence interval for the mean distance from home to work for all residents of this state. Droble
Answers
Answer:
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
Step-by-step explanation:
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 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{2.7}{\sqrt{400}} = 0.35[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8.84 - 0.35 = 8.49 miles.
The upper end of the interval is the sample mean added to M. So it is 8.84 + 0.35 = 9.19 miles.
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
Which types of triangles can have three angles that measure less than 90°?
acute triangle
equilateral triangle
right triangle
isosceles triangle
Answers
Answer:
An acute triangle
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Robin, Steven, and John are comparing tree diagrams for rolling double sixes on two six-sided number cubes (6, 6). Robin thinks the probability is 136 based on the tree diagram they created. Steven disagrees and argues that the probability of rolling double sixes is 16. John counts twelve outcomes and claims the probability is 112.
Who correctly found the probability of rolling double sixes using the tree diagram?
A
Robin because there are 36 outcomes and only one is (6, 6).
B
Steven because there are 6 outcomes and only one is (6, 6).
C
Steven because there are 36 outcomes and six of them are (6, 6).
D
John because there are 6 outcomes for each and only one is (6, 6).
Answers
Answer:
A. Robin because there are 36 outcomes and only one is (6, 6).Step-by-step explanation:
You would get the probability of double sixes as:
P(6, 6) = 1/6*1/6 = 1/36Correct choice is A
The Robin because there are 36 outcomes and only one is (6, 6) is the correct option.
We have given that,
Robin, Steven, and John are comparing tree diagrams for rolling double sixes on two six-sided number cubes (6, 6).
Robin thinks the probability is 136 based on the tree diagram they created.
Steven disagrees and argues that the probability of rolling double sixes is 16.
John counts twelve outcomes and claims the probability is 112.
What is the probability?The formula to calculate the probability of an event is as follows. Probability(Event) = Favorable Outcomes/Total Outcomes
You would get the probability of double sixes as:
P(6, 6) = 1/6*1/6 = 1/36
Correct choice is A.
Therefore the Robin, because there are 36 outcomes and only one is (6, 6).
To learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ2
Select ALL ordered pairs that are located in the first quadrant of the coordinate plane.
A (-3,8)
B (9,-7)
C (5,4)
D (2,6)
Answers
Answer:
C, D
Step-by-step explanation:
in the first coordinate plane, both numbers in a coordinate must be positive
IF ITS RIGHT ILL MARK BRAINLIEST
Answers
Answer:
Answer is 12
Step-by-step explanation:
angle BCF+angle CFE=180(being co-interior angle)
4x+11x=180
15x=180
x=180/15
x=12
The diagram shows a cylindrical tank.
The radius is 30 cm and the height is 80 cm.
(a) Calculate the area of the base of the tank.
(b) Calculate the volume of the tank in litres.
Answers
Step-by-step explanation:
a) A=π302=900π CM2 =2,827 CM 2
b) V=Ah=900=72000 π cm 3 = 226,195 cm3
Let x stand for the percentage of an individual student's math test score. 64 students were sampled at a time. The population mean is 78 percent and the population standard deviation is 14 percent. What is the standard deviation of the sampling distribution of sample means?
Answers
Answer:
[tex]\sigma_x= 1.75\%[/tex]
Step-by-step explanation:
Given
[tex]n = 64[/tex]
[tex]\mu = 78\%[/tex]
[tex]\sigma = 14\%[/tex]
Required
The sample standard deviation
This is calculated as:
[tex]\sigma_x= \frac{\sigma}{\sqrt n}[/tex]
This gives:
[tex]\sigma_x= \frac{14\%}{\sqrt {64}}[/tex]
[tex]\sigma_x= \frac{14\%}{8}[/tex]
[tex]\sigma_x= 1.75\%[/tex]
Constant of Variation
For the function defined by y = 1/x², y varies inversely as what quantity?
a. x
b. 2x
c. y
d. x²
Please select the best answer from the choices provided
Answers
Answer:
D. x²
Step-by-step explanation:
I calculated it logically
If a rectangle has a length of 10 cm and a width of 12 cm, what is it's perimeter () and area
Answers
Answer:
p=44,A=120
Step-by-step explanation:
P=10+12+10+12
P=44cm
A=10*12
A=120cm^2
Pls help extra points and mark brainlist
Answers
Answer:
12
Step-by-step explanation:
The range is the difference from the greatest data point and the least data point. By looking at the box plot, the lowest value would be 0 while the highest would be 12. You use the definition of range to find it:
12 - 0 = 12
What is the volume of a regular triangular pyramid with an apothem of 2.3ft, a side length of 8ft and a height of 25 feet
Answers
230FT
Regular tetrahedron
Solve for volume
V≈1.15×107
Use the formula for the volume of a triangular pyramid: V=13Ah , where A = area of the triangular base, and H = height of the pyramid.
A={the letters of the word ,HIPPOPOTAMUS}
Answers
•ω• Hewo fren!
☆☆●◉✿Answer:✿◉●☆☆
The letters of hippopotamus is H-I-P-P-O-P-O-T-A-M-U-S
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
I’m sowy, I didn’t really understand your question... did you want to learn about a hippopotamus? If so, please tell me in the comments I would answer there too!
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
move two choices to the blanks to correctly complete the sentences.
Answers
Answer:
(A) There should have been 5 outcomes of HT
(B) The experimental probability is greater than the theoretical probability of HT.
Step-by-step explanation:
Given
[tex]S = \{HH,HT,TH,TT\}[/tex] -- Sample Space
[tex]n(S) = 4[/tex] --- Sample Size
Solving (a); theoretical outcome of HT in 20 tosses
First, calculate the theoretical probability of HT
[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]
[tex]P(HT) = \frac{1}{4}[/tex]
Multiply this by the number of tosses
[tex]P(HT) * n= \frac{1}{4} * 20[/tex]
[tex]P(HT) * n= 5[/tex]
Solving (b); experimental probability of HT
Here, we make use of the table
[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]
[tex]P(HT) = \frac{6}{20}[/tex]
[tex]P(HT) = 0.30[/tex] ---- Experimental Probability
In (a), the theoretical probability is:
[tex]P(HT) = \frac{1}{4}[/tex]
[tex]P(HT) = 0.25[/tex] ---- Experimental Probability
By comparison;
[tex]0.30 > 0.25[/tex]
What is the area of the sector for the following circle? Round your answer to 4 decimal places. *
Answers
Answer:
13.0833 ft²
Step-by-step explanation:
From the question given above, the following data were obtained:
Radius (r) = 5 ft
Angle sustained by the sector (θ) = 360 – 300
= 60°
Pi (π) = 3.14
Area of sector (A) =?
The area of the sector can be obtained as follow:
A = θ/360 × πr²
A = 60/360 × 3.14 × 5²
A = 1/6 × 3.14 × 25
A = 1/6 × 78.5
A = 78.5/6
A = 13.0833 ft²
Thus, the area of the sector is 13.0833 ft²
Step-by-step explanation:
The angle of the minor sector will be ,
> 360 - 300 = 60° .
Area of sector :-
> Area = ∅ / 360 × πr²
> A = 60/360 × 3.14 × 5ft²
> A = 13.09 ft²
(x^5-y^5) divided (x-y)
See in the picture I have done till here but can anyone tell me next step
Answers
Answer:
[tex]\frac{x^6-yx-y^5}{x}[/tex]
Step-by-step explanation:
x^5-y^5 divided x-y
[tex]\frac{(x^5-y)x}{x} -\frac{y^5}{x}[/tex]
[tex]\frac{(x^5-y)x-y^5}{x}[/tex]
=> [tex]\frac{x^6-yx-y^5}{x}[/tex]
A giant tortoise can travel 0.19 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1 mile?
Answers
Answer:
5.26 hours or 315.6 minutes
Step-by-step explanation:
If he travels 0.19 miles in 1 hour
Then 1 mile is traveled (1x1)/0.19
5.26 approx. hours or 5.26 x 60 mins = 315.6.
Avery spent 10 minutes outside. If
she spent 64 minutes riding her bike,
48 minutes on the trampoline, and the
rest of the time swimming, how many
minutes did Avery spend swimming?
Answers
Answer:Cannot be solve how much time did she spend all together but adding it all together would be 122 minutes/ she never went swimming
Step-by-step explanation:
Plz help me well mark brainliest if correct....????
Answers
Answer:
C
Step-by-step explanation:
18 boys
Answer:
i think 18 msy be
Step-by-step explanation:
Pls help ill give u brainlest!! 40 points
Hakeem owns seven less than 3/5 the number of DVDs that Manuel owns. Hakeem owns 20 DVDs. How many DVDs does Manuel own? Show your work.
Answers
Answer:
Manuel owns 5 DVDS
Step-by-step explanation:
3/5 = 12/20
12 - 7 = 5
you watch seven deadly sins?
Explanation: 3/5 =12/20
12-7 = 5
Find 14.32 ÷ 3.5. Round your answer to the nearest hundredth.
Answers
Answer: 4.09
Step-by-step explanation:
4.09142857 rounded to the nearest hundredth is: 4.09
Please help me
Find the circumference and the area of this shape
I'll give brainliest
Answers
Area = 176.7
22,19,16,13 what is the 37th term
Answers
Answer:
-86
Step-by-step explanation:
3x10=30
22-3=19-3=16-3=13
so if its tthe 37th term, lets do 30x3=90
now 13-90=-77
-77=34th term
now just -3 until 37
-80
-83
-86
the 37th term is -86
A binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of U.S. adults found that 37% have been to court. You randomly select 30 U.S. adults and ask them whether they have been to court.
Answers
Answer:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.
The mean is of 11.1 and the standard deviation is of 2.64.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Using the normal distribution to approximate the binomial distribution.
This is possible if:
[tex]np \geq 10, n(1-p) \geq 10[/tex]
A survey of U.S. adults found that 37% have been to court. You randomly select 30 U.S.
This means that [tex]p = 0.37, n = 30[/tex]
Test if it is possible:
[tex]np = 30*0.37 = 11.1[/tex]
[tex]n(1-p) = 30*0.63 = 18.9[/tex]
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.
Mean and standard deviation:
[tex]E(X) = np = 30*0.37 = 11.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.37*0.63} = 2.64[/tex]
The mean is of 11.1 and the standard deviation is of 2.64.
What are 3 combinations to equal the total
Answers
Answer:
1x 2x 3x
Step-by-step explanation: