Answer:
The point estimate for the true difference between the population means is of -2.62 years.
The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.
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 of normal variables:
When we subtract normal variables, the mean is the subtraction of the mean, while the standard deviation is the square root of the sum of variances.
A sample of 138 cars owned by students had an average age of 5.13 years. The population standard deviation for cars owned by students is 3.45 years.
This means that:
[tex]\mu_{s} = 5.13, \sigma_{s} = 3.45, n = 138, s_s = \frac{3.45}{\sqrt{138}} = 0.2937[/tex]
A sample of 111 cars owned by faculty had an average age of 7.75 years. The population standard deviation for cars owned by faculty is 2.08 years.
This means that [tex]\mu_{f} = 7.75, \sigma_{f} = 2.08, n = 111, s_f = \frac{2.08}{\sqrt{111}} = 0.2658[/tex]
Difference between the true mean ages for cars owned by students and faculty.
s - f
Mean:
[tex]\mu = \mu_s - \mu_f = 5.13 - 7.75 = -2.62[/tex]
This is the point estimate for the true difference between the population means.
Standard deviation:
[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2937^2+0.2658^2} = 0.3961[/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 - 0.95}{2} = 0.025[/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 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs = 1.96*0.3961 = 0.78[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is -2.62 - 0.78 = -3.4
The upper end of the interval is the sample mean added to M. So it is -2.62 + 0.78 = -1.84
The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
It is Marcie’s first turn to roll. Which ratio shows the theoretical probability that she will not land on a star space?
1/6
1/3
1/2
2/3
The answer is D. 2/3
no one else had the answer so here it is xx
Answer:
d
Step-by-step explanation:
Answer:
Answer D:2/3
Step-by-step explanation:
Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
Answer:
4x-3
Step-by-step explanation:
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
What are equation of a line that is parallel to that line?Two lines are said to be parallel if they always maintain the same distance apart. If two lines are drawn so that they could extend into infinity without ever meeting each other, these lines are called parallel. Parallel lines are also called Equidistant lines.
Given
Equation of line y = 4x + 1
Point = (1, 1)
Equation of the line that is parallel to y = 4x + 1 is y=kx + b
Here k =4
y = 4x + b and contains the point (1,1)
Substitute the point (1,1) in y= 4x + b
⇒ 1 = 4(1) + b
⇒ 1 - 4 = b
⇒ b = -3
y = 4x + b
⇒ y = 4x - 3
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
Find out more information about equation of line here
https://brainly.com/question/402319
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Will give BRAINLIEST if you help me out
Does anyone know this please help
Answer:
b.12/25
c.4/15
d.8/15
e.6/12
2a.15/24=5/8
b.20/40=1/2
Cassandra works for a company that is based off her sales. If she is paid 9.5% of her total monthly sales, calculate her pay for the month if she sells $15,670 of product.
Answer:
I don't understand what you mean. but 10.43 i guess
A summer movie club charges a $30
membership fee and then $5 per movie.
Which equation can be used to find y, the
total cost of the movie club, if x represents
the number of movies watched.
Is B right?
pls help i dont have much time whoever answers correctly ill mark brainliest
What is the area of the trapezoid shown below?
Answer:
114 it think but maybe not
Step-by-step explanation:
a
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
Solve the Following inequality by choosing the Possible range of Values that make the Statement True
x + 3 ≥ 13
Answer:
x has to be greater than or equal to 10 (x ≥ 10)
Step-by-step explanation:
x + 3 ≥ 13
x ≥ 13 - 3
x ≥ 10
9(3y-5) expanded
HELPP
Answer:
x=9(3y-5)
Step-by-step explanation:
Choose the fraction pair that is equivalent.
16/64 and 1/4
8/9 and 9/8
5/8 and 25/48
3/6 and 1/3
Answer:
16/64 and 1/4
Step-by-step explanation:
1/4 x 16/16 = 16/64
1 x 16 / 4 x 16 = 16/64
16/64 = 16/64
Please help me
Adjust to compatible numbers that count by 50s, and then subtract to
estimate the difference.
301 - 52 =
Answer:
249
Step-by-step explanation:
301 - 52 = 249
A dressmaker needs to cut 9-inch pieces of ribbon from rolls of ribbon that are 12 feet in length. How many 9-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?
Answer:
She can cut 6 nine inch pieces.
Step-by-step explanation:
12x5=60 and 9 goes into 60 6 times which equals 54.
Step-by-step explanation:
i can't help you because that i am no a unit test i am so sorry for not help you
What is the approximate volume of a cylinder with a radius of 7 cam and a height of 4 cm
Answer:
volume =
[tex] {7}^{2} \times 3.14 \times 2 \times 4[/tex]
Step-by-step explanation:
volume =area of the base circle × height
If anyone knows the answer, could you help LOL
What is the equation of the line that passes through the point (4, -7) and has a slope of -1/2 ?
Answer:
y = -1/2x - 5
Step-by-step explanation:
To solve this (and questions like it), use the formula for the equation of a line:
y=mx+c, where y and x are any given co-ordinates, m is the slope, and c is the y-intercept.
Since we know that the slope is -1/2, we can plug this into our equation to replace m:
y=mx+c
y=-1/2x+c
To find c, we plug in our co-ordinate (4,-7), so that c is the only unknown, and we can solve for it:
y=-1/2x+c
-7=-1/2(4)+c
-7=-2+c
c=-5
Now that we know c, we can finish off our equation:
y = -1/2x + c
y = -1/2x - 5
A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
Answer : 169
Step-by-step explanation:
4(x+19) = 752
4x +76 = 752
4x = 752 - 76
x = 676/4
x=169
Hope this helps ;)
Please mark me the BRAINLIEST
Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathroom scales. The readings on 28 of the scales were too light, and the readings on the other 22 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight? Find the P-value and state a conclusion. The P-value is . Round the answer to four decimal places. We cannot conclude that more than half of bathroom scales underestimate weight.
Answer:
the P-value = 0.1977
conclusion: Since the p-value is not small;
we reject null hypothesis
hence, the data does not support claim that more than half of the bathroom scales underestimate weight.
Step-by-step explanation:
Given the data in the question;
let X represent the number of successes ( the weight is underestimated ) in n independent Bernoulli trials, each with the success probability p
X - Bin( n,p).
so
Null hypothesis H₀ : p ≤ 0.5
Alternative hypothesis Hₐ : p > 0.5
now, compute np₀ and n( 1 - p₀ )
np₀ = (50)(0.5)
np₀ = 25
n( 1-p₀ ) = (50)(1 - 0.5)
n( 1-p₀ ) = 25
we can see that both values are greater than 10.
∴ the sample proportion is approximately normally distributed;
P" - N ( p₀, [tex]\frac{p_{0}(1-p_0)}{n}[/tex] )
sample proportion p" = 28/50 = 0.56
standard deviation will be;
σ[tex]_{p"[/tex] = √( p₀(1-p₀) / n )
σ[tex]_{p"[/tex] = √( 0.5(1-0.5) / 50 )
σ[tex]_{p"[/tex] = √( 0.25 / 50 )
σ[tex]_{p"[/tex] = 0.07071
Next is the Z-score
z = p" - p₀ / σ[tex]_{p"[/tex]
z = 0.56-0.5 / 0.07071
z = 0.06 / 0.07071
z = 0.85
from table,
the probability that a standard normal random variable takes on a value greater than 0.85 is approximately 0.1977
Therefore, the P-value = 0.1977
conclusion: Since the p-value is not small;
we reject null hypothesis
hence, the data does not support claim that more than half of the bathroom scales underestimate weight.
p = 0.197663
3. What is the axis of symmetry of the graph of function f(x) = x² - 6x – 1
Answer:
guihnijiop;kl;lkm
Step-by-step explanation:
Answer:
A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.
f(x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2)^2 - 5/4 => vertex = (-3/2, -5/4)
f(x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2)^2 - 21/4 => vertex = (3/2, -21/4)
f(x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3)^2 - 6 => vertex = (-3, -6)
f(x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3)^2 - 10 => vertex = (3, -10)
Therefore, f(x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.
Step-by-step explanation:
plz mark me as brainlist
Is that the answer please help no links no links please help
Answer:
360
Step-by-step explanation:
V= L•W•H/3
10×12×9÷3
helppppppppppppppppppppppppppppp
Answer:
3) Not equivalent
4) Equivalent multiply by 2
5) Equivalent multiply by 2
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
I will ONLY give you a brainliest of you answer this questions CORRECTLY!
Answer:
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Step-by-step explanation:
Surface area of a cylinder = 2πrh+2πr² = 2π(rh+r²)
Cylinder A = 2π(rh+r²)
Cylinder B = 2π((2r)(2h)+(2r)²) = 2π(4rh+4r²)=2π(4(rh+r²))
To find how many times greater Cylinder B's surface area is than Cylinder A's surface area, divide:
[tex]\frac{Cylinder B}{Cylinder A}[/tex]
=2π(4(rh+r²))/2π(rh+r²)
(divide top and bottom by 2π)
=4(rh+r²)/(rh+r²)
(divide top and bottom by (rh+r²))
=4
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Fran has 18 paperback books and 24 hardcover books. What is the ratio of hardcover to paperback books?
WILL GIVE BRAINLIEST
3:4
4:3
3:7
7:3
Nicholas is currently in eighth grade and intends to attend a state college when he finishes high school. Nicholas’s parents currently have some money invested in mutual funds, but would like to invest this money in a more secure investment now to pay for college in 4 years. If they will need $25,000, how much do Nicholas’s parents have to invest now in a 48month CD that has a rate of 4.59% compounded monthly?
Answer: he has 10 monthly
Step-by-step explanation:
see from the question
AHHH HELP ILL GIVE BRAINLIEST!!!
Answer:
B
Step-by-step explanation:
If the energy required to harvest and refine an energy resource is 10,000 megawatts (MW) and the energy actually obtained from using the fuel is 12,400 MW, what is the EROEI of this resource?
Answer:
22,4000 answer i tinking
The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
Answer:
The p-value for a two-tailed test of hypothesis is 0.0164.
Step-by-step explanation:
The test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
This means that we look at the z-table, and we have to find:
[tex]P(|Z| > 2.4)[/tex]
Which is the pvalue of Z = -2.4 multiplied by 2, or 2 multiplied by 1 subtracted by the pvalue of Z = 2.4.
Looking at the z-table, z = 2.4 has a pvalue of 0.9918
1 - 0.9918 = 0.0082
2*0.0082 = 0.0164
The p-value for a two-tailed test of hypothesis is 0.0164.
PLZ HELP AND HURRY!!!!
Answer:
Complementary
Step-by-step explanation:
adding up to 90 degrees
Imagine you deposit $4,500 into an account that pays 5,5 percent interest compounded
daily. How much interest will you earn in 30 days?
Answer:
500
Step-by-step explanation:
Help I really need this answer 5,000 mL =
Answer:
5L
Step-by-step explanation:
[tex]\frac{5000mL}{1}*\frac{1L}{1000mL} = 5L[/tex]
Answer:
5L
Step-by-step explanation:
If you are trying to find out how many liters there are in 5000 milliliters then it is 5
So theres an equation here....
p<_ 7.5
Omar can buy at least_____pairs of socks.
Options:-
1. He can buy at least 7 socks
2. He can buy at most 7 socks
3. He can buy at least 8 socks.
4. He can buy at most 8 socks
ALSO I NEED THIS ASP PLUS BRAINLIEST
10 points tho bc ppl steal points and dont answer :/
Answer:he can buy at least 7 pairs of socks
Step-by-step explanation:
