You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.
Answers
Question:
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% confidence interval for the population mean.
Answer:
At the 90% confidence level, confidence interval = 110.2484 < μ < 117.7516
At the 95% confidence level, confidence interval = 109.53 < μ < 118.48
The 95% confidence interval is wider
Step-by-step explanation:
Here, we have
Sample size, n = 45
Sample mean, [tex]\bar x[/tex] = $114.00
Population standard deviation, σ = $15.30
The formula for Confidence Interval, CI is given by the following relation;
[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]
Where, z is found for the 90% confidence level as ±1.645
Plugging in the values, we have;
[tex]CI=114\pm 1.645 \times \frac{15.3}{\sqrt{45}}[/tex]
or CI: 110.2484 < μ < 117.7516
At 95% confidence level, we have our z value given as z = ±1.96
From which we have [tex]CI=114\pm 1.96 \times \frac{15.3}{\sqrt{45}}[/tex]
Hence CI: 109.53 < μ < 118.48
To find the wider interval, we subtract their minimum from the maximum as follows;
90% Confidence level: 117.7516 - 110.2484 = 7.5
95% Confidence level: 118.47503 - 109.5297 = 8.94
Therefore, the 95% confidence interval is wider.
Answer:
B. is the correct option.
With 90% the population mean price is
in lies in (127.01,134.99). With 95% confidence, it can be said that the population mean price lies in ( 126.24,135.76)
Therefore, the 95% confidence interval is wider than 90%.
The calculation is attached
Related Questions
A circle has a circumference that is greater than 8 meters. The inequality 3.14 d greater-than 8 can be used to determine the possible lengths of the diameter of the circle. What are the possible values of d, the length of the diameter in meters?
Answers
Answer:
The possible values of d, the length of the diameter is d > 2.55 meters.
Step-by-step explanation:
The circumference of a circle is:
[tex]C=2\pi r=\pi\ d[/tex]
Here,
C = circumference
r = radius
d = diameter
It is provided that the circumference is greater than 8 meters.
That is,
[tex]C>8\\\pi\cdot d>8[/tex]
Use the value of π as 3.14.
Compute the range of values of d as follows:
[tex]\pi\cdot d>8\\\\3.14\times d>8\\\\d>\frac{8}{3.14}\\\\d>2.55[/tex]
The diameter of the circle is greater than 2.55 meters.
Thus, the possible values of d, the length of the diameter is d > 2.55 meters.
Answer:
To simplify the answer above, D
Step-by-step explanation:
21 = 1/4x what is x.
Answers
I typed it into desmos
Answer:
84
Step-by-step explanation:
Hello there!
We could solve this with an equation, but just think about it. The given expression shows that 21 is 1/4 of x. So just multiply 21 by 4 and get 84.
;)
A plane flies 1640 miles in 4 hours . What is the average speed of the plane ??
Answers
Answer:
410 miles
Step-by-step explanation:
total distance covered (d) = 1640 miles
total time taken (t) = 4 hrs
average distance per hour= d/t
= 1640/4
= 410 miles
Answer:
410 mph
Step-by-step explanation:
[tex]average \: speed \\ = \frac{1640}{4} \\ = 410 \: mph[/tex]
The absolute value of three, written as |3| because ?
Answers
Answer:
Then people will know anything inside those lines is positive.
Step-by-step explanation:
Hope this helps:)
Answer:
because there is 3 sides
Step-by-step explanation:
T= M (4+FG) solve for F
Answers
Answer:
f= t/mg - 4/g
Step-by-step explanation:
So the final solution for [tex]\( F \)[/tex]is:
[tex]\[ F = \frac{T - 4M}{MG} \][/tex]
To solve the equation [tex]\( T = M(4 + FG) \)[/tex] for [tex]\( F \)[/tex], you would follow these steps:
Step 1: Distribute the [tex]\( M \)[/tex]to terms inside the parentheses:
[tex]\[ T = 4M + MFG \][/tex]
Step 2: Move the term containing [tex]\( F \)[/tex] to one side of the equation:
[tex]\[ MFG = T - 4M \][/tex]
Step 3: Divide both sides by [tex]\( MG \)[/tex] to isolate [tex]\( F \)[/tex]:
[tex]\[ F = \frac{T - 4M}{MG} \][/tex]
Complete correct question:
How do you solve [tex]T=M(4+FG)[/tex] for [tex]F[/tex] ?
Mr. Akmal owns a bakery, he bought 100 eggs this week.15 out of them cracked. Find the percentage of cracked eggs.
Answers
Answer:
Step-by-step explanation:
[tex]\frac{15}{100}[/tex]×100 = 15%
What is the factored form of y^2 + xy − 6x^2?
Answers
Answer:
-((2x - y) (3x + y))
Step-by-step explanation:
The cost for a pizza at Pizza Palace depends on the size of the pizza and the number of toppings for a large pizza the cost in dollars, C, with t numbers of toppings can be determined with the equation C = 2 t + 18 what does 2 represent in the equation
Answers
Answer:
C = 2 t + 18
This equation satisfy the general formula from a linear model:
[tex] y= mx +b[/tex]
Where m represent the slope and b the intercept.
And for this case the number 2 represent the slope for the model and is telling to us that if we increase the number of toppings by 1 unit we would expect an increase in the cost of 2 dollars.
The 18 is a fixed cost and represent the intercept for the model
Step-by-step explanation:
For this case we know that the cost in dollars, C for a pizza based, with t numbers of toppings can be determined with the equation
C = 2 t + 18
This equation satisfy the general formula from a linear model:
[tex] y= mx +b[/tex]
Where m represent the slope and b the intercept.
And for this case the number 2 represent the slope for the model and is telling to us that if we increase the number of toppings by 1 unit we would expect an increase in the cost of 2 dollars.
The 18 is a fixed cost and represent the intercept for the model
what is 1.83333 as a fraction
Answers
Answer:Para pasar el número decimal 1.83333 a fracción, siga los siguientes pasos:
Paso 1: Escriba el número como una fracción de 1 (uno):
1,83333 = 1,83333/1
Paso 2: Multiplica simultáneamente el numerador y el denominador por 10 tantas veces cuánto los dígitos después de la coma (separación entre la parte entera y la parte fraccionaria del número):
Como tenemos 5 números después de la coma, multiplique el numerador y el denominador por 100000. Así,
1,83333/1 = (1,83333 x 100000)/(1 x 100000) = 183333/100000.
Tenga en cuenta que multiplicar por 10 es el mismo que desplazar la coma a la derecha una posicion.
Una vez que esta fracción es irreductible, es decir, está en forma reducida, ya no podemos simplificarla. La respuesta es la fracción anterior.
Como el numerador es mayor que el denominador, tenemos una fracción IMPRORIA, entonces podemos expresarla como un NÚMERO separación, así 183333/100000 también es igual a 1 83333/100000 cuando se representa por un número mixto.
Step-by-step explanation:
The difference between two numbers is 12. Four times the larger number decreased by 25 equals 48 increased by 3 times the smaller number. Find the numbers.
Answers
The larger number is 37 and the smaller number is 25.
Explanation:To solve this problem, let's assume that the larger number is x and the smaller number is y.
According to the problem, x - y = 12 and 4x - 25 = 48 + 3y. We can solve this system of equations by substituting the value of x from the first equation into the second equation.
Substituting x = y + 12 into the second equation, we get 4(y + 12) - 25 = 48 + 3y. Simplifying this equation, we have 4y + 48 - 25 = 48 + 3y. By combining like terms, we get 4y + 23 = 48 + 3y. Subtracting 3y from both sides, we obtain y + 23 = 48. Finally, subtracting 23 from both sides, we find y = 25. Plugging this value into the first equation, we can solve for x: x - 25 = 12. Adding 25 to both sides, we get x = 37.Therefore, the larger number is 37 and the smaller number is 25.
Learn more about Solving a system of equations here:https://brainly.com/question/32115090
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A cylinder has a height of 5 centimeters and a radius of 2.3 centimeters. What is the volume of this cylinder?
A 3.32 cm3
16.62 cm
С
83.10 cm3
o o
D
180.64 cm
Answers
Answer:
c 83.10
Step-by-step explanation
3.14 times 2.3 times 5
Karlen started painting the walls at 10:45 am, and he said that he could complete the job at 5:25 pm. His father said that five eighths of that time was enough to paint the walls. However, when Karlen finished the job, they noticed that it actually took him 80% of an hour longer than the time predicted by the father. How much longer did Karlen predict it would take than the time it actually took him to complete the job (what part of an hour)? Please help as soon as possible
Answers
Answer:
karlen predicted it will take 1.7 hours longer than he actually did
Step-by-step explanation:
If Karlen started painting the walls at 10:45 am, and he said that he could complete the job at 5:25 pm.
Which means he thought he would spend 6 hrs 40 minutes or 6⅔ hours or 20/3
Now, his father said ⅝ of that time was going to be enough to paint the whole wall.
Thus; estimated time by father to paint whole wall = ⅝ x 20/3 = 25/6 hours.
Now, it says karlen took 80% of an hour longer than the time predicted by his father to finish the painting.
Thus, karlen actually spent;
25/6 + 80/100 hours = 25/6 + 4/5 = 149/30 hours
Thus, since karen predicted he was going to spend 20/3 hours, the difference is;
20/3 - 149/30 = 1.7 hours
So karlen predicted it will take 1.7 hours longer than he actually did
Answer:
1.7 hours
Step-by-step explanation:
Item 16 A scale drawing of a triangular sign has a scale factor of 1:8. Which statements are true? The ratio of the area of the scale drawing to the area of the sign is 1:8. The ratio of the area of the scale drawing to the area of the sign is 1:16. The ratio of the perimeter of the scale drawing to the perimeter of the sign is 1:8. The ratio of the area of the scale drawing to the area of the sign is equal to the square of the scale factor.
Answers
Answer:
The correct option is;
The ratio of the area of the scale drawing to the area of the sign is equal to the square of the scale factor
Step-by-step explanation:
Here we have a scale factor of 1:8
Therefore area of drawing = 1/2×base, b×height, h = 1/2×b×h
Hence, the area of the triangular sin will be given by 1/2×8×b×8×h
Area of triangular sign = 64 × 1/2×b×h
Hence the ratio of the area of the scale drawing to the area of the triangular sign is equal to the square of the scale factor.
Answer:
the scale factor is 2
the area of the scale drawing is 3.75
and the last one is square
Step-by-step explanation:
edge 2021
imension
What is the area of the rectangle?
09
15 m2
7 m
17
19 m2
2 m
Intro
Done
Answers
Answer:
sorry can we have more info?
Step-by-step explanation:
Answer:
15m2
Step-by-step explanation:
hope this help.
larry purchsed 3 pairs of pants for 24 each and 5 shirts for 18 each. how much larry spend
Answers
Answer:
162
Step-by-step explanation:
24 x 3 = 72
5 x 18 = 90
90 + 72 = 162
Answer:
162
Step-by-step explanation:
3*24=72 and 5*18=90 then add them together and they equal 162
Harry's Electronics kept track of how many customers bought a newly released gaming system during the first month it was available. The following box plot was created from this data.
Which of the following properly describes the data?
Answers
The correct statement is
The data is skewed right.
What is Box and whisker plot?The lower and upper quartiles are shown on the left and right sides of a box and whisker plot, respectively. The interquartile range, which contains 50% of the data, is covered by the box. The median is the vertical line that divided the box in half.
We have a box and whisker plot.
Based on the position of the median value in the box plot, we may decide if a distribution is skewed or not. The distribution is right-skewed (or "positively" skewed") when the median is closer to the bottom of the box and the whisker is shorter on the lower end of the box.
A right-skewed distribution with a positive skewness is one in which the median is smaller than the mean. The median of a left-skewed distribution is bigger than the mean when the skewness is negative, on the other hand.
Here, the data is shorter on the lower end of the box.
Thus, the plot is positively skewed.
Learn more about Box and whisker plot here:
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What is the slope of the
points (4, -2) and (-4, -4)?
Answers
Answer:
= 1/4
Step-by-step explanation:
We can find the slope given two points by using the following formula
m = (y2-y1)/(x2-x1)
= (-4 - -2)/(-4 -4)
= (-4+2)/(-4-4)
= -2/-8
= 1/4
Answer:
I think the slope is 1/4
Step-by-step explanation:
if you use the slope equation y1-y2/x1-x2, then you get (-2 - -4)/(4 - -4), which is 2/8, which is 1/4
[tex]q^{6}[/tex]÷[tex]q^{5}[/tex]
Answers
Answer:
q
Step-by-step explanation:
q^6 / q^5
Division by exponents is done by subtraction
a^b / a^c = a^(b-c)
q^6 /q^5 = q^(6-5) = q^1 = q
Find and interpret the mean absolute deviation of the data. round your answer to the nearest tenth if necessary.
__________
| 1 | 5 | 2 | 2 |
| 2 | 4 | 4 | 0 |
__________
please let someone know how to answer this!!
Answers
Answer:
21.89
Step-by-step explanation:
add and subtract
in the right triangle shown, m of angle G equals 45 and HI equals 7 how long is GH
Answers
Answer:7 sr 2
Step-by-step explanation:
The length of side GH in an isosceles right triangle where angle G is 45 degrees and side HI is the hypotenuse equal to 7, is 7/√2 or 7√2/2 when rationalized.
You asked about finding the length of side GH in a right triangle where angle G equals 45 degrees, and side HI equals 7. In an isosceles right triangle, the lengths of the two legs are equal. As angle G is 45 degrees, it indicates that triangle GHI is an isosceles right triangle. Using the concept that in such a triangle, the lengths of the legs are equal, since they correspond to the sine and cosine of 45 degrees, which both equal 1/√2.
Given that HI is the hypotenuse and GH is one of the legs, we can use the relationship between the sides: GH = HI * cos(45°) = 7 * 1/√2. Therefore, the length of side GH is 7/√2 or 7√2/2 when rationalized.
PLZ HELP THIS IS HARD I WILL FIVE BRAINLIEST
Answers
Answer:
[tex]2\frac{1}{3}\: ft[/tex]
Step-By-Step Explanation:
[tex]Height\: of \:sail = 1\frac{1}{6}\: ft = \frac{7}{6}\: ft\\Base\: of \:sail = 4\: ft \\Area\: of \:sail =\frac{1}{2} \times base \times height\\=\frac{1}{2} \times \frac{7}{6} \times 4\\= \frac{7}{6} \times 2\\=\frac{7}{3}\\=2\frac{1}{3}\: ft[/tex]
how many real roots does the quadratic function f(x)= -5x^2 have?
a. 0
b. 1
c. 2
d. infinitely many
Answers
Two angles form a linear pair. One angle measures 8 less than three times the other. Find the measures of the angles.
Answers
Answer:
47⁰, 133⁰
Step-by-step explanation:
Angles : x , 3x - 8
Sum = 180
x + 3x - 8 = 180
4x = 188
x = 47
Angles are 47 , 133
PLZ HELP ASAP 15 POINTS FIRST ANSWER GETS BRAINLEST AND 5 STARS
Answers
Answer:
£503.75
Step-by-step explanation:
Can you please find the quotient of 9/18÷ 3/6. I am pretty sure that the answer is 1
Answers
Answer:
It is 1
Step-by-step explanation:
Answer:
lol yeah its 1, you're right.
Step-by-step explanation:
Solve: g^2x+1=g^3x-2
x=?
Answers
Answer:
the answer you will be looking for is g^2x - g^3x = -3
Step-by-step explanation:
as much as I would like to, I'm really not that great at explaining things
Answer:
Solve: 9^2x+1 = 9^3x-2
= 3
Step-by-step explanation:
What is the approximate distance between points P and Q? Round your answer to the nearest hundredth.
A.
4 units
B.
4.12 units
C.
4.89 units
D.
5.1 units
Answers
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Wulaliguld prisms
What is the volume of the rectangular prism?
5 cm
8 cm
1 cm
Answers
Answer:40
Step-by-step explanation:
us 40
The formula a=119e^0.027t models the population of a particular city, in thousands, t years after 1998, when will the population of the city reach 178 thousand
Answers
Answer:
By year 2092
Step-by-step explanation:
In this question, we are asked to calculate the year at which the population of the city will reach 178,000
The equation that models the population of the city is given as;
A = 119e^0.027t
Here, we plug A to be 178,000
178000 = 119e^0.027t
we take the natural logarithm of both sides)
ln 178,000 = ln (119e^0.027t)
12.09 = 0.027t ln 119
12.09/ln 119 = 0.027t
2.53 = 0.027t
t = 2.53/0.027
t = 93.7 which is approximately 94 years
Since t is number of years after 1998, the exact time the population will reach 178,000 will be 1998 + 94 years = 2,092
Answer:
The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.
Step-by-step explanation:
The equation to be solved is:
[tex]178 = 119\cdot e^{0.027\cdot t}[/tex]
Now, the variable is cleared with the help of algebraic handling:
[tex]\frac{178}{119} = e^{0.027\cdot t}[/tex]
[tex]\ln \frac{178}{119} = 0.027\cdot t[/tex]
[tex]t = 37.037\cdot \ln \frac{178}{119}[/tex]
[tex]t \approx 14.913\,yr[/tex]
The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.
It has been decided that 100 people need to be surveyed to decide the publics opinion on a school building project. A student suggests that they survey the first 100 people who enter the school. Do you think that this proposed way of sampling is an unbiased way to perform the survey?
Answers
Answer:
The proposed way of sampling is a biased way to perform the survey.
Step-by-step explanation:
Convenience sampling is a kind of non-probability sampling method that comprises of the sample being taken from that portion of the population that is near to hand. In this type of sampling method, all items doesn’t have an equivalent chance of being selected, which doesn’t comprises of random collection of items.
Convenience sampling is where we take in items which are easy to reach.
Convenience sampling consists of selection bias, i.e.e the bias involved in the sample due to inappropriate selection procedures.
For example, randomly selecting 4 people sitting near him to guesstimate the mean age of the class is a convenience sampling example. or gathering information on customer satisfaction by interviewing 6 randomly selected customers from a local store is an illustration of convenience sampling.
In this case, the sample suggested by the students consists of surveying the first 100 people who enter the school, about the public opinion on a school building project.
This is an example of convenience sample.
So, there is a selection bias present in the sample.
Thus, the proposed way of sampling is a biased way to perform the survey.