A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.69 hours, with a standard deviation of 2.42 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.32 hours, with a standard deviation of 1.83 hours.
Construct and interpret a 95% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).
Answers
Answer:
95% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).
(0.4144 , 2.3256)
Step-by-step explanation:
Given sample size 'n' =n₁ = n₂ = 40
The mean of the first sample (x₁⁻) = 5.69 hours
The standard deviation of the first sample (S₁)= 2.42 hours
The mean of the second sample( x₂⁻) = 4.32 hours
The standard deviation of the second sample (S₂)= 1.83 hours
95% of confidence intervals for (μ₁ - μ₂)are determined by
\((X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))\)
where
The standard error of the difference between two means
\(se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{S^{2} _{1} }{n_{1} }+\frac{S^{2} _{2} }{n_{2} } }\)
\(se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{(2.42)^2 }{40 }+\frac{(1.83)^2 }{40 } }\)
\(se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{0.2301325} = 0.47972\)
Degrees of freedom γ = n₁ +n₂ -2 = 40+40 -2 =78
\(t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025}\)
t₀.₀₂₅ = 1.992
95% of confidence intervals for (μ₁ - μ₂)are determined by
\((X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))\)
(5.69 -4.32)- 1.992(0.47972)), (5.69-4.32)+1.992(0.47972))
(1.37 -0.9556 , 1.37+0.9556)
(0.4144 , 2.3256)
Conclusion:-
95% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).
(0.4144 , 2.3256)
Following are the calculation to the confidence interval:
Given:
\(\bar{x_1}= 5.69\\\\\bar{x_2}= 4.32\\\\s_1=2.42\\\\s_2=1.83\\\\n_1=40\\\\n_2=40\\\\\)
To find:
confidence interval=?
Solution:
\(\to a=0.1\\\\ \to Z(0.05)=1.645\) (from standard normal table)
Calculating the confidence interval when its value is \(95\%\):
\(\to (\bar{x_1}-\bar{x_2}) \pm Z \times \sqrt{(\frac{s^2_{1}}{n_1}+ \frac{s^2_{2}}{n_2})}\)
\(\to (5.69-4.32)\pm 1.645 \times \sqrt{(\frac{2.42^2}{40}+\frac{1.83^2}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564}{40}+\frac{3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564+3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{9.2053}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{0.2301325}\\\\\to (1.37)\pm 1.645 \times 0.4797212 \\\\\to (1.37)\pm 0.789\\\\\to (2.159, 0.581 )\)
Therefore, the final answer is "(2.159 and 0.581)".
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Related Questions
an air plane is travaling at 400 miles per hour. which equation can be used to find the total distance the plane will travel in h hours?
Answers
Answer:
I think 400+24=424
Step-by-step explanation: i think its that equation because there are 24 hours in a day so if you put that with 400 you'll get 424
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Solve for x by simplifying both sides of the equation, then isolating the variable.
x=−2
hope this is what your looking for
Answer:
x = -2
Step-by-step explanation:
\(-4+x=\frac{3}{4}x-\frac{9}{2}\)
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\(-4+x+4=\frac{3}{4}x-\frac{9}{2}+4\)
\(Simplify\)
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~lenvy~
Which is NOT a line of symmetry?
1
2
3
4
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Gravity acceleration at the Earth surface is 9.81 m/s². What is the acceleration in inches/s² (rounded to the nearest tenth) ?
Answers
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.
1 meter is equal to 39.37 inches.
To convert the units, we can set up the following conversion factor:
1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²
Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:
Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²
Acceleration in in/s² ≈ 15222.7568 in/s²
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
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What are the intercepts of the graph of
the equation 4y - x = 8
Answers
Answer:
x intercept: (-8,0)
y intercept: (0,2)
a) Work out the percentage population increase from 2001 to 2011.
Give your answer to 1 decimal place.
Answers
The percentage population increase from 2001 to 2011 is 50%.
To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.
The formula to calculate the percentage increase is:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
Plugging in the values:
Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%
Therefore, the percentage population increase from 2001 to 2011 is 50%.
Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.
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look at pic 10 pts will mark brainilest
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Answer:
D
Step-by-step explanation:
Help meeeeeeeeeeeeeeee
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Answer:
75
Step-by-step explanation:
f(4) means to use 4 in place of x.
f(x) = 3(5)^(x-2)
fill in 4 for
f(4) = 3(5)^(4-2)
do the 4-2 subtraction first
f(4) = 3(5)^2
do the 5 to the 2nd power next.
f(4) = 3(25)
last, multiply.
f(4) = 75
This is just following the typical order of operations.
Please help me i need the answer if i knew it i will complete all of them by my self (: .
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10 x 10 = 100
The right answer is 100 units^2
please see the attached picture for full solution
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Good luck on your assignment,
Write and solve an inequality to find the possible values of x.
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The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
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3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
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3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
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Shown below is a wooden six-sided (hexagon) frame. Which of
the following best approximates the slopes of the six line
segments?
O The slopes are approximately -1.4, 0, and 1.4.
O The slopes are approximately -1.7, 0, and 1.7.
O The slopes are approximately -1.8, 1, and 1.4.
O The slopes are approximately -1.7,0, and 1.4
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The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.
How to find the slope between two coordinates?The formula to find the slope between two coordinates is expressed as:
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of each line above the x-axis are:
Slope 1 = (5 - 0)/(5 - 8)
Slope 1 = -1.7
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Slope 2 = 0
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Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answers
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
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Answers
Answer:
72
Step-by-step explanation:
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The attendance for the last
years at a county fair is shown in the table.
This year, the first
of people attending the fair will receive a raffle ticket. Of the people who receive raffle tickets,
will receive a small prize.
• Based on the data in the table, determine a reasonable estimate of the number of people who will attend this year's fair. Explain how you found your estimate.
• Use your estimate to find the approximate number of people who will receive a small prize at this year's fair.
• Show your work or provide an explanation of how you found the approximate number of people who will receive a small prize at this year's fair.
Enter your answers and your work or explanations in the box provided.
Answers
The approximate number of people who will receive a small prize at this year's fair is 12,000.
What is number?
A number is a mathematical concept used to represent a quantity or value. It can be represented by numerals, symbols, or words.
To estimate the number of people who will attend this year's fair, we can calculate the average attendance of the last 5 years:
Average attendance = (270,000 + 280,000 + 300,000 + 320,000 + 330,000) / 5
= 300,000
Therefore, a reasonable estimate of the number of people who will attend this year's fair is 300,000.
To find the approximate number of people who will receive a small prize at this year's fair, we need to multiply the number of people who receive raffle tickets by the proportion of those who will receive a small prize:
Number of people who will receive a small prize = 60,000 x 0.2
= 12,000
Therefore, the approximate number of people who will receive a small prize at this year's fair is 12,000.
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Answers
Answer:
\(q=45\)
Step-by-step explanation:
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Answers
Answer:
A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)
B=(-4x3y2z)( x2y3)3xy
Step-by-step explanation:
ok :)
Lauren visits the park every 4 days and goes to the library every 10 days. If Lauren does both of these today, how many days will pass before Lauren gets to do them both on the same day again?
A.20 days
B. 14 days
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Answers
Answer:
20 days
Step-by-step explanation:
Bill can mow the lawn in 2 hours, his younger brother Tom can mow it in 3 hours. If both brothers mow the lawn together, how long would it take?
Answers
Answer:
1 job / 2 hours + 1 job / 3 hours = 1 job / time it takes for both when working together
time it takes for both when working together = 1.2 hours
Step-by-step explanation:
Are there answer choices? I would say about an hour 15 min
PLEASE HELP I WILL MARK
BRIANLIST Caitlin has $24 to spend. She spent $8.50, including tax, to buy a book. She needs to save $6.25, but she wants to buy some candy. If each piece of candy costs $0.25 including tax, what inequality would show the maximum number of pieces Caitlin can buy? Let x represent the cost of one piece of candy.
Solve your inequality by showing your work and steps.
Answers
Answer: 37 pieces of candy
Step-by-step explanation:
24-8.50 is 15.50 she wants to save 6.25, so, 15.50-6.25 is 9.25. 9.25 divided by the cost of each candy (0.25) is 37
A wall is 3 yards and 10 inches
long. What is the length of the
wall in inches?
Answers
Answer:
118 inches
Step-by-step explanation:
This is a conversion problem, so first we will need to change the yards to inches
3y=(3ft/1y)=9ft
9ft=(12in/1ft)=108in
add the 108 inches to the 10 inches
118 inches length
3^4 x 10^6
What is the answer ??
Answers
Given AC and BD bisect each other at O prove AC is congruent to c
Answers
The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .
Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.
We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.
Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)
Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.
Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD
Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC
Therefore, AC is congruent to c .
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hiw many 2/3 are in 2 1/3
Answers
Answer:
3.5
Step-by-step explanation:
2 1/3 is equal to 7/3 and 2 goes into 7, 3.5 times.
Answer:
there are 3 2/3 in 2 1/3 with 1/3 left over
Step-by-step explanation:
Hope this helps.
Have a nice day :)
Can you give me brainliest plz :)
Enter your answers in the boxes to correctly complete the question.
Answers
Answer:
296
Step-by-step explanation:
Refer to attachment.
Hope it helps.
Answer/Step-by-step explanation:
37 x 8 = (30 + 7) x 8
= 30 x 8 + 7 x 8
= 240 + 56
= 296
[RevyBreeze]
a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
Answers
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A
How to find the expressionThe vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.
In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:
\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is \((x - 4)^2 - 20.\)
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Pleeeeeeeeeseee help meee!!!
Answers
Answer:
y= 44
Step-by-step explanation:
you know 4y so just
×11 and you get 44
What are the factors of
f(x) = x ^2 + 2x - 8
Answers
Answer:
(x - 2)(x + 4)
Step-by-step explanation:
What are the factors of: f(x) = \(x ^2 + 2x - 8\)
\(x ^2 + 2x - 8\)
a = 1
b = 2
c = -8
Find two numbers that add to 2 and multiply to -8:
-2 + 4 = 2
-2(4) = -8
factors are:
(x - 2)(x + 4)
6 times the sum of a number and 5 is equal to 3
Answers
Let be "y" the unknown number.
In order to solve this exercise you need to remember the following:
1. The word "times" indicates multiplication.
2. The Sum is defined as the result of an Addition.
3. The word "equal" indicates that you must use the following sign. This is:
\(=\)Then, "the sum of a number and 5" can be expressed as following:
\(y+5\)Therefore, you can determine that "6 times the sum of a number and 5 is equal to 3" can be represented with the expression shown below:
\(6(y+5)=3\)The answer is:
\(6(y+5)=3\)Answer:
See below
Step-by-step explanation:
x = number
x+5 is " sum of a number + 5 "
6 (x+5) is " six times the sum of a number and 5"
6 ( x+5) = 3
x+5 = 1/2
x = - 4.5
Write the equation of the line fully simplified slope-intercept form
Answers
Answer:
y = 4/3x - 3
Step-by-step explanation:
y = mx + b
m is the slope and b is the y - intercept
The slope is rise/run, count how much it rises, or goes down, and how much it goes to the right. So there are points highlighted for us already, pick 2 points and count the units between them for rise it's 4, for run it's 3. So the slope is 4/3
b is the y-intercept, it's where the line goes through the y-axis, in this case it's -3
So plug the numbers in and it's y = 4/3x - 3
Converting with Measurem
Mona's new bicycle weighs 18 pounds.
Weight Equivalent
1 kg - 2.2 pounds
Using the table above, about how many kg does her bike weigh?
8
16
41
84
Answers
Answer:
70.2
Step-by-step explanation: