One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples and calculate the given summary statistics of the boys and the girls for comparable math classes. In calculus, 15 boys had a mean percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean average of 81.2 with standard deviation of 6.7. What assumptions need to be made in order to determine the 90% confidence interval for the difference in the mean percentage scores for the boys in calculus and the girls in calculus? Supposing the assumption is true, calculate the interval. 1. Test and Assumptions A. Since the population is not specified as Normally Distributed, the problem cannot be solved. B. We can assume that the population is normally distributed and solve using a Two Sample z- test for means. C. We can assume that the population is normally distributed and solve using a Two Sample t- test for means. 2. Confidence Interval A. [-0.633, 2.833] B. [-3.237, 5.437] C. [-3.203, 5.404] D. [0.789, 1.411] E. [-7.373, 11.573] 3. In interval estimation, the t distribution is applicable only when A. the population has a mean of less than 30. B. the sample standard deviation (s) is given instead of the population standard deviation (o). C. the variance of the population is known. D. the standard deviation of the population is known. E. we will always use the t distribution.
Previous question
Answers
The correct answer to question 1 is C. The variances of the two populations are equal.
The correct answer to question 2 is C.
For question 3, the correct answer is B.
The correct answer to question 1 is C. We can assume that the population is normally distributed and solve using a Two Sample t-test for means.
To calculate the confidence interval, we need to assume that the difference in mean percentage scores for the boys and the girls follows a t-distribution. This assumption is valid as long as the following conditions are met:
Both samples are independent simple random samples.
The populations from which the samples are drawn are normally distributed or have a sufficiently large sample size (Central Limit Theorem).
The variances of the two populations are equal.
Since we are not given any information about the population distributions or sample sizes, we can assume that they meet these conditions.
Using the Two Sample t-test for means, we calculate the point estimate of the difference in means as:
point estimate = x1 - x2 = 82.3 - 81.2 = 1.1
where x1 and x2 are the sample means for the boys and girls, respectively.
Next, we calculate the standard error of the difference in means as:
SE = sqrt[(s1^2/n1) + (s2^2/n2)] = sqrt[(5.6^2/15) + (6.7^2/12)] = 2.117
where s1 and s2 are the sample standard deviations for the boys and girls, respectively, and n1 and n2 are the sample sizes.
Using a 90% confidence level and degrees of freedom (df) = n1 + n2 - 2 = 25, we find the t-value from a t-table or calculator to be 1.711.
Finally, we can calculate the 90% confidence interval as:
CI = (point estimate) ± (t-value)(SE)
= 1.1 ± (1.711)(2.117)
= [ -3.203, 5.404]
Therefore, the correct answer to question 2 is C. [-3.203, 5.404].
For question 3, the correct answer is B. The t distribution is applicable only when the sample standard deviation (s) is given instead of the population standard deviation (σ). When the population standard deviation is known, we use the z-distribution for interval estimation.
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Related Questions
if the measure of an interior angle of a regular polygon is 120 degrees, how many sides does the polygon have?
Answers
Answer:
6 sides
Step-by-step explanation:
since the measure of an interior angle of a polygon can be found with the formula 180(n-2) / n where n is the number of sides we can substitute 120 to the answer and cross multiply to find that
120n = 180(n-2)
120n = 180n-360
360 = 60n
n = 6
What is the solution of 2 - ?
Type the solution as a mixed number. Use the on-screen keyboard to type your answer in the box below
Answers
Whenever you have a 90 degree rotation you need to switch your x and y values.
True
False
Answers
Answer:
true
Step-by-step explanation:
hope its help bro
ok
8 ÷ 28 *has to be in decimal form*
Answers
Answer: 0.28571428571
Step-by-step explanation: 8 dived by 28
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 what is the sample mean?
Answers
The sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.
Given: The sample of seven infants was selected randomly and the weights are: {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6} (in pounds)
What is a sample?
A sample can be defined as a part of something big or a whole. It can be some of the elements from a given set of elements.
For example: Let us consider the set of natural numbers. The set of natural numbers has an infinite number of elements in it. We choose some numbers from the set, say {2, 7, 9, 10, 99, 200, 234}. These chosen numbers are known as samples from the set of natural numbers.
What is the sample mean?
The sample mean is the average value of the samples or it is the mean of all the elements which exist in the given sample.
The sample mean is denoted by x⁻ which is pronounced as x bar.
The formula to calculate sample mean (x⁻) is:
Sample Mean (x⁻) = Summation of all the elements in the sample / Total number of elements in the sample.
x⁻ = ∑xₙ / n
where,
∑xₙ = Summation of all the elements in the sample
n = Total number of elements in the sample
x⁻ = Sample mean
Now let's solve the given question:
The given sample is {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6}
The summation of the elements in the sample is:
∑xₙ = 9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6
∑xₙ = 52.9
The total number of elements in the sample is:
n = 7
Therefore, the sample mean (x⁻) is:
x⁻ = ∑xₙ / n
x⁻ = 52.9 / 7
x⁻ = 7.5571 ≈ 7.6
Hence the sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.
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Disclaimer: The question is incomplete. The complete question is mentioned below:
Question: A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?
In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $44 and standard deviation of $10. Estimate how much a typical parent would spend on their child's birthday gift (use a 99% confidence level). Give your answers to one decimal place. Provide the point estimate and margin or err
Answers
Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.
To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.
To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.
Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.
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A political scientist received a grant to fund a research project on voting trends. The budget includes $3,200 for conducting door-to-door interviews on the day before an election. Undergraduate students, graduate students, and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews for$100. Each graduate student will conduct 25 interviews for $150. Each faculty member will conduct 30 interviews for$200. Due to limited transportation facilities, no more than 20 interviewers can be hired. How many undergraduate students, graduate students, and faculty members should be hired in order to maximize the number of interviews? What is the maximum number of interviews?
Answers
To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.
Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function
N = 18x + 25y + 30z.
The total cost of hiring interviewers is given by the function
C = 100x + 150y + 200z.
The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.
The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.
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PLEASE HELP!!!!!! FAST!!!!!!!!
An Olympic gymnast scored a 14.6 on her vault out of a possible 16.0. What was her percent error?
Answers
Answer:
%8.75 error
Step-by-step explanation:
14.6/n = 16/100
16n = 1460
n = 91.25
100-91.25 = 8.75
Answer:
Percentage wise, her score is a 91%. So, her error would be only 9%
Step-by-step explanation:
14.6/16=0.91
(the actual answer is 0.9125, I just rounded to the 2nd decimal place)
Find the best buy for the item. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to the nearest thousandth as needed.) OA. The best buy for granulated sugar is the 10lb size and its unit price is $ B. The best buy for granulated sugar is the 4lb size and its unit price is $ GRANULATED SUGAR Size Price 4 lb 10 lb $2.93 $8.45
Answers
The best buy for granulated sugar is the 4lb option since it is lesser.
To find the best buy for the item , we calculate the cost per pound of the item :
Cost of item4lb = $2.93
10lb = $8.45
Cost per lb for 4lb :
2.93/4 = $0.7325 per lb
Cost per lb for 10lb :
8.45/10 = $0.845 per lb
Since the cost per lb for 4lb granulated sugar is lesser, then it is the best buy.
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aaliyah compares the heights of two plants to see which plant grows more per day. The table shows the height of Plant 1, in centimeters, over 5 days. The graph shows the height of Plant 2, in centimeters, over 10 days. aaliyah says that since Plant 1 grows 4cm per day and Plant 2 grows 6cm per day, plant 2 grows more per day. Do you agree with aaliyah? Explain your response.
A. I agree that plant 2 grows more per day than plant 1, but I disagree with aaliyahs's reasoning.
B.
I think that plant 1 grows more per day than plant 2, but I agree with aaliyah's reasoning.
C.
I think that plant 1 grows more per day than plant 2, and I disagree with aaliyahs's reasoning.
D.
I agree that plant 2 grows more per day than plant 1, and I agree with aaliyah's reasoning.
Answers
The table that shows the growth rate of Plant 1 which is 4 cm/week, and the graph that gives the growth rate of Plant 2 as 2 cm/week gives the correct option as C;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
What is a proportional relationship?A proportional relationship between two variables is one in which one variable is a multiple of the other.
The possible table in the question is presented as follows;
Plant 1
Week; 2, 3, 4, 5Height; 8, 12, 16, 20The values on the graph are;
Plant 2
Week; 2, 4, 6, 8, 10Height; 4, 8, 12, 16, 20The rate, r1, of growth of Plant 1 is therefore;
r1 = 8 cm/(2 weeks) = 4 cm/week
The rate, of growth, r2, of plant 2 is found as follows;
r2 = 4 cm/(2 weeks) = 2 cm/week
Given that Plant 1 grows faster at 4 cm/week, than Plant 2, that grows at 2 cm/week, the correct statement is since Plant 1 grows 4 cm/week and Plant 2 grows 2 cm/week, Plant 1 grows more per day.
The correct option is therefore;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
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PLEASE HELP ASAP IM FREAKING OUT
Answers
Answer:
30 cm
Step-by-step explanation:
Make sure all units are the same!
P = Perimeter
A = Area
Formula used for similar figures:
\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)
\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)
Applying eq(ii):
∴\(\frac{25}{P_{2}} = \frac{10}{12}\)
Cross-multiplication is applied:
\((25)(12) = 10P_{2}\)
\(300 = 10P_{2}\)
\(P_{2}\) has to be isolated and made the subject of the equation:
\(P_{2} = \frac{300}{10}\)
∴Perimeter of second figure = 30 cm
Choose the system of equations which matches the following graph.
A. 3x-6y=12
9x-18y=36
B. 3x+6y=12
9x+18y=36
Answers
The system of equations that matches the given graph is:
A. 3x - 6y = 12
9x - 18y = 36
To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.
Looking at the options provided:
A. 3x - 6y = 12
9x - 18y = 36
B. 3x + 6y = 12
9x + 18y = 36
Let's analyze the equations in each option:
For option A:
The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.
The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.
In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.
For option B:
The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.
The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.
In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.
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Which is greater, the circumference of a circle with radius 3 ft, or the distance around a semicircle with diameter 16 ft? by how much?.
Answers
The circumference of a circle with a radius of 3 ft is greater than the distance around a semicircle with a diameter of 16 ft by approximately 2.84 ft.
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius. For the given circle with a radius of 3 ft, the circumference would be C = 2π(3) = 6π ft.
The distance around a semicircle is calculated by finding half the circumference of the corresponding full circle. In this case, the diameter of the semicircle is 16 ft, which means the corresponding full circle has a radius of 8 ft. The circumference of the full circle is C = 2π(8) = 16π ft. Therefore, the distance around the semicircle is half of that, which is 8π ft.
Comparing the two values, 6π ft is greater than 8π ft by approximately 2.84 ft. Hence, the circumference of the circle with radius 3 ft is greater than the distance around the semicircle with a diameter of 16 ft by approximately 2.84 ft.
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A cone has a volume of 100x cubic centimeters and a height of 12 centimeters. What is the radius of the base of the
cone in centimeters?
A. 10 cm
B. 5 cm
C. 25 cm
D. Not here
Answers
Please help! I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
Answers
1/6 and you got the comment why
Answer:
1/6
Step-by-step explanation:
Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!
The length of a rectangle is two feet greater than its width. If the area of the rectangle is 24 square feet, what is its length?
Answers
The length of the rectangle is 6 ft
What is a Rectangle?The rectangle is a four sided polygon or quadrilateral with two pairs of opposite sides that are congruent.
How to Find the Area of a Rectangle?Area of a rectangle = length × width of the rectangle.
Let the width of the rectangle be represented as x. Therefore, we will have the following:
Width of rectangle = x
Length of the rectangle = (x + 2) ft
Area of the rectangle = 24 square feet
Thus, we would create the following equation:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
Factorize the equation
(x - 4)(x + 6) = 0
x = 4, x = -6
The width = x = 4 ft
Length of the rectangle = (x + 2) ft
Plug in the value of x
Length of the rectangle = (4 + 2) ft
Length of the rectangle = 6 ft
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13. Yao has 8 hours to finish reading a 300-page book. He has already read 120 pages. Yao read 50
pages the first hour. He does not read the next two hours. What is the least number of pages Yao
must read per hour to finish reading the book?
A 25 pages per hour
B 26 pages per hour
C 27 pages per hour
D 36 pages per hour
Answers
The least number of pages Yao must read per hour to finish reading the book is 26 pages per hour. which is the correct answer would be an option (B)
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Calculate the total number of hours Yao has left to finish reading the book by subtracting the number of hours he has already spent reading from the total number of hours he has available:
8 hours - 1 hour = 7 hours.
The number of pages Yao has left to read : 300 pages - 120 pages = 180 pages.
The number of pages Yao must read: 180 pages / 7 hours = 25.7 pages/hour.
Round up the number of pages Yao must read per hour to the nearest whole number. The least number of pages Yao must read per hour is 26 pages/hour.
Therefore, the minimum number of pages Yao must read each hour to finish the book is 26 pages per hour.
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what is the slope of the line that contains the points (-2,6) and (2,-2)
Answers
Answer:
\(-\frac{8}{4}\)
Step-by-step explanation:
To find slope from 2 points: \(\frac{y2-y1}{x2-x1}\)
\(\frac{-2-6}{2-(-2)} =-\frac{8}{4}\)
Express in its simple form: (4a2b)3?
(note: 2 and 3 are suppose to be small numbers)
Answers
Answer:
\( 64{a}^{6} {b}^{3} \)
Step-by-step explanation:
\((4 {a}^{2} b) ^{3} \\ \\ = {(4)}^{3}.( {a}^{2})^{3} . {(b)}^{3} \\ \\ = 64. {a}^{2 \times 3}. {b}^{3} \\ \\ = 64{a}^{6} {b}^{3} \)
what is the answer?
-2x + 5y = -1
3x + 2y =11
Answers
Answer: -44
Step-by-step explanation:
A square and a rectangle have equal
pieremeter the length of a ste of the
square is 4x-1 the length of the
rectangle is 2x + 2 and the width is
2x Write and solve an equation to find x
Answers
The value of x is 1 unit
• In Mathematics, rectangle and square are both four sided polygon, having all the internal angles equal to 90.The opposite sides of the rectangle are equal in length whereas in square all the sides are same which makes rectangle different from square.
• Area of rectangle is the product of length and breadth of rectangle. Perimeter of rectangle is twice the sum of its length and breadth. Area of square is side * side and perimeter of square is 4* side.
• Area of rectangle = l*b
Perimeter of rectangle = 2(l+b)
• Area of square = side * side
Perimeter of square = 4 * side
We are given that perimeter of square and rectangle is same and the side of square is 4x-1 and length of rectangle is 2x+2 and width of rectangle is 2x.
Perimeter of Square = Perimeter of rectangle
4 * (4x-1) = 2(4x+2)
16x -4 = 8x + 4
8x = 8
x = 1
The value of x is 1
Side of square = 4 – 1 = 3
Length of rectangle = 4
Breadth of rectangle = 2
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top brainalist question
Answers
Answer: it's 9 too lol so A.
Step-by-step explanation: they are visually equal and if they are the same length im pretty sure they both would be 9
A bag contains 11 red M&Ms, 8 green M&Ms, and 6 blue M&Ms
What ratio of the blue M&Ms to green M&Ms?
__________________________________
What is the ratio of blue M&Ms to the total number of M&Ms?
_______________________________________________
Answers
Answers:
Blue to green - 3:4
Blue to total - 6:25
CONGRATULATIONS!!!
You've been selected to be today's troll victim!
How about you rizz the green M&M?
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can someone help with this
Answers
Answer:
df= 6g-10
Step-by-step explanation:
\(\frac{df+10}{6}\)= g
df+10= 6g
df= 6g-10
What is the value of m in the equation 1/2m - 3/4n when n = 8?
Answers
Answer:
m = 12Step-by-step explanation:
What is the value of m in the equation 1/2m - 3/4n when n = 8?
1/2m - 3/4*8 =
1/2m = 6
m = 12
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SOLVE THIS 4/Z+4/3Z=Z/3
Answers
Answer:
z= 0.0000 - 2.0000 i
z= 0.0000 + 2.0000 i
Step-by-step explanation: i used an algebraic calculator to find the two answers
Answer:
4/z + 4/3z - z/3= 0
12+4-z²/3z=0
12+4-z²=0
Z²=16
SO Z could be -4 or 4
I hope it helps❤
please give me brainliest
Will give brainliest, thanks, and 5 stars! LOTS OF POINTS! 50 POINTS!
I need help with these questions! Please help me. The choices are all true/false.
Please help me!!!!!!
Please provide in depth explanation too!!
Answers
Answer in order:
False
True
False
False
False
False
False
True
True
Step-by-step explanation:
All of the solutions to the equation\(3x^2 - 12 = 0\)are x = 12 and x = -12
Solve:
Common factor - \(3(x^2-4)=0\)
Divide both sides
\(x^2-4=0\)
Use the quadratic formula
\(x=\sqrt{4,x}=\sqrt{-4\)
x = 2, x = -2
Thus, This is false..
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There are two unique solutions to the equations (x-3)^2 = 16
one variable in matrix = one possible value.
Therefore, x = 7, x = -1
Hence this is True
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The solutions for the equation 2(x-3)^2-18 = 0 are x = 6 and x = 0
\(2x^3-18x^2+54x-72=0\)
\(x=5.080084\)
Hence this is false
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The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7
Add both sides by 8
2(x-5)^2-8+8=0+8
2(x-5)^2=8
(x-5)^2=4
x = 7, x = 3
Hence, this is false
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The solutions for the equation (x + 3)^2-25 = -8 are x = 2 and x = -8
\((x+3)^2=17\)
\(x=\sqrt{17-3,}=-\sqrt{17}-3\)
Hence this is false.
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The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4
\((2x-1)^2=9\)
x=2, x = -1
Hence this is false.
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The only solution for equation (2x-1)^2-49=0 is x = 4
\((2x-1)^2=49\)
x = 4, x = -3
Hence, this is false
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The solutions for the equation 3(x+2)^2 - 3 = 0 are x = -3 and x = -1
\(3(x+2)^2=3\)
\((x+2)^2=1\)
x = -1, x = -3
Hence, this is true
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The solutions for the equation 5x^2 - 180 = 0 are x = 6 and x = -6
Add 180 to both sides
\(5x^2-180+180=0+180\)
\(5x^2 = 180\)
\(x^2 = 36\)
\(x=\sqrt{36},x=-\sqrt{36}\)
x = 6, x = -6
Hence, this is true.
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[RevyBreeze]
Answer to all 3? Please put the answer
Answers
A. The slope is 55, representing the trip fee.
B. The slope is 70, representing the old cost.
C. The slope is 15, representing the cost per hour.
D. The slope is 1/15, representing the cost per hour.
Answers
Answer:
c. the slope is 70, representing the old cost
Please help me out. I'm stuck on this question. Will mark brainliest.
Answers
Answer:
is a linear m=4 y=3
Step-by-step explanation: