a) For a 90% confidence interval: (117.838, 130.056)
b) For a 95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.
To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.
a) For a 90% confidence interval:
Sample mean = 123.947
Sample standard deviation = 11.669
Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]
90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)
b) For a 95% confidence interval:
Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]
95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval:
Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]
99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.
The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.
Kim had 160 cards in a box.She gave 4/10 of the cards to maddy.How many cards did Kim have left in the box
In a recent year 36% of all college students were enrolled part time. If 6.2 million college students were enrolled part time that year what was the total number of college students. Round to the nearest million
To find the total number of college students, we solve a proportion equation using the given 36% for part-time students and 6.2 million part-time students to find a total of approximately 17 million students.
Explanation:This problem can be addressed with a simple proportion equation. We know that 36% (or 0.36 in decimal form) of all enrolled college students equals 6.2 million. So, if we let X be the total number of college students, the equation becomes 0.36X = 6.2 million.
To solve for X, we divide both sides of the equation by 0.36 and hence, X=6.2 million / 0.36. After doing the calculation, we get approximately 17.22 million. Since the question asks us to round to the nearest million, our final answer is approximately 17 million total college students.
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What is the slope of the line that passes through (3, -4) and (-2, 5). A)-5/9 B)-9/5 C)9/5 D)5/9
can someone help me? im not sure if my answers are right
Trig question how do I find m
The distance between city A and city B is 22 miles. The distance between city B and city C is 54 miles. The distance betweeb city A and city C is 51 miles.
What type of trianglr is created by the three cities?
A. An acute triangle, beacuse 22^2+54^2>51^2
B. An acute triangle, beacuse 22^2+51^2>54^2
C. An obtuse triangle, beacuse 22^2+54^2>51^2
D. An obtuse triangle, beacuse 22^2+51^2>54^2,
The answer is B. It is an acute triangle because of 22^2 + 51^2 > 54^2. To identify the type of triangle referred to the problem, we use the Pythagorean Theorem which involves squaring the lengths of all sides of the triangle. If the hypotenuse’s square is less than the two smallest sides' squares added together, than it is an acute triangle. However, if the hypotenuse’s square is larger, then it is an obtuse triangle.
54 is the hypotenuse since it is the longest side.
Following the Pythagorean Theorem, a^2 + b^2 = c^2:
54^2=2916
51^2=2601
22^2=484
It becomes 2601+484 = 2916.
When the two shorter sides are added, the sum is greater than the square of the hypotenuse which is 2916. Thus, the formed triangle is acute.
Answer:
B
Step-by-step explanation:
use the formula a=h/n to find the batting average a of a batter who has h hits in n times at bat.Solve the formula for h. if a batter has a batting average of .290 and has at bat 300 times, how many hits does the batter have?,
The area of a right triangle is 336 square centimeters. The base of the right triangle is 48 centimeters. What is the length of the hypotenuse of the right triangle? Enter your answer in the box.
Answer:
50
Step-by-step explanation:
First we have to find the height. Since we know the area we can use it to find the height. The area of a triangle is A=bh1/2 or half of the base times the height. So if we plug in what we know and solve, we can find the height. 336=48 x h x 1/2. The height is 14. Now we can solve for the hypotenuse using the Pythagorean Theorem. a^2 + b^2 = c^2 plug in what we know... 14^2 + 48^2 = c^2 simplify to get 196+2304= c^2 and further 2500= c^2 so find the square root of 2500. You will get 50.
A ship is 2.8 degree off course .If the ship is traveling at 14.0 miles per hour,how far off course will it be after 2 hours?
When the sum of 7 and three times a positive number is subtracted from the square of the number, 0 results. find the number?
The required number is 10.
Given that,
When the sum of 7 and three times a positive number is subtracted from the square of the number, 0 results. That number is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Let the number be x,
The sum of 7 and three times a positive number is subtracted from the square of the number 0.
x²-x(3 + 7) = 0
x² = x(10)
x = 10
Thus, the required number is 10.
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6 grade course 1 countdown 8 and 7 weeks
How many lines intersect at point O?
4
2
1
3
PLEASE HELP ASSSAAAAPPPP
64,55,46,37,28,19 find the math patter what goes next
A coach bought some shirts and 5 pairs of shorts. each shirt cost $12 and each pair of shorts cost $10. let t represent the number of shirts. write an expression that can be used to find the total cost of the shirts and shorts. answer
At the snack bar, a hot dog costs $1.50 and a slice of pizza costs $2. What percent of the cost of a slice of pizza is a cost of a hot dog? Which equation can be written to represent this scenario?
A. 1.5p=2
B. 1.5=2p
C. 2(1.5)=p
D. 2/1.5=p
How would you determine this answer?
What’s the correct answer
How to solve this???
Perform the indicated operation. (2x + y)(3x^2 + y)
Answer:
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
Step-by-step explanation:
The given expression is [tex](2x+y)(3x^2+y)[/tex].
We expand the parenthesis using the distributive property to obtain;
[tex](2x+y)(3x^2+y)=2x(3x^2+y)+y(3x^2+y)[/tex]
We expand further to get;
[tex](2x+y)(3x^2+y)=6x^3+2xy+3x^2y+y^2)[/tex]
This gives us;
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
What is the measure of angle 1?
Find the Value of X.
3
8
4
6
The equation x2+y2−4x+2y=b describes a circle. Complete the square to find the center of the circle. The center of the circle is ( , ) The radius of the circle is 7 units. What is the value of b in the equation? b=
In a pond, lotus flower multiply its self after every 4 days. One lotus multiplies into two after four days, into 4 after 8 days, into 8 after 16 days and so on. If you see one lotus flower in a pond today, how many flowers will be there in the pond after 32 days.
The mass of Venus is
4.87 x 10^24 kilograms, and the mass of Jupiter is
1,898 x 10^24 kilograms.
The mass of Jupiter is about _____ times the mass of Venus.
Answer:
The mass of Jupiter is about 389.7331 times the mass of Venus.
Step-by-step explanation:
The question is asking for how much the two masses vary from one another. Since the mass of Jupiter is greater than that of Venus, what value is to be multiplied by the mass of Venus that would give the mass of Jupiter?
Thus, to determine this, we divide the mass of Jupiter by the mass of Venus;
= [tex]\frac{1898*10^{24} }{4.87*10^{24} }[/tex]
= [tex]\frac{1898}{4.87}[/tex]
= 389.7331
Therefore, the mass of Jupiter is about 389.7331 times the mass of Venus.
What is 4.738rounded to the nearest thousandth? (Points : 1) 4.73 4.74 4.738 4.739
4.738 rounded to the nearest thousandth remains 4.738, as it is already at the required decimal precision.
To round to the nearest thousandth, you look at the digit in the thousandth place, which in this case is an 8. You do not need to alter the number since it is already at the thousandth decimal place. Therefore, 4.738 rounded to the nearest thousandth is simply 4.738.
⭐️ Anyone know how to work this?...
What happens to the maximum point of f(x) = -2x2 + 3x + 1, when the function is changed to f(x) = -2x2 + 9x + 1?
A) it shifts up and left
B) it shifts up and right
C) it shifts down and left
D) it shifts down and right
Answer: B
Step-by-step explanation: I did the usa test prep
Divide by splitting up the numerator. 21x^3y^4-7x^2y^3+14x^2y^2-xy over 7x^2y^2
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
Instead of focusing on the absence of mental illness as an indication of mental health, Abraham Maslow and CarlRogers would focus more on____________ (1 point),