Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 109.7 118.9 134.8 109.6 127.3 115.6 130.4 130.2 111.7 105.5 Assume that bushels per acre. a) Find the 90% confidence interval for the mean yield for this variety of corn. b) Find the 95% confidence interval. c) Find the 99% confidence interval. d) How do the margins of error in (a), (b), and (c) change as the confidence level increases?

Answers

Answer 1
There is a relationship between confidence interval and standard deviation:
[tex]\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}[/tex]
Where [tex]\overline{x}[/tex] is the mean, [tex]\sigma[/tex] is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first: 
[tex]\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}[/tex]
When we do all the calculations we find that:
[tex]\overline{x}=123.8\\
\sigma=11.84[/tex]
Now we can find confidence intervals:
[tex]($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\[/tex]
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing
Answer 2

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.


Related Questions

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

Answers

[tex]\text {Total cards = 160}[/tex]

[tex]\text {Cards gave to Maddy = } \dfrac{4}{10} \times 160 = 64 [/tex]

[tex]\text {Cards left = } 160 - 64 = 96 [/tex]

------------------------------------
Answer: Cards left = 96 
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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

Answers

If 36% equals 6,200,000, then
1% equals 6,200,000/36, and
100% equals 6,200,000/36*100 = 16,315,789

Hence, there were about 16,000,000 (sixteen million) students.

Final answer:

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

Answers

m = (y2 - y1) / (x2 - x1)
Call (3,-4) one point
Call (-2,5) the second point.

m = (5- -4) / (-2 - 3)
m = 9/-5 = - 9 / 5

B<<<< answer

can someone help me? im not sure if my answers are right

Answers

Your answers are both correct

Trig question how do I find m

Answers

Angle E = the arc tangent (4 / 8)
Angle E = 26.565 Degrees


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,

Answers

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?,

Answers

Part 1: Solving for h:
The formula given is:
a = [tex] \frac{h}{n} [/tex]

To solve for h, we need to isolate the h on one side of the equation.
This can be done as follows:
a = [tex] \frac{h}{n} [/tex]

Multiply both sides by n:
an = [tex] \frac{h}{n} [/tex] * n
h = a*n

Part 2: getting the value of h:
We are given that:
The average (a) = 0.290
n = 300 times

Substitute with the givens in the equation we got in part (1) to get the value of h as follows:
h = a * n
h = 0.290 * 300
h = 87 hits

Hope this helps :)

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.

Answers

[tex] Area of Triangle = \frac{1}{2} bh [/tex]
[tex]336 = \frac{1}{2} 48h [/tex]
[tex]336 = 24h [/tex]
[tex] \frac{336}{24} = h [/tex]
[tex] 14 = h [/tex]
Then using Pythagorean theorem 
[tex] b^{2} + h^{2} = Hyp^{2} --> 48^{2} + 14^{2} = hyp^{2} [/tex]
[tex] hyp = \sqrt{2304 + 196} = 50 cm [/tex]

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?

Answers

During the two hours, the ship will have traveled 28 miles off course. The sin of the off course angle, 2.8, multiplied by 28 will give the answer: 1.37 miles.

When the sum of 7 and three times a positive number is subtracted from the square of the​ number, 0 results. find the number?

Answers

The answer is...
x^2 - (7 + 2x) = 0
x^2 - 2x - 7 = 0

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.

What is arithmetic?

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

Answers

Part A - 80 /5 = n
Part B - 16
2. Box number 1 and 2
3. I am not sure.

How many lines intersect at point O?


4


2


1


3

Answers

2 lines intersect at point O
2 lines can intersect at point O

PLEASE HELP ASSSAAAAPPPP

Answers

All you need to do is plug 2 in for x
[tex]f(x) = 5^x \\ f(2) = 5^2 = 25[/tex]
The answer is 25 dsfsdffasfa

64,55,46,37,28,19 find the math patter what goes next

Answers

Hi there!

From one number to the next, the number decreases by 9.
10 goes next, since 19 - 9 = 10

Hope This Helps!

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

Answers

t=number of shirts
T=total cost (shirts + shorts)

12t+5(10)=T
12t+50=T

Answer: 12t  + 50=T
t=number of shirts
T=total cost. 

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?

Answers

That percent is 133
There are several answers for this
A and D
its 2/1.5=p because u would need to know how much more the pizza is than the hot dog and that answer would be .50 

What’s the correct answer

Answers

140 because each week it goes up by 14 so 14 times 10 weeks is 140
Equation:
[tex]total = 11 + 3x[/tex]
For 10 weeks:
[tex]14 + 17 + 20 + 23 + 26 + 29 + 32 + 35 + 38 + 41 = 275[/tex]
Total:
Andrew will have earned $275 after 10 weeks

How to solve this???

Answers

11. Opposite angles of a cyclic quadrilateral are supplementary. You have two angles in the ratio of 2:4 that add to 180°. The larger angle will be 4/(2+4) = 4/6 of 180°, so is 120°.

Perform the indicated operation. (2x + y)(3x^2 + y)

Answers

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?

Answers

The sum of the two remote angles = the non connecting exterior angle. In plain simple English it means that
80o + 60o = <1
140 = <1 <<<<<<< ==== answer.

Find the Value of X.
3
8
4
6

Answers

X = 4. The difference between the small and large sides on the left side is 1. (6-5=1).
You should take that difference and compare If to the size of the wheel left side, 6.

The difference should be equivalent for the other sides as well.
1:6 2:?

1:1 =2:12

2x+ 4 = 12
2x = 8
X=4

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=

Answers

look to the coefficients on the middle terms (-4x and 2y)

divide each coefficient by 2 and square to determine what to add.

(-4/2)^2 = 4 needs to be added to complete the square for x.

(2/2)^2 = 1 needs to be added to complete the square for y.

add to both sides of the equal sign to keep the equation balanced.

x^2 - 4x + 4 + y^2 + 2y + 1 = b + 4 + 1
factor
(x - 2)^2 + (y + 1)^2 = b + 5

The general equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
with center (h,k) and radius r

compare this to the equation. you see that the center is: (2, -1)

we can write
r^2 = b + 5
given that r = 7
49 = b + 5
49 - 5 = b
44 = 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.

Answers

The answer is 32 flowers. You can create the following table to see the pattern more clearly:

# of flower: 1, 2, 4, 8, 16
# of days: 4, 8, 16, 32

You are doubling the number of flowers to find the number of days. Or half the number of days is the number of flowers. So, in 32 days there are 16 flowers.

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.

Answers

Mass Jupiter / mass of venus = 1898 * 10^24 / 4.87 * 10^24 = 1898 / 4.87 = 390 times heavier. I hope that comma is correct.

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

Answers

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?...

Answers

4 + 16 + 36 + 64
    so its 120

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

Answers

Hello,

One way to do this problem, is to identify the vertex. Since it is a parabola that opens downward, the maximum point is the vertex.

Using the expression: -b/2a, you can find the x-coordinate for the vertex.
Then, input that value into the function to find the y-coordinate for the vertex.

For the first equation, you will get (0.75, 2.125) for the vertex.
For the second equation, you will get (2.25, 11.125) for the vertex.

By comparing these points, you see that the vertex shifts up and to the right.
Option B is correct.

I hope this helps, Good luck!

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

Answers

[tex](21x^3y^4-7x^2y^3+14x^2y^2-xy) \div (7x^2y^2)[/tex]

[tex]\dfrac{21x^3y^4}{7x^2y^2} - \dfrac{7x^2y^3}{7x^2y^2} - \dfrac{14x^2y^2}{7x^2y^2} - \dfrac{xy}{7x^2y^2}[/tex]

[tex]3xy^2 - y - 2 - \dfrac{1}{7xy} [/tex]

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?

Answers

Answer
18 feet and 4.5 inches

Explanation
You are going to use the concept of similar triangle.
∆CED≡∆CBA
This is because they share the angle at C and also they both have an angle of 90o.
Let EC = X, then BE = 2.5X. So, BE = (X + 2.5X) = 3.5X
The scale factor EC/BC=x/3.5x=2/7
EC/BC=ED/BA=2/7
BA=7/2×63 in
The height of the tree = 220.5 inches. This is equal 18 feet and 4.5 inches.  

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),

Answers

Abraham Maslow and Carl Rogers would focus on the individual's coming to understand his or her self. Both studied effects of societal influences with the idea that individuals had free will.
If your choices are the following:
satisfying basic physiological needs
creating pyramidal charts
outcome and behavior
the full realization of an individual's self

Then the answer is the last option.
Abraham Maslow and CarlRogers would focus more on the full realization of an individual's self.
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