A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medical study is (1850, 2000). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 18 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.

Answers

Answer 1

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

[tex]M = \frac{1850 + 2000}{2} = 1925[/tex]

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.898

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Since [tex]M = 75, T = 2.898, n = 18[/tex]

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]75 = 2.898\frac{s}{\sqrt{18}}[/tex]

[tex]s = \frac{75\sqrt{18}}{2.898}[/tex]

[tex]s = 109.7992[/tex]

The sample standard deviation is of 109.7992 calories.


Related Questions

Which of the following expressions could NOT be used to find the volume of the sheet cake? Select all that apply.

Answers

Incorrect

60 × 3

Correct

12 + 5 + 3

Incorrect

3 × 5 × 12

Correct

12 × 5

Correct

(12 × 5) + 3

What is 7 / 2 0 to 5

Answers

7/20 to 5 is 1 3/4 or 7/4.

Liam is going to invest in an account paying an interest rate of 5.7% compounded daily. How much would Liam need to invest, to the nearest ten dollars, for the value of the account to reach $23,000 in 5 years?

Answers

Answer:

The answer is 17300./ Hope this helps

Given the function
f(x)=4x−1
, evaluate and simplify the expressions below. See special instructions on how to enter your answers.
f(a)=
f(a+h)=
f(a+h)−f(a)h=
Instructions: Simplify answers as much as possible. Expressions such as 4(x+2)and (x+5)2 should be expanded. Also collect like terms, so 3x+x should be written as 4x.

Answers

Answer:

[tex]f(a) = 4a - 1[/tex]

[tex]f(a+h) = 4a+4h - 1[/tex]

[tex]f(a + h) - f(a)h= 4a + 5h - 4ah- 1[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 4x - 1[/tex]

Solving (a): f(a)

Substitute a for x

[tex]f(a) = 4a - 1[/tex]

Solving (b): f(a + h)

Substitute a + h for x

[tex]f(a+h) = 4(a+h) - 1[/tex]

[tex]f(a+h) = 4a+4h - 1[/tex]

Solving (c):f(a + h) - f(a)h

[tex]f(a + h) - f(a)h= f(a + h) - f(a) * h[/tex]

Substitute values for f(a + h) and f(a)

[tex]f(a + h) - f(a)h= 4a + 4h - 1 - (4a- 1) * h[/tex]

Open bracket

[tex]f(a + h) - f(a)h= 4a + 4h - 1 - 4ah+ h[/tex]

Collect like terms

[tex]f(a + h) - f(a)h= 4a + 4h + h - 4ah- 1[/tex]

[tex]f(a + h) - f(a)h= 4a + 5h - 4ah- 1[/tex]

What does b represent in the expressions.

Answers

I think it represents the price of each granola

y = 4x + 2
6x + 2y = 8
What is the value of x + y?

Answers

Answer:

24/7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/CoefficientsFactoringFunctionsCoordinates (x, y)Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y = 4x + 2

6x + 2y = 8

Step 2: Solve for x

Substitution

Substitute in y:                                                                                                  6x + 2(4x + 2) = 8Factor GCF:                                                                                                       2[3x + (4x + 2)] = 8[Division Property of Equality] Divide 2 on both sides:                                  3x + 4x + 2 = 4Combine like terms [Addition]:                                                                        7x + 2 = 4[Subtraction Property of Equality] Subtract 2 on both sides:                        7x = 2[Division Property of Equality] Divide 7 on both sides:                                  x = 2/7

Step 3: Solve for y

Substitute in x [Original equation]:                                                                  y = 4(2/7) + 2Multiply:                                                                                                             y = 8/7 + 2Add:                                                                                                                   y = 22/7

Step 4: Evaluate

Substitute in variables:                                                                                     2/7 + 22/7Add:                                                                                                                   24/7

4. tan Θ if sin = 1/2 90° ≤ Θ ≤ 180°

a. -√(3)/2
b. -√(3)/3
c. √(3)/2
d. √(3)/3

5. Find the value of
tan Θ if cot Θ = 2 0 ≤ Θ < 90° (write your answer as a fraction)

tan =

Answers

9514 1404 393

Answer:

  4. b =-√(3)/3

  5. 1/2

Step-by-step explanation:

4. The tangent is negative in the second quadrant. The sine value tells you the reference angle is 30°, so the actual angle is 150°. The corresponding tangent is ...

  tan(150°) = -(√3)/3

__

5. The cotangent is the inverse of the tangent, and vice versa.

  tan = 1/cot

  tan(θ) = 1/2

1 1/4 x 2 1/4 = ? i need help plzzz

Answers

Answer:

2,13/16

Step-by-step explanation: you can put it in the calculator and the answer given would be 2 13/16 hope it helps!

Answer:

2 13/16 or 45/16

PLEASE HELP what is the solution to |2x-8|<2

Answers

Answer:

A

Step-by-step explanation:

You have two inequalities:

2x-8<2 = 2x<10 = x<5

-2x+8<2= -2x<-6 = x>3

Combine the two to get 3<x<5

Hope this helps!

Answer and Step-by-step explanation:

The answer would be A, in which x can be any value between 3 and 5, exclusive, or not including.

This is because in this situation, if you put any number greater than or equal to 5, or any number less than or equal to 3 it would be greater than 2 due to the absolute thing (noted as |  |  )

So, any number thats between 3 and 5 will work, as it will be less than 2.

#teamtrees #POG (Plant Our Garden)

PLS HELPP What is the volume of the larger rectangular prism in the figure?
A)
26 cm3
B)
28 cm3
C)
80 cm3
D)
108 cm3

Answers

Answer:

80.

Step-by-step explanation:

I've seen this question before and got it right. It's really simple. One of the other questions is what is the total volume and its 108. The smaller one is 28. You just add them up and get 108.

In ΔDEF, the measure of ∠F=90°, FD = 33 feet, and DE = 92 feet. Find the measure of ∠D to the nearest tenth of a degree.

Answers

ADED = F=90ْ plus 90 ==1 - 2 6+6 =p

Answer:

69

Step-by-step explanation:

i don't know

I really need help pls ty

Answers

Answer:

m<3 = 58

Step-by-step explanation:

lllllllllllllllll

angle 3 = 58°.
angle 7 and angle 5 are alternate interior angles, so they’re congruent. since 5 and 6 make up a complementary angle, they equal 90°. 90 — 32 = 58. angle 6 and angle 3 are vertical angles, so they’re congruent. If angle 6 equals 58, then so does angle 3.

builder is buying property where she can build new houses. The line plot shows the sizes of the lots for each house. What is the average size of the lots?

Answers

Answer:

I think she put it in the 2nd place because it has the smallest amount of x's , and 1 and 3 has more

add. simplify the answer and write it as a mixed number 2/15+3/10+4/5

Answers

Answer:

1 7/30

Step-by-step explanation:

First find common denominator then solve

[tex]\frac{2}{15} + \frac{3}{10} + \frac{4}{5}\\\\\frac{4+9+24}{30} = \frac{37}{30} = 1\frac{7}{30}[/tex]

What is the formula for area of Parallelogram

Answers

Answer:

See below

Step-by-step explanation:

Area of parallelogram = base * height

Answer:

A= b×h

Step-by-step explanation:

b= base

h= height

hope it helped

BRAINLIEST STARS

Find the area of the circle if r = 5 meters. Leave the answer in terms of pi.
A) A=100pi square meters
B) A=25pi square meters
C) A= 5pi square meters
D) A=10pi square meters

Answers

Answer:

B: A=25pi square meters

Step-by-step explanation:

Answer: 25pi square meters

Use the distributive property to write an equivalent expression. 4(x+2)

Answers

Answer:

4x+8

Step-by-step explanation:

4*x = 4x

4*2 = 8

4x+8

The equivalent expression using the distributive property is 4x + 8.

How to determine the distributive property to write an equivalent expression.

To use the distributive property to write an equivalent expression for 4(x + 2), we need to multiply each term inside the parentheses by the factor outside.

Using the distributive property, we multiply 4 by both x and 2:

4(x + 2) = 4 * x + 4 * 2

Simplifying further:

4(x + 2) = 4x + 8

Therefore, the equivalent expression using the distributive property is 4x + 8.

Learn more about equivalent expression at https://brainly.com/question/15775046

#SPJ2

A rectangular garden has dimensions of 100 feet by 10 feet. Next season, the garden is decreased to 25 of its size. What is the scale of the new drawing?

Answers

Answer:

40 feet by 4 feet

Step-by-step explanation:

Given length (l) = 100 feet

width (w) = 10 feet

As mentioned in the question the size of garden is decreased to 2/5 of its size. It will effect the length and width with the same proportion.

So,

New length = 100 * 2/5 = 40 feet

New width = 10 * 2/5 = 4 feet

Therefore, the scale of new drawing would be 40 feet by 4 feet.

1.1.2
Calculate the amount of VAT payable on a coffee mug that costs R75.90
(VAT exclusive)​

Answers

6999999 huhuijuu harder daddy

13 in
10 in.
7 in
3. What is the perimeter of the
(19)
trapezoid?

Answers

37 because you add 13+10=23 7+7=14 and 23+14=37

What is the distance between the points (-9 , 23) and (2 , 23) in the coordinate plane

Answers

Answer:

d=11

Step-by-step explanation:

d = √[(2 - (-9))^2 + (23 - 23)^2]

= √[(2 + 9)^2 + (0)^2]

= √[11^2 + 0^2]

= √(121 + 0)

= √121

= 11

Therefore, the distance between the points (-9, 23) and (2, 23) is 11 units.

Find the unknown number 10% of what number is 300

Answers

Answer:3,000

Step-by-step explanation:

Answer:

3000

Step-by-step explanation:

300    x

10     100

300x100

30,000

30,000/10

3000

which monomial represents the number of square units in the area of a circle with radius 4x^3 units

Answers

Answer:

For a circle of radius R, the area is written as:

A = pi*R^2

Where pi = 3.14

Then if the radius of the circle is R = 4*x^3

The area of this circle will be:

A = 3.14*(4*x^3)^2 = 3.14*(4)^2*(x^3)^2

Here you need to remember that:

(a^n)^m = a^(n*m)

Then the area of the circle is:

A = 3.14*(16)*(x^(3*2) = 3.14*16*x^6 = 50.24*x^6

So the monomial that represents the number of square units in the area of the circle is:

A(x) =  50.24*x^6

The length of a shadow of a building is 29 m. The distance from the top of the building to the tip of the shadow is 36 m. Find the height of the building. If
necessary, round your answer to the nearest tenth.

Answers

Answer:

21.3 m

Step-by-step explanation:

The perimeter of a rectangle is 18 cm. If its length is 5 cm, find its breadth.​

Answers

Answer:

Hope that answers your question, you're welcome

[tex] \longmapsto \: perimeter \: of \: rectangle = 2(l + b) \\ \\ \longmapsto2(5 + b) = 18 \\ \\ \longmapsto \: 5+ b = 9\\ \\ \longmapsto \: b = 4cm[/tex]

help please!
will give brainliest

Answers

Answer:

The answers will placed according to the order that they were given

6.93

15.75

17.64

6.93

Step-by-step explanation:

Help please I give brainliest

Answers

Answer:

(8,5)

Step-by-step explanation:

Your X coordinate would determine how far right or left something would be on a plot. The more left, the lower the number, and the more right, the higher the number. Y coordinate controls the height. Therefore, the coordinates with the highest X value would be the answer.

Write down the value of the 5 in each of these
numbers.
8.154
751 602
1 567 324 896​

Answers

Answer:

8.154 - 0.05

751 602 - 50 000

1 567 324 896 - 500 000 000

What does it mean to be “in the red?”
a.
You have more credits than debits.
b.
You have more debits than credits.
c.
You cannot find your financial records.
d.
Your financial records are inaccurate.

Answers

Answer:

b.

You have more debits than credits.

Step-by-step explanation

Being in the red means that you are in debt so im 90% sure its B

If you get this wrong then i am very sorry.This is my input :)

Answer:

B

Step-by-step explanation:

In accounting, if the debit balance is more than the credit balance on income statement, there is a loss.

If the credit balance is more than the debit balance on income statement, there is a profit.

Option C and D are both not correct because this does not relate to whether a Financial record is accurate or not.

WILL GIVE BRAINLIEST URGENT

Answers

Answer:

CHICKEN CHEESE BUTT

Step-by-step explanation:

5+5 = 69 :)

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