Researchers planning a study of the reading ability of third-grade children want to obtain a 95% confidence interval for the population mean score on a reading test, with margin of error no greater than 3 points. They carry out a small pilot study to estimate the variability of test scores. Assume the population standard deviation to be 12 points.

a. The study budget will allow as many as 100 students. Calculate the margin of error of the 99% confidence interval for the population mean based on n = 100.
b. There are many other demands on the research budget. If all of the various demands are met, there would be funds to measure only 10 children. What is the margin of error of the confidence interval based on n = 10 measurements?
c. Find the smallest value of n that would satisfy the goal of a 95% confidence interval with margin of error 3 or less. Is this sample size within the limits of the budget?

Answers

Answer 1

Answer:

A) M = 3.016

B) M = 9.79

C) 62

Step-by-step explanation:

A) We are given;

Population size; n = 100

standard deviation; σ = 12

Formula for the margins of error is;

M = z × σ/√n

At 99% confidence interval, z = 2.58

Thus;

M = 2.58 × 12/√100

M = 3.016

B) n is now equal to 10, thus at same confidence interval used in option A, we have;

M = 2.58 × 12/√10

M = 9.79

C) to solve this, we will use the formula;

n ≥ (zσ/m)²

Where;

z at 95% confidence interval has a value of 1.96

m is the margin of error = 3

Thus;

n ≥ (1.96 × 12/3)²

n ≥ 61.4656

Thus,approximately n = 62


Related Questions

304 students went on a field trip. Seven buses were filled, and 17 students traveled in cars. How many students were in each bus?

Answers

304 - 17

287

287 / 7

41

Answer: 41

Consider the steps to convert 49% to a decimal.

The decimal point will move
places.
The decimal point will move to the
.
49% written as a decimal is
.​

Answers

9514 1404 393

Answer:

2 placesto the left0.49

Step-by-step explanation:

It can be useful to consider the percent symbol (%) as a shorthand way to write /100. That is, where you see %, /100 is completely equivalent.

  49% = 49/100

If you recognize that 1/100 (one hundredth) is 0.01 in decimal (one hundredth), then you can see that 49/100 = 49×0.01 = 0.49.

__

A lot of folks consider the % symbol to be separate from the number, just as units of degrees or hours or inches might be. So, they tell you to do the conversion by moving the decimal point on the % value 2 places to the left (and drop the % symbol):

  49% = 49.% = .49

_____

Additional comment

As you can tell, I think of the % symbol as part of the number 49%, just as /100 is part of the number 49/100. Forty-nine hundredths can be written as any of 49/100 or 0.49 or 49%.

Answer:

2 places

to the left

0.49

Step-by-step explanation:

For a science class, Sweet T counts clusters of bacteria growing in two Petri dishes. He records his findings as a linear function of time. Which statement is true?

Answers

Answer:

dish A has a greater rate of change

Step-by-step explanation:

Answer:

Dish A has a greater rate of change

Step-by-step explanation:

If:
BC= 4x + 2,
AB = 8x + 8, and
AC = 22,
Find BC.

Answers

Answer:

BC = 6.8

Step-by-step explanation:

The distance from A to B, then from B to C, is the same distance as from A to C.

Thus,

AB + BC = AC

AB = 8x + 8

BC = 4x + 2

AC = 22

AB + BC = AC

(8x + 8) + (4x + 2) = 22

Expanding the parenthesis:

8x + 8 + 4x + 2 = 22

8x + 4x + 8 + 2 = 22

12x + 12 = 22

Subtracting 12 from both sides:

12x = 10

Dividing both sides by 12:

x = 10/12 = 1.2

x = 1.2

We're looking for BC. As we know,

BC = 4x + 2

Let's now put in x = 1.2 into this equation:

BC = 4x + 2

BC = 4 * 1.2 + 2

Since 4 * 1.2 is 4.8:

BC = 4.8 + 2

BC = 6.8

Answer: BC = 6.8

18r-4r=28 solve for r

Answers

Answer:

r=2

Step-by-step explanation:

18r-4r=14r

14r=28

r=2

Answer:

R=2

Step-by-step explanation:

18r-4r=14r

14r=28

r=2

Answer for 100 points! Also check the picture in full screen!

Answers

Answer:

A

Step-by-step explanation:

The answrr is A I think I need points

Mr. Joaquin had $71.25 in his bank account, but then
he bought some new ties and pants. After the purchase,
he was in debt $25.20. What was the change in Mr.
Joaquin's account balance due to the purchases?
A.$46.05
B.$-46.05
C.$96.45
D.$-96.45

Answers

Answer:

A.46.05(subtract from the bank account)

si quema o no quema cuh​

Answers

Answer:

Si quema cuhh

Step-by-step explanation:

Rewrite x - 3y = 6 in slope-intercept form.
А
X= 3y +6
В
y=x - 2
С
у = 3х -6
D
Зу = 6-х

Answers

Answer:

use formula y=mx+c

[tex]x - 3y = 6 \\ x - 6 = 3y \\ x - \frac{6}{3} = y \\ x - 2 = y \\ y = x - 2[/tex]

so the answer is B

I think it’s either B or C

MULTIPLE CHOICE QUESTION
The area of a rectangular picture frame is 93.5 square inches. The area formula for a rectangle is A = lw. Write and solve an equation to find the width, w, of the picture frame.

Answers

Answer:

w = 8.5

Hope it helps!:)

Answer:

93.5

Step-by-step explanation:

There are 90 dogs and 150 cats at an animal shelter. Of these animals, 9 dogs and 27 cats receive medication daily. What percentage of the animals in the shelter receive medication daily?

Answers

Answer:

15%

Step-by-step explanation:

Hope this helps! :3

500 POINTS PLEASE HELP ME I WILL GIVE ALL POINTS PLEASE PLEASE HELP ME ASAP

Answers

Answer:

its only says you will give 14 point so not ancering hahaha loser

Step-by-step explanation:

Answer:-_-

Step-by-step explanation:

A $890 computer loses value at a rate of about $25 per month. Equation Y equals 890-25X represents the value of the computer after X months. Identify and interpret the x and y intercepts. Explain how you can use the intercepts to help you graph the equation

Answers

Answer:

x-int. (35.6, 0)

represents number of

yrs before computer has

no value; y-int. (0, 890)

represents initial value;

Plot intercepts, draw

line through them.

Step-by-step explanation:

A triangle has sides with lengths of 6
centimeters, 11 centimeters, and 13
centimeters. Is it a right triangle? How
do you know?


Plss help

Answers

Answer:

no

Step-by-step explanation:

6^2 + 11^2 = 36 + 121 = 157

13^2 = 169

those are not equal so it is not a right triangle

through: (1, -3), slope = -4
A) y=-x+4 B) y = x +4
C) y = 4x + 1 D) y=-4x + 1

Answers

Answer:

D) y = -4x + 1

Pipers Pizza shop used 18% more cheese this month than last month, due to having a discount on the extra chesse toppings. If the pizza shop used 150 pounds of cheese last month how much did it use this month

Answers

Answer:

177 pounds

Step-by-step explanation:

Create an equation to represent the system.

Since it's 18% more than what was used last month an equation can be written such as the one below:

(118%)( last month's cheese ) = this month's cheese

Convert the percentages into decimals by moving the decimal place at the end of 118.00 two places to the left

118% = 1.18

( 1.18 )( last month's cheese ) = this month's cheese

Next, plug in the number for last month's cheese

( 1.18 )( 150 pounds) =

177 pounds

please help asap!!!!!

Answers

Answer:

36 units

Step-by-step explanation:

8+8+10+10=
36 units is the answer.

What is the area of this shape

Answers

Answer:

108 units^2

Step-by-step explanation:

(1+8)/2 = 4.5 and 4.5*24=108

Dante's family has completed 40% of a trip. They have traveled 25 miles. how far is the entire trip?

Answers

Answer: The entire trip is 62.5 miles

Step-by-step explanation:

25 miles = 0.4x

Divide both sides by 0.4

25/0.4 = 62.5 miles

What is the constant of proportionality for the relationship shown in this table?
I need your help

x 1 2 3 4
y 4 8 12 16

14

4

8

16
PLEASE

Answers

Answer:

2

Step-by-step explanation:

help me pls with these 2 find the slope with the graph

Answers

Answer:

Remember that the best way to remember is that when it’s a straight line, it can be able to form into zero. As for the ones below, they can form to be the letter u which can then be interpreted as undefined. There is the demonstration down below.

Step-by-step explanation:

did i get this right? if not could you tell me what it is.

Answers

Let’s simply step-by-step.
-9+1/4x-6-1/8x
=-9+1/4x+-6+-1/8 x
COMBINE LIKE TERMS:
=-9+1/4 x + -6 + -1/8 x
=(1/4 x + -1/8 x) + (-9+-6)
Answer
=1/8x -15

Find the slope of the line that goes through the given points.
(9,6) and (6, -3)

Answers

Answer:

3

Step-by-step explanation:

Slope of a line is expressed as;

m = y2-y1/x2-x1

m = -3-6/6-9

m = -9/-3

m = 3

Hence the slope of the line passing through the points is 3

If I already owe you 5 apples and now I owe you 10 more apples, how many apples do I owe you now?

Answers

Answer:

15 apples

Step-by-step explanation:

It's kinda obvious ;-;

Answer: 15 because it + so 5 + 10 = 15

Step-by-step explanation:

five years ago ,a father was four times as old as his son.In five years time the father will be twice as old as the son.If x and y are the present ages of the father and the son respectively,the equation relating x and y are:
Please I need an explanation
The options are
A: 4y-x=0;x-2y=0
B: 4y-x=15;x-2y=5
C: 4y-x=25;x-2y=5
D: x-4y=15;y-2x=5

Answers

B 4y-y=15;x-2y=5 is the correct one

HELPPPPPPPPPP MEEEEEE​

Answers

Answer:

D. x ≥ -10

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 Subtract Property of Equality

Step-by-step explanation:

Step 1: Define

10 - 4x ≤ 50

Step 2: Solve for x

Subtract 10 on both sides:                      -4x ≤ 40Divide -4 on both sides:                          x ≥ -10

Here we see that any value x greater than or equal to -10 would be a solution to the inequality.

Members of a lacrosse team raised $1396.75 to go to a tournament. They rented a bus for $850.50 and budgeted $28.75 per player for meals. Determine the number of players the team can bring to the tournament.

Answers

Answer:

19 players

Step-by-step explanation:

If the team raises $1396.75 and the bus costed $850.50 then the remaining budget is = 546.75

If each meal is $28.75 then you could buy 19 meals for 19 players to take to the tournament.

What is the volume of the rectangular prism?

Answers

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Step-by-step explanation:

The volume of a rectangular prism is the measure of the space the fills it. A rectangular prism is a 3-dimensional object with six rectangular faces. A rectangular prism is also referred to as a cuboid, rectangular hexahedron, right rectangular prism or a rectangular parallelepiped.Its formula is V=W×H×L.

Write inequalities to represent the situations below.
The distance to the nearest exit door is at most 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.

Answers

Answer:

d ≤ 150

Step-by-step explanation:

D is less than or equal to 150 meaning that it can be l3ess or 150 but it cant be more.  Hope it helped.

Solve for x.
x-1 is in exponential form
2^x-1 = 31

Answers

5.95 blah blah i have to add more characters to send the answer
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