An IQ test is designed so that the mean is 100 and the standard deviation is 21 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with ​99% confidence that the sample mean is within 6 IQ points of the true mean. Assume that σ=21 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answers

Answer 1

Answer:

The required sample size is 82. This number of people could be sampled in an afternoon, for example, at a commercial center in a city, which means that it is a reasonable sample size for a real world calculation.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Assume that σ=21 and determine the required sample size.

A sample size of n is needed.

n is found when M = 6. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 2.575\frac{21}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 2.575*21[/tex]

Dividing both sides by 3

[tex]\sqrt{n}= 2.575*3.5[/tex]

[tex](\sqrt{n})^2 = (2.575*3.5)^2[/tex]

[tex]n = 81.2[/tex]

Rounding up:

The required sample size is 82. This number of people could be sampled in an afternoon, for example, at a commercial center in a city, which means that it is a reasonable sample size for a real world calculation.


Related Questions

Jillian tracks her progress on her spelling tests over a period of four weeks. Which list shows her scores from greatest to least
Weeks 1,3,2,4
Weeks 3,1,4,2
Weeks 3,1,2,4
Weeks 1,3,4,2

Answers

Answer: B

Step-by-step explanation:

The pair of equations that can be used to find x and y are:

x + y = 62

(1.02)x = 7

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here, we have,

The form of the pair of equations would be:

hours worked last week + hours worked this week = total hours worked both weeks equation 1

(1 + percent increase/100) x hours worked last week = hours worked this week equation 2

x + y = 62 equation 1

(1 + 20/100) ×x = y

(1.02)x = 7 equation 2

The two equations can be solved using either of these three methods:

elimination method

substitution method

graph method

To learn more about mathematical equations, please check: brainly.com/question/26427570

#SPJ2

complete question:

Jillian worked 62 hours this week and last week. She worked x hours last week and y hours this week. She worked 20% more hours this week than last week. What pair of equations can be used to find x and y?

The letters of the words "possible outcomes" are put in a bag. Find the probability of picking the letter p.

Answers

Answer: 1/16

Step-by-step explanation:

total number of letters in word =16

probability of p=?

in given words p is only used one time so

1/16 is the probability


Find the surface area of the regular pyramid to the nearest tenth

Answers

Answer:

668.17

Step-by-step explanation:

solve by regrouping 2x2+6x+54+18x

Answers

Answer:

I believe the answer is=2x2+342.

The letters in VIRGINIA are each written on a separate card. Mark picks one card at random, keeps it, and then picks a second card. What is the probability that he picks an "I" and then picks a consonant?


3/14


3/16


1/4


2/7

Answers

Answer:

okay I would say 1/4

Step-by-step explanation:

the originally eight letters, and then you take one out so there's seven and then your chances of getting the I are two so that's 2/7. then there's only one consonant the R so 1/4.

Simplify: -5 + 3a +
6 - 4a.

Answers

Answer:

-a+11

Step-by-step explanation:

hard to explain. but should be correct

What is 2x-3y=-1
y=x-1

Answers

Answer: (4, 3)

Step-by-step explanation:

Let's use substitution.

So for y in the first equation we will substitute the expression for y in the second.

2x - 3(x-1) =  -1

2x -3x + 3 = -1

-1x + 3 = -1

       -3    -3

-1x = -4

-1x / -1 = -4 / -1

x = 4

Now plug in x for the second equation

y = 4 - 1

y = 3

Now check it using the first equation:

2(4) - 3(3) = -1

8 - 9 = -1

-1 = -1

It's true so it's correct

5.5 as a mixed number.

Answers

Answer: 5 1/2

Step-by-step explanation:

You keep your whole number which is five, then you see that the other 5 is in the tenths place in the decimal (5.5) so you put 5 over 10 and combine the fraction (5/10) with the whole number (5) and that is 5 5/10. But you see that it is not simplified so you simplify and get 5 1/2. I hope this helps :)

Mixed number is 5 1/2

Eric is a car salesman. He earns a weekly salary of $175 plus 4% commission on sales. This
week he sold a car for $35,450.
A) How much commission did he earn this week?
B) What did he earn in TOTAL this week?
(urgent pls show work)

Answers

Answer:

Step-by-step explanation:

Convert the decimal 0.07 to a fraction.

Answers

Answer:

7/100

Step-by-step explanation:

two decimal places so 100

Write the standard equation of a circle with its center at the origin and radius 3.

Answers

Answer:

9 = x^2+y^2

Step-by-step explanation:

3^2 = (x-0)^2 + (y-0)^2

9 = x^2+y^2

Need help quick please

Answers

Answer:

line 2

Step-by-step explanation:

on line 2 the two minuses at the end turn into a + (where the -2 is there should be a +2) because - x - = +

Please help, test due in 1 hour! I will give brainliest!

Answers

i think it’s a sphere
sorry if it’s wrong

Any tips for a gaming addicted brother? :-/

Answers

Answer:

Step-by-step explanation:

I would take his phone for a bit and also reduce screen time to 6 hours a week at MOST. It would help a lot.

write an explicit formula for an the nth term of sequence 100,20,4

Answers

Answer:

a_3=4

Step-by-step explanation:

a1 = 100

r = 1/5

an = 100 (1/5)^(n - 1)

so we now have the answer for a_3

a_3 = 100 * (1/5)^(3 - 1)

a_3 = 100 * (1/5)^2

a_3 = 100 * 1/25

a_3 = 4  

i believe this is it, although i'm not entirely sure

good luck :)

**please let me know if this was wrong/not what you were looking for or both**

have a nice day!

Find the number to add to x^2+14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.

Answers

Answer:

The number is 13

[tex] {x}^{2} + 14x + 13 \\ (x + 13)(x + 1)[/tex]

Step-by-step explanation:

I hope that is useful for you :)

Answer:

Step-by-step explanation:

What is the greatest common factor of 6, 42, and 30?

Answers

Answer:

6

Step-by-step explanation:

I found that the greatest common factor for those numbers is 6

What is HK?............help me answer this

Answers

Answer

C

Step-by-step explanation:

The decimal number 2.0159793 when rounded to 3 significant figures is?​

Answers

Answer:

2.02 may be I thinks tell me if it's right

2.02 would be your answer

Juan Rios rented a car for a 3-day weekend. The
car cost $35 per day plus $0.15 per mile. Juan
drove the car 425 miles and spent $53.75 on gas.
What was Juan's total cost? What was the cost
per mile?

Answers

Answer:

17000

Step-by-step explanation:

I hope this helps:)

____________________

Answers

Answer:

the equation for that line would be y=0

Step-by-step explanation:

The slope is 0 so if one were to plug in 0 as a slope to y=mx+b you would get y=0x which can be simplified to y=0. Hope this helped. :)

A number, f is positive

Answers

what are you asking?

Answer:

Not enough information.

Step-by-step explanation:

Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT.

Answers

Answer:

C closed

Step-by-step explanation:

the rule for converting yards to feet

Answers

the rule is you must multiply by 3

Answer:

1 yard=3 feet

Step-by-step explanation:

If it needs more, then 3 feet=36in.

Using the graph, determine the coordinates of the vertex of the parabola.

Answers

I don’t know for sure, but I think the vertex is (-5, 9)

If it’s wrong, hopefully this bobcat will make your day better

Heeeeeelp! I’m literally so behind

Answers

Answer:

That would be 9 my good sir ( or ma'am )

Step-by-step explanation:

basicly round the 61 so that there would not be a remainder and divide 54 by 6 you will get 9, so therefore the same case is for 540 by 60.

Have a nice day

A photographer is arranging 3 puppies in a row for a photo. There is one black puppy (B), one tan puppy (T), and one white puppy (W). Which list shows all the possible arrangements of the puppies?
Select one:

BTW, BBB, TTT, WWW, BBT, BBW, TTB, TTW, WWB, WWT

BTW, BWT

TWB, TBW, BTW, BWT, WBT, WTB

TWB, BTW, WBT
If you don't answer, I'll report you!

Answers

There are 6 combinations:
TWB TBW BTW BWT WBT WTB

Find the 10th term of the arithmetic sequence -x + 9, 4x + 14, 9x + 19, ...

Answers

Answer:

44x + 54

Step-by-step explanation:

The nth term of an arithmetic sequence is given by :

Tn = a + (n - 1)d

d = common difference = T2 - T1

d = T2 - T1

a = first term = - x + 9

d = 4x + 14 - (-x + 9)

d = 4x + 14 + x - 9

d = 5x + 5

The 10th term:

T(10) = (-x + 9) + (10 - 1)*(5x + 5)

T(10) = - x + 9 + 9(5x + 5)

T(10) = - x + 9 + 45x + 45

T(10) = 44x + 54

Hence, the 10th term is 44x + 54

giving out BRAINLIEST ANSWER HELP ME OUT PLEASE !!

Answers

Answer:

y = 8 !!! hope this helps !!

Step-by-step explanation:

whats x value please help

Answers

Answer:Step-by-step explanation:

x+46=90

x=90-46

x=44°

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