A polling company conducted a survey asking 40 fourth year students from Ohio and 33 fourth-year students from Pennsylvania about on average, how many hours they spend on the computer per week. Ohio had an average of 52, while Pennsylvania had an average of 33. Ohio and Pennsylvania have standard deviations of 7.22 and 10.11 respectively. Construct a 99.9% confidence interval for the difference between these results.

Answers

Answer 1

Answer:

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of variances.

Ohio had an average of 52, standard deviation of 7.22, sample of 40.

This means that [tex]\mu_O = 52, s_O = \frac{7.22}{\sqrt{40}} = 1.1416[/tex]

Pennsylvania had an average of 33, standard deviation of 10.11, sample of 33.

This means that [tex]\mu_P = 33, s_P = \frac{10.11}{\sqrt{33}} = 1.76[/tex]

Distribution of the difference:

[tex]\mu = \mu_O - \mu_P = 52 - 33 = 19[/tex]

[tex]s = \sqrt{s_O^2 + s_P^2} = \sqrt{1.1416^2 + 1.76^2} = 2.1[/tex]

Confidence interval:

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 - 0.999}{2} = 0.0005[/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 - 0.0005 = 0.9995[/tex], so Z = 3.29.

Now, find the margin of error M as such

[tex]M = zs[/tex]

[tex]M = 3.29*2.1 = 6.91[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 19 - 6.91 = 12.09 hours per week

The upper end of the interval is the sample mean added to M. So it is 19 + 6.91 = 25.91 hours per week.

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.


Related Questions

21. Find the value of x.

22. Find the value of x.

Answers

Answer:

62° & 54°

Step-by-step explanation:

Answer 21 :-

We know that the measure of a straight line is 180° .

x + 118° = 180° x = 180° - 118° x = 62°

Answer 22:-

2x + 1 + 71 = 180 2x = 180 - 72 2x = 108 x = 54°

Answer:

62° & 54°

Step-by-step explanation:

Answer 21 :-

We know that the measure of a straight line is 180° .

x + 118° = 180°

=> x = 180° - 118°

=> x = 62°

Answer 22:-

2x + 1 + 71 = 180

=> 2x = 180 - 72  

=> 2x = 108

=> x = 54°

A rectangle is 32 meters long and 4 meters wide. Which equation represents the area (A) of the rectangle?

A= 32 x 4
32= A x 4
32= (4x A) x 4
A=( 2x4) + (2x32)

Answers

I think the answer is A. Because, 32 * 4, you would have to find the answer (A) so 32 * 4 = A.

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?

Answers

Answer:

Be quiet you nerd

Step-by-step explanation:

Help me with questions 14 and 15! I will give brainliest!!

Answers

Answer:

14=9-11

15= 82.2%

Step-by-step explanation:

23/28=0.8214

Padma's three fastest times in the 50-meter backstroke event were 49.06 seconds, 49.55 seconds, and 48.97 seconds. What is the difference, in seconds, between her two fastest times?​

Answers

Answer:

0.51 seconds

Step-by-step explanation:

49.55 - 49.06 = 0.51 seconds

6^2x+2.6^3x=1 solve x=

Answers

Answer:

Step-by-step explanation:

if it is  [tex]6^{2}x+ 2.6^{3}[/tex]x = 1  

36x+17.576x = 1

53.576x = 1

x = 1 / 53.576

x = 1 /  [tex]\frac{6697}{125}[/tex]

x = [tex]\frac{125}{6697}[/tex]

or is it

6[tex]x^{2}[/tex] + 2.6[tex]x^{3}[/tex]=1      ?

Answer:

This is what I got.

Step-by-step explanation:

The bar graph shows the number of check-ins at a motel each day for one week. What percent of the check-ins occurred on Friday or Saturday? Round your answer to the nearest hundredth of a percent.

Answers

26/64 is correct

have a great day

What is the average rate of change for f(x) = 2x - 4 over the interval 2 Sxs 6?
A)
8
B)
10
C)
15
D)
18

Answers

Answer:

8 i think i hope it helps

good night

Indicate the effect each separate transaction has on investing cash flows. (Amounts to be deducted should be indicated with a minus sign.) Sold a truck costing $45,500, with $24,200 of accumulated depreciation, for $10,200 cash. The sale results in a $11,100 loss. Sold a machine costing $12,800, with $9,100 of accumulated depreciation, for $7,200 cash. The sale results in a $3,500 gain. Purchased stock investments for $17,100 cash. The purchaser believes the stock is worth at least $32,200.

Answers

$4,000 just because

Answer:

the answer is 4000$ i hope that helps

Help please.................

Answers

Answer:

X > 2

Step-by-step explanation:

CE and FH are parallel lines.

Which angles are supplementary angles?

Answers

Answer:

<CDG and <CDB are supplementary angles.

Answer:

hff

Step-by-step explanation:

< CDG and <CDB are supplementary angles.

msm555 is correct

hope it is helpful to you ☺️☺️☺️

Which is the graph of f(x) = 100(0.7)?

Answers

Answer:

f(x) = y = 70

Step-by-step explanationsince

since 100 · 0.7 = 70

      f(x) = y = 70

Answer:

Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Step-by-step explanation:

Edge

A Solve each problem.
1. Henry flies his plane at 240 mph for 3 hours. How far does he travel?​

Answers

Distance = speed x time

Distance = 240 x 3 = 720 miles

Answer:

henry doesn't travel but plane travel

Step-by-step explanation:

240m×3hour240m×60×60sec2592000m/s

evaluate the expression when b= 2 and c = 12



Answers

9 is your answer.

6+3 is 9. You added these two because a=3.

can u solve it please.​

Answers

Answer:

No I'm doing this for a quest

Step-by-step explanation:

Hope you find the answer though

Help
This is trigonometry

take it seriously, karma exists
I can help you too
I just wanna know if the result is 10.0 rounded to the nearest tenth
I used Sin
Please correct me

Answers

Answer:

Yes, your solution is correct

Step-by-step explanation:

sine = opposite leg / hypotenusesin 51° = √61 / WYWY = √61 / sin 51°WY = 10.0499134825 ≈ 10.0

Jackson's puppy gains 104 pounds in 52 weeks. At that rate, how many pounds would his puppy gain in 40 weeks?

Answers

Answer:

80

Step-by-step explanation:

104:52 = 2:1 = 2 pounds per (1) week

40 × 2 = 80

find the next number 2,5,12,25,54 ​

Answers

Answer:

Step-by-step explanation:

The next number is 110

190% of what number is 76
Plz hurry I really want to get this done

Answers

Answer:

190 is 76% of 250

Step-by-step explanation:

We have, 76% × x = 190

Multiplying both sides by 100 and dividing both sides by 76,

we have x = 190 × 100/76

x = 250

If you are using a calculator, simply enter 190×100÷76, which will give you the answer.

what do entertainment, utilities, and reserves have in common?

Answers

Answer:

these are some factors need to have a business

hope this helps

have a good day :)

Step-by-step explanation:

If m\angle A=(6x+10)^{\circ}∠A=(6x+10) ∘ and m\angle B=(4x+30)^{\circ}∠B=(4x+30) ∘ , then find the measure of \angle B∠B.​

Answers

A=6 × + 10=88555%__/455

The diameter of a semicircle is 4 kilometers what is the semicircle's radius

Answers

Answer:

To find the radius, just take half of the diameter. The answer is 2.

Step-by-step explanation:

Semicircle Area and Perimeter

Area (A)

6.2832in²

A = πr²/2 = 2 * π [in²] ≈ 6.2832 [in²]

Perimeter (L)

10.2832 in

L = πr + d = 2 * π + 4 [inch] ≈ 10.2832 [inch]

Hope this helped!!!

The radius of the semicircle is 2 kilometers.

What is a diameter?

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

Given:

The diameter of a semicircle is 4 kilometers.

Then the radius of the semicircle,

= diameter / 2

= 4/2

= 2 kilometers.

Therefore, the radius is 2 kilometers.

To learn more about the diameter;

https://brainly.com/question/5501950

#SPJ2

You were born, your mother deposited 2000 in an account that pays 5% simple interest. How much would the balance be in your account when you enter college 18 years after?

A. 18000
B. 1800
C. 3800
D. 20000

Answers

Answer:

C

Step-by-step explanation:

the formula for simple interest is given as A=P(1+rt), where A is the final balance, P is the initial principal balance (the amount of money that you start out with), r is the annual interest rate, and t is the time

we know that the mom deposited 2000 into an account when the person was born. This is our initial principal balance (the amount of money started out with)

substitute that value into the formula to get:

A=2000(1+rt)

we also know the rate, which is 5% and the time, which is 18

5%=0.05 (we need it as a decimal)

so substituting the values into the equation:

A=2000(1+0.05*18)

A=2000(1+0.9)

A=2000(1.9)

A=3,800

therefore the answer is C

Hope this helps!

What is the average rate of change for the function f(x) = 3x2 – 5 on the interval –3 < x < -1​

Answers

Answer:

Algebra Examples

Popular Problems Algebra Graph f(x)=3x^2-5

f

(

x

)

=

3

x

2

5

Find the properties of the given parabola.

Tap for more steps...

Direction: Opens Up

Vertex:  

(

0

,

5

)

Focus:  

(

0

,

59

12

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

61

12

Select a few  

x

values, and plug them into the equation to find the corresponding  

y

values. The  

x

values should be selected around the vertex.

Tap for more steps...

x

y

2

7

1

2

0

5

1

2

2

7

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex:  

(

0

,

5

)

Focus:  

(

0

,

59

12

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

61

12

x

y

2

7

1

2

0

5

1

2

2

7

image of graph

Step-by-step explanation:

If you spin this spinner 30 times, how many times would you expect to get not get yellow?

Answers

It would be a 1/5 chance so maybe 10

7 and - 1 1/2 on the number line?

Answers

Your answer would be B
You can ignore the fraction and do
7-1
Which gives you 6.

Then add the fraction, and your final answer is

6 1/2

2. One pound of pineapples costs $4.80. Jessica bought
3/4 pounds. How much did Jessica spend on pineapples?

Answers

Answer:

$3.60

Step-by-step explanation:

Jessica spent $3.60 on 3/4 pounds of pineapple.

Which of the following rational functions is graphed below?

Answers

Answer:

[tex]A = \frac{1}{(x-1)(x+1)}[/tex]

Step-by-step explanation:

Looking at the dashed lines in the graphic, these functions have two discontinuities, at x = -1 and at x = 1.

A discontinuity in a rational function is a point in which the denominator of the function is 0.

For these options, the denomiator is 0 at both x = -1 and x = 1 for only option A, so the answer is:

[tex]A = \frac{1}{(x-1)(x+1)}[/tex]

Hey yall!! How do I do this ???

Answers

put the y= equation into a calculator and then click graph and then after you see the graph , click 2nd and then graph to get the coordinates

Answer:

Step-by-step explanation:

just pick three values (numbers)  into the function and calculate the other unknown

You can pick an X or you can pick a Y, then solve for Y or X respectively.

Record these x,y pairs in the table

once you have at least two points you can graph the function

           y = mx + b     y-intercept form of the line function

                                  m = slope    b is the value of y when x = 0

   y = -5x/2 -5      let x = 0      solve for y

   y = -5(0)/2 -5

   y =    0 - 5

   y = -5

  y = -5x/2 -5                          solve for x            

  y + 5 = -5x/2 - 5 + 5             add 5 to both sides

  y + 5 = - 5x/2

 (y +5 )(-2/5)  = (-5x/2) (-2/5)

 (y +5 )(-2/5)  = x       let y = 0    

(0) +5)(-2/5)  = x

      5(-2/5)  = x

           -2   =  x

I'll let you have the third variable to pick  and solve for the dependent variable.  The dependent variable is just wha it sounds like, it is dependent on which ever independent (the value you randomly pick) variable.

Pick either x or y then solve for y or x

  y = -5x/2 -5              solve for y

  x = (-2/5) (y +5)        solve for x

Solve x² + 5x + 6 = 0​

Answers

Answer:

x=-2,-3

Step-by-step explanation:

x^2+5x+6=0

(x+2)(x+3)=0

x+2=0

x=-2

x+3=0

x=-3

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