A school has found from past records that the average scores for boys is 75 in a sample of 45 boys, and the average scores for girls is 85 in a sample of 30 girls. The population standard deviations for boys' and girls' scores were 25 and 17, respectively. The 90% confidence interval for the difference of the population means is approximately (_____, −2.022). Assume that the distributions of the scores of men and women are normally distributed. Round your answer to two decimal places.



Confidence Level Corresponding zc Value
90% confidence zc=1.645
95% confidence zc=1.96
99% confidence zc=2.576

Answers

Answer 1

Answer:

The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).

Step-by-step explanation:

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

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

Boys:

Mean of 75, sample of 45, standard deviation of 25.

This means that [tex]\mu_B = 75, s_B = \frac{25}{\sqrt{45}}[/tex]

Girls:

Mean of 85, sample of 30, standard deviation of 17.

This means that [tex]\mu_G = 85, s_G = \frac{17}{\sqrt{30}}[/tex]

Distribution of the difference of mean grades of boys and girls:

[tex]\mu = \mu_B - \mu_G = 75 - 85 = -10[/tex]

[tex]s = \sqrt{s_B^2+s_G^2} = \sqrt{(\frac{25}{\sqrt{45}})^2+(\frac{17}{\sqrt{30}})^2} = 4.85[/tex]

Confidence interval:

As stated, the critical value is [tex]z = 1.645[/tex]

The margin of error is of:

[tex]M = zs = 1.645*4.85 = 7.98[/tex]

Lower bound:

[tex]\mu - M = -10 - 7.98 = -17.98[/tex]

Upper bound:

[tex]\mu + M = -10 + 7.98 = -2.02[/tex]

The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).


Related Questions

Based on the stated expectations of the sit-and-reach test, which of the following is TRUE?
A.
Men are generally more flexible than women.
B.
Women are generally more flexible than men.
C.
Men and women are about equally flexible.
D.
No broad conclusions can be drawn about flexibility.

Answers

Answer:

B

Step-by-step explanation:

Find the surface area of the following figures.

with solution please. T-T​

Answers

Answer:

I will do 1 2 3 and 5 for you:

Since a cube has a given length of 5, we know that all sides will be the same therefore your lengths will be the same.

There are 6 sides of a cube so,

5 x 5 = 25 area of one flat surface.

Now 25(an area of one flat surface) x 6(flat surfaces) = 150 cm for question 1

We need to find area of the two circles:

3(given radius)^2(radius being squared) x 3.14(pi)

3 x 3 = 9

9(after radius being squared) x 3.14(pi) = 28.26(area of one circle)

28.26 x 2 = 56.52 (area of 2 circles)

Now we need to find the round surface, but first we need to find circumference:

2 x 3.14 x 3 = 18.84

18.84(circumference) x 5(height) = 94.2 (area of round surface)

Now lets add all the given areas to find surface area:

56.52 + 94.2 = 150.72 cm^2 is your answer for question 2

2 x 4 = 8

8 x 2 = 16

4 x 5 = 20

20 x 2 = 40

2 x 5 = 10

10 x 2 = 20

Add all given areas:

16 + 40 + 20 = 76 cm^2 is your answer for question 3

452.16 cm^2

4 x 3.14 x 6^2

4 x 3.14 x 36 = 452.16 cm^2 is your answer for question 4

8 x 4 = 32, 32 divided by 2 = 16

since there are 4 sides,

4 x 16 = 64

Don't forget the bottom!

4x 4 = 16

Lets add the given areas:

64 + 16 = 80 for question 5

Qu
Peter hired a cleaning company to clean his house. The cleaning company charges a
fixed fee of $15 plus $17 per hour to clean a house.
a. Write an equation that can be used to determine, c, the total amount in dollars that
the cleaning company charges to clean a house in h hours.

Answers

To find the total cost you need to multiply the hourly rate by the number of hours they work and add the fixed fee.

C = 17h + 15

HELP ME PLEASEEEEEEEEEEEEEEEEEEE

Answers

Answer:

The second answer choice

Step-by-step explanation:

The pyramid shown is a triangular pyramid. A triangular pyramid consist of 4 faces; 1 triangular base and 3 triangular lateral faces.

Hence, the correct answer would be the second choice.

Hey luvs!

The endpoints of AB are A(1,4) and B(5,-1). What are the coordinates of the point that divides AB in the ratio
2:3?

Answers

Answer:

I don't know I'm sorry.............

I need help answering this question please help

Answers

40

Or at least that what my calculator says.

What does the digit 7 represent in 701, 280?
O Seven hundred
O Seventy thousand
Seven hundred thousand
Seven thousand

Answers

Answer: seven hundred thousand

Answer:

The 7 represents the 10,000

Step-by-step explanation:

Its not the hundred because the 2 in 280 is

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis​ test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that d​3.125, ​2.911, and n​8, and that you wish to test the hypothesis below at the​ 10% level of significance. What decision rule would you​ use? ​: 0 against ​: 0

Answers

Answer:

Decision Rule

The critical region for one tailed test with 7 d.f is t > 1.415 for

H0 : ud ≤ 0 against the claim Ha: ud > 0

Step-by-step explanation:

The data given is

Population mean = ud= 0

Sample difference mean = d`= 3.125

Sample difference standard deviation = sd= 2.911

Sample size= n= 8

Formulate the null and alternate hypotheses as

H0 : ud ≤ 0 against the claim Ha: ud>0

The significance level ∝= 0.1

The degrees of freedom = n-1 = 8-1 = 7

The critical region for one tailed test with 7 d.f is t > 1.415

The test statistic is

t= d`- ud/ sd/ √n

Putting the values

t= 3.125-0 / 2.911/√8

t= 3.125/1.0292

t= 3.036

since the calculated value of t falls in the critical region we reject the null hypothesis .

A bag contains eight white marbles, six red marbles and four blue marbles.
How many blue marbles must be added to the bag so that the probability
of choosing a blue marble is 1/2?
a. 6
b. 5
c. 10
d. 0

Answers

Answer:

c) 10

Step-by-step explanation:

you need to add the white and red marbles which would be 14.

then you subtract 14 by the amount of blue marbles.

no links Pwease help this is very important I will give you brain thing if its correct ♡

Answers

Answer:

B, C

Step-by-step explanation:

HELP WITH THIS ASAP!

Answers

Answer:

Hi, there your answer will C. 85pi ft^2

Step-by-step explanation:

pi(5)(12)+pi(5)^2

60pi+25pi

85pi ft^2

Hope this helps :)

How do the angles and side lengths of the preimage relate to the corresponding angles and side lengths of the image of a dilation with a scale factor not equal to 1?

Answers

Answer:

The angles are proportional and the side lengths are proportional.

Step-by-step explanation:

Savaas Realize

Can someone help! This is due right now and I'm a little confused! Thank you!

Answers

Answer:

a) 10 cucumbers

b) two fifth x, or 2/5x

c) 15 vegetables

Giving brainliest ; What is the mean of the data set? {20,1,14,14,9,8} Enter your answer in the box.

Answers

Answer:

11

Step-by-step explanation:

(20 + 1 + 14 + 14 + 9 + 8) / 6

= 66 / 6

= 11

2. Use the image to answer the questions.
(a) What is the center and the radius of the circle?
(b) What are the equations of the circle in graphing form and in general form? Show your work.

Answers

Answer:

Center = (-1, 1)

Radius = 3

Graphing form

(x + 1)² + (y - 1)² = 3²

General form

x² + y² + 2x - 2y - 7 = 0

Step-by-step explanation:

Center = (-1, 1)

Radius = 3

Graphing form

(x + 1)² + (y - 1)² = 3²

General form   \Expand graphing form\

(x² + 2x + 1) + (y² - 2y + 1) - 9 = 0

Rearrange

x² + y² + 2x - 2y - 7 = 0

100 POINTS!!!!!! HELP
Question 23
Max and Jay are among 12 contestants in the school spelling bee. If the top two finishers win prizes, what is the probability both Max and Jay will be the two prize winners?
A
1766
B
136
C
166
D
1132

Answers

A - 1766! I hope this helps

A bank is offering 3.5% simple interest on a savings account. If you earned $525 in interest
in 2 years, how much did you deposit in the savings?
O $7,500
O $8,000
O $7.250
$7.000

Answers

Answer:

$7500

Step-by-step explanation:

Given

[tex]I = 525[/tex]

[tex]R = 3.5\%[/tex]

[tex]T =2[/tex]

Required

The Principal

This is calculated using:

[tex]I =PRT[/tex]

Make P the subject

[tex]P = \frac{I}{RT}[/tex]

So, we have:

[tex]P = \frac{525}{3.5\% * 2}[/tex]

[tex]P = \frac{525}{7.0\%}[/tex]

[tex]P = 7500[/tex]

I will go potty now thx​

Answers

ummmm tmi but ok... 0-0

Find the surface area and volume of the figure. Round to the nearest tenth.

Answers

surface area = 374 cm^2 and volume 384 cm^3. I think . try to go ok calculator.net

question number nine answer

Answers

Answer:9

Step-by-step explanation:

Answer:

I think it's either A or D

is 2 a solution to the equation 1/2 x 4 = 5 ?​

Answers

Answer:

yes it is good luck with your work

Two parallel lines cut by a transversal are shown. What is the value of X, in degrees?

Answers

9514 1404 393

Answer:

  x = 15°

Step-by-step explanation:

Same-side interior angles are supplementary.

  (4x° +12°) + 108° = 180°

  4x° = 60° . . . . . . . . . . . . . . subtract 120°

  x = 15° . . . . . . . . . . . . divide by 4

A radioactive substance with initial value of 800g decays according to the exponential model A= 800e^(kt). After 10 years, only 400g of the substance remains. Find the value of k. Round your answer to the nearest thousandth. ​NO LINKS!!!!

Answers

Answer:

k ≈ - 0.069

Step-by-step explanation:

Given

A = 800 [tex]e^{kt}[/tex]

Substitute A = 400 and t = 10 into the equation

400 = 800 [tex]e^{10k}[/tex] ( divide both sides by 800 )

0.5 = [tex]e^{10k}[/tex] ( take the ln of both sides )

ln [tex]e^{10k}[/tex] = ln0.5

10k lne = ln0.5 [ lne = 1 ]

10k = ln 0.5 ( divide both sides by 10 )

k = [tex]\frac{ln0.5}{10}[/tex] ≈ 0.069 ( to the nearest thousandth )

Answer:

Step-by-step explanation:

400 = 800 * e^(k*t)

What are the units of t? I'm taking it as years.

Divide by 800

400/800 = e^(k*10)

1/2 = e^(k*10)

ln(1/2) = ln(e)^(k*10)

ln(1/2) = k*10 * ln(e)

ln(e) = 1

-0.69314 = k*10

-0.069314 = k

Check

A = 800 e^(-0.069314*10)

A = 800 e^(-0.69314)

A = 800 * 0.50000359

A = 400.0028722

Which is close enough to 400

A circle has a radius of 4 inches. What is
the circumference?
A.25.12 inches
B.12.56 inches

Answers

Answer:

4 x 3.14 x 2 = 25.12 inches

Step-by-step explanation:

Formula of circumference:

3.14(pi) x 2(the number is just always there when finding circumference) x radius(half of your diameter or just your given radius).

The number of red tiles in a sack is 5 more than 3 times the number of green tiles in the sack. The
sack contains 35 red tiles, How many green tiles does the sack contain?
Pls help I need this pls help have a good day

A.12
B.10
C.9
D.not here

Answers

Answer:

B. 10

Step-by-step explanation:

10 x 3 = 30+5 = 35


write the percent of each figure
that is shaded.

Answers

Answer:

1. 21%   2.  70%

Step-by-step explanation:

1. 21 out of 100 are filled in

2. 7/10 are filled in

What is the distance between the points (6, 4) and (-3, 17)?
A) 22
B) √250
C) 125
D) √88

Answers

D IS THE CORRECT ANSWER

Find the distance of the two given points (1,5) and (4,10)

Answers

Answer:

5.831

Step-by-step explanation:

Distance between both given points=Lenght=5.831

Multiply 4/5 by 10 ​, and then multiply that product by 17 .

Answers

Answer:

your answer is 406.

Step-by-step explanation:

4/5 x 10 will equal to 8. 8 times 17 equals 406.

Jovi distributed 3(n+2) and got 3 x n + 3 x 6 is his answer correct

Answers

Answer:

Step-by-step explanation:

since 3 is outside the parenthesis (n + 2) you multiply the 3 by the n and the 2 and

3n + 6

next subtract the 6 and add the 6 to the other side

3n - 6 = 6

3n = 6

n = 2

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