Suppose you are asked to take a sample of men and women in order to measure their emotional IQ. The emotional IQ scale that you administer has a minimum of 0 and a maximum of 100, with higher scores indicating higher emotional intelligence (the range of the scale is not pertinent to the question -- I simply provide it so that you have some context in which to provide your answer). You sample 25 men and 25 women. The mean for men is 70 with a standard deviation of 10 and the mean for women is 82 with a standard deviation of 15.

Required:
What is the 99% confidence interval for the scores of men and women?

Answers

Answer 1

Answer:

The 99% confidence interval for the scores of men is (64.406,75.594).

The 99% confidence interval for the scores of women is (73.609,90.391).

Step-by-step explanation:

We have the standard deviations for the sample, which means that the t-distribution will be used to solve this question.

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 = 25 - 1 = 24

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797.

For men:

Standard deviation of 10.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{10}{\sqrt{25}} = 5.594[/tex]

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

The lower end of the interval is the sample mean subtracted by M. So it is 70 - 5.594 = 64.406

The upper end of the interval is the sample mean added to M. So it is 70 + 5.594 = 75.594

The 99% confidence interval for the scores of men is (64.406,75.594).

For women:

Standard deviation of 15.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{15}{\sqrt{25}} = 8.391[/tex]

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

The lower end of the interval is the sample mean subtracted by M. So it is 82 - 8.391 = 73.609

The upper end of the interval is the sample mean added to M. So it is 82 + 8.391 = 90.391

The 99% confidence interval for the scores of women is (73.609,90.391).


Related Questions

1. Two-thirds of the sum of the number x and 5 is written
2x+5
a.
2
-x+ 5
3
b. §
(5x) <(x+5)
d.
e. x+ķ(x+5)
{(+5)
3

Answers

9514 1404 393

Answer:

cba

Step-by-step explanation:

This is as much about English comprehension as it is about math. When you read an English sentence, you need to figure out what each of the pronouns, phrases, and modifiers is referring to. When the sentence refers to math operations, you need to determine what each math operation is being applied to. In most cases, a math operation involves two operands, so the trick is to figure out what those are.

__

1. "Two-thirds of the sum ..." will look like 2/3( + ). "The sum of a number and 5" will look like (x+5). So, the words are describing ...

  2/3(x +5) . . . . matches C

__

2. "Seven decreased by ..." will look like 7 -( ). "The quotient of a number and 3" will look like (n/3). So, the words are describing ...

  7 -n/3 . . . . matches B

__

3. Consider the order of operations. When you evaluate 2x²+9, the last operation you perform is addition. That is, the result is a sum. One of the elements of that sum is 9 (the second one). The other element of that sum is the product 2x². The elements of that product are 2 and the square of x. So, one way to describe this expression is ...

  the sum of the product of 2 and the square of a number, and 9.

The order of operations requires that squares be evaluated before multiplication and division, so it is not unreasonable (if slightly more ambiguous) to write this as ...

  the sum of 2 times a number squared and 9 . . . . choice A

How many one-to-one functions are there from the set {A, B, C} to the set {x, y, z, t, w, k}?

Answers

Answer:

120 different one-to-one functions

Step-by-step explanation:

A one-to-one function means that each element from the domain can be mapped into only one element from the range (like for a typical function), and each element from the range can be mapped only once.

This means that, for two different inputs x₁ and x₂, we can't have:

f(x₁) = f(x₂)

Because that would mean that two different values of the domain are being mapped into the same element from the range.

Ok, now that we know this, let's count the number of possible "mappings" for each element in the domain.

For the first element, A, we have the options {x, y, z, t, w, k} (a total of 6 options).

For the second element, B, we will have an option less (because one was already taken) so here we have 5 options.

For the last element on the domain, C, there will be again an option less than in the previous case, so here we have 4 options.

The total number of combinations (each combination defines a different one-to-one function) is equal to the product between all the options for each case, then the total number of one-to-one functions is:

C = 6*5*4 = 120

There are 120 different one-to-one functions.

Describe the transformation of f(x) = sin x to g(x) = sin x – 7.

Answers

9514 1404 393

Answer:

  C.  7 units down

Step-by-step explanation:

The y-coordinate of a point on a graph is the function value. It tells how far up from the x-axis the point is located. When 7 is subtracted from the function value, the y-coordinate is 7 less than it was. That is, the point has moved 7 units down.

i need to know how to solve this

Answers

Answer:

C

Step-by-step explanation:

I think you have to call a = 14/32 and b = 7/4

3a = 3 * 14/32 = 42/32

b = 1 3/4 = (4 + 3)/4 = 7/4

42/32 // 7/4                        Invert and multiply

42/32 * 4/7                         Cancel 4 into 32 and 7 into 42

6/8 = 3/4

I make the answer C

Answer:

So the square seems to multiply the first number by three and then divide it by the second number.

So,

14/32 * 3

=

42/32

Simplify

21/16

And now for division, we flip the diveding fraction and multiply.

21/16 * 4/7

Which is after some fraction simplifing:

3/4

One of the questions Rasmussen Reports included on a 2018 survey of 2,500 likely voters asked if the country is headed in right direction. Representative data are shown in the DATAfile named Right Direction. A response of Yes indicates that the respondent does think the country is headed in the right direction. A response of No indicates that the respondent does not think the country is headed in the right direction. Respondents may also give a response of Not Sure.
(a) What is the point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction?
(b) At 95% confidence, what is the margin of error for the proportion of respondents who do think that the country is headed in the right direction?
(c) What is the 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction?
(d) What is the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction?
(e) Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?
The confidence interval in part (c) has a (Smaller or Larger) margin of error than the confidence interval in part (d). This is because the sample proportion of respondents who do think that the country is headed in the right direction is (closer to .5 / closer to 1 / farther from .5 / farther from 1) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Dataset:
553 - No
70 - Not Sure
384 - Yes

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

553 - No

70 - Not Sure

384 - Yes

Total = (553 + 70 + 384) = 1007

Proportion who do think country is headed in the right direction :

P = yes / total = 384/1007 = 0.381

b.) Error margin at 95%

Margin of Error = Zcritical * √p(1-p)/n

1-p = 1 - 0.381 = 0.619

Zcritical at 95% = 1.96

Margin of error = 1.96 * √0.381(0.619)/1007

Margin of error = 0.030

C.)

95% confidence interval for heading in the right direction:

P ± margin of error

P ± 0.030

Lower boundary = 0.381 - 0.030 = 0.351

Upper boundary = 0.381 + 0.030 = 0.411

(0.351 ; 0.411)

D.)

Confidence interval for people who don't think :

P = 553 / 1007 = 0.549

Confidence interval = P ± margin of error

Error margin at 95%

Margin of Error = Zcritical * √p(1-p)/n

1-p = 1 - 0.549 = 0.451

Zcritical at 95% = 1.96

Margin of error = 1.96 * √0.549(0.451)/1007

Margin of error = 0.031

P ± margin of error

P ± 0.031

Lower boundary = 0.549 - 0.031 = 0.518

Upper boundary = 0.549 + 0.031 = 0.580

(0.518 ; 0.580)

E.)

The interval with smaller error margin is ; 0.030 (those who think country is headed in the right direction because sample proportion is farther from .5 / farther from 1)

Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one tail. What sets of elements are included in the sample space?

Answers

Answer:

a)  [tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]

b)  [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]

Step-by-step explanation:

From the question we are told that:

3 coin are tossed

Therefore

Sample space [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]

Generally the sets that correspond with the result of at most one tail is therefore given as follows

[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]

Therefore

The result is at most one tail when

[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]

In triangle​ ABC, the measure of angle B is 22° more than three times the measure of angle A. The measure of angle C is 53° more than the measure of angle A. Find the measure of each angle.

Answers

Answer:

105

Step-by-step explanation:

53+22=75, 180-75=105

1. Estimate the area of the irregular shape. Explain your method and show your work.
2. The coordinates of the vertices of △LMN are L (-2, 4), M (3, -1), and N (0, -4). Determine whether △LMN is a right triangle and support your decision. Show all work.
3. The coordinates of the vertices of quadrilateral PQRS are P (-6, 2), Q (-1, 4), R (2, 2), and S (-3, 0). Alexandra states that quadrilateral PQRS is a parallelogram. Prove or disprove Alexandra’s statement. Show all work.

Answers

Answer:

Step-by-step explanation:

1. Do not see a figure, and unsafe to download and execute .docx.

2. Vectors LM<5,-5>, NM<3,3>, NL<2,-8>

Since LM.NM = 15-15 = 0, LM and NM are orthogonal, hence the given points form a right triangle.

3. A parallelogram has opposite sides parallel.

Slope PQ = (4-2) / (-1 - -6) = 2/5

Slope RS = (2-0) / (2- -3) = 2/5

Therefore PQ || RS

Slope PS = (2-0)/(-6- -3) = -2/3

Slope QR = (4-2)/(-1 -2) = -2/3

Therefore PS | QR

Since opposite sides are parallel, PQRS is a parallelogram

Answer:

Step-by-step explanation:

1. There are 31 complete are almost complete squares.

Top line is about 3.5 squares

Right side is about 1.8

Bottom about 3.5 and left side about 1.2.

Total approximately 41 square units.

2. If it is a right triangle then 2 sides will be perpendicular.

Slope of LM = (-1-4)/(3 +2 = -1

Slope of MN = (-4+1)/ -3 = -3/-3 = 1.

So as the product of the slope = -1 * 1 = -1 the angles between LM and MN is a right angle and LMN is a right triangle.

HELP I HAVE TO PASS!
What is the average rate of change for this quadratic function for the interval from x=0 to x=2?

A) -4
B) -2
C) 2
B) 4

Answers

Answer:

At X = 0     Y = 10

At X = 2      Y = 6

Rate of  change = change in Y / change in X = -4 / 2 = -2   or B

A custodian has 5 1/2 gallons of paint. Each of the bookcases she is painting requires 1/2 gallon of paint. How many bookcases will the custodian be able to paint with that amount of paint
A. 3
B. 4
C. 11
D. 15

Answers

It would be C:11, for every book case requires 1/2 a gallon so when you divide 5 1/2 / 1/2, you get 11 gallons in total

HELP ASAP PLEASE Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represents the amount of money in Alaina's account?​

Answers

Answer:

-17

Step-by-step explanation:

28-45= -17 dollars in her account

Two workers paint lines for angled parking spaces

Answers

Answer:

2nd option

Step-by-step explanation:

The lines are parallel because the angles are congruent since they are Alternate exterior angles.

Charlie weighed 8 lbs. 11 oz. at birth given that 1 pound is equivalent to 16 ounces what is Charlie’s birthweight expressed in ounces

Answers

Answer:

139 oz.

Step-by-step explanation:

If 1 pound equals 16 ounces, multiply 8 by 16 and you will get 128, then add the original 11 ounces to get 139.

question- pls help me find the answer ​

Answers

Answer:

(d) -1

Step-by-step explanation:

Hope you have good grades and study well..btw make me as brainliest....ty sweetie

(a) 1

The two diagonals are equal in length so we can write
3x - 2 = 2x - 1
3x - 2x = -1 + 2
x = 1

You could have substituted each answer until you found the one that worked.

A comet travels at an average speed of 273,000 km/h.
It takes 8 days for the comet to reach Earth.
Find the distance, in km, the comet travelled

Answers

Answer: 52,416,000 km

Step-by-step explanation:

If a comet travels 273,000 km/hr

1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day

2) multiply the answer from 1 by 8 to determine how far it travels in 8 days

1) [tex]\frac{273,000 km}{hr}[/tex]*[tex]\frac{24 hr}{1 day}[/tex] = [tex]\frac{6,552,000km}{day}[/tex] (hours cancel out)

2)[tex]\frac{6,552,000km}{day}[/tex]*8 day= 52,416,000 km in 8 days

The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)

What's the area
5.1 5.1 5.1 ?

Answers

Answer:

Are you talking about the are of a 3d cube? then it would be 156.06 because you take the length times width to get the area of one side then multiply it by 6 to gets all the sides.


Find the area of the isosceles triangle.
13 cm
10 cm
Overview
Pythagoras' Theorem - An Algebraic Approac View One Minute Version

Answers

Answer:

area of an isosceles triangle=bh/2

Step-by-step explanation:

base=10

height=13

10×13/2

=65

A shopkeeper bought bycicle for rs 3520 and a mobile for rs 4690 . he sold both the items for rs 8650 calculate how much money did he gain​

Answers

Answer:

Rs 440

Step-by-step explanation:

Price of bicycle = 3520

Price of mobile = 4690

Cost Price of both mobile and bicycle = 3520 + 4690

=> 8210

Selling price of both mobile and bicycle = 8650

Profit = selling price - cost price

= 8650 - 8210

= 440

Therefore he gained Rs 440

Find the Surface Area and the Volume.

Answers

Answer:

Surface area = 850 cm²

Volume = 1000 cm³

Step-by-step explanation:

Applying,

A = h(a+b+c+d)................ Equation 1

Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.

From the diagram in the question,

Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm

Substitute these values into equation 1

A = 25(6+14+7+7)

A = 25(34)

A = 850 cm²

From the volume,

V = A'h...................... Equation 2

Where A' = Area of the base.

From the diagram,

A' = 1/2(6+14)4

A' = 40 cm²

Therefore,

V = 40×25

V = 1000 cm³

Which of the following statement is incorrect? .
a.Closure property is true for subtraction of Rational numbers

b.Commutative property is true for subtraction of Rational numbers

c.Closure property is true for addition of Rational numbers

d.Closure property is true for multiplication of Rational numbers​

If you answer the question I will follow you

answer fast

Answers

Answer:

b.Commutative property is true for subtraction of Rational numbers

Step-by-step explanation:

Option B is the correct answer as it is the incorrect statment in the given options.

109.06 in scientific notation is

Answers

The correct answer is 1.0906
1.0906 if not sorry

1/6 of ______ equals 9

What is the blank?

Answers

Answer:

54

Step-by-step explanation:

1/6 × y = 9

y ÷ 6 = 9

y ÷ 6 × 6 = 9 × 6

y = 54

Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on all 7 days of a given week,and the average​ (mean) value is 120.7 volts.
A. The given value is a parameter for the week because the data collected represent a population.
B. The given value is a statistic for the week because the data collected represent a population.
C. The given value is a statistic for the week because the data collected represent a sample.
D. The given value is a parameter for the week because the data collected represent a sample

Answers

Answer:

A. The given value is a parameter for the week because the data collected represent a population    

Step-by-step explanation:

Parameters in a study refers to the numbers that are used to summarize the data for the entire population. Whereas, a statistic are used to summarize the data from a sample only.

In the context, it is given that a person measures the voltage supply to his home for all the seven days and finds the average value of the voltage. The homeowner here considers the population of his sample to make his study.

Thus it is a parameter for the entire week as the data represents a population.

A boat can carry 22 people 940 people went on the boat how many trips did the boat do

Answers

Answer:
42 trips

You just divide 940 by 22

Identify the pairs of congruent angles and proportional corresponding side lengths

Answers

Answer:

∠B=∠D, ∠C=∠E, ∠A=F.

Step-by-step explanation

FE/AC=6/8=3/4, FD/AB=9/12=3/4,DE/BC=13.5/18=3/4. Since all proportions are equal to 3/4, the corresponding side lengths are proportional.

Which expression can be used to convert 22 Australian dollars to US dollar

Answers

Answer:26.4

Step-by-step explanation:1.2 x22

Calculate the BMI for a woman who is 165 cm tall and weighs 65 kg. ​

Answers

According to BMI chart and their classification, BMI score of 23.88 for 65 kilograms weight & 165 cm tall indicates that your weight is Normal. The Body Mass Index of 23.88 is derived from the weight of 65 kilograms divided by the square of height 165 centimeters.

3(x - 4) = -3. Solve for x.

Answers

Answer:

x = 3

Step-by-step explanation:

3(x - 4) = -3

Divide by 3

3/3(x - 4) = -3/3

x-4 = -1

Add 4 to each side

x-4+4 = -1+4

x = 3

Answer:

x = 3

Step-by-step explanation:

Divide each term by  3  and simplify.

x - 4 = [tex]\frac{-3}{3}[/tex]

Cancel the common factor of  3 .

x - 4 = -1

Move all terms not containing  x  to the right side of the equation.

x = -1 + 4

Add -1 and 4.

x = 3

Hope this helps!

Find the investment value when compounded anually.
P = $120,000, r= 5.3%, t = 8 yr​

Answers

Given:

[tex]P=\$120,000[/tex]

[tex]r=5.3\%[/tex]

[tex]t=8\text{ years}[/tex]

To find:

The value of the investment when the interest is compounded annually.

Solution:

The formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is the principal, r is the rate of interest in decimal, n is the number of time interest compounded in an years, and t is the number of years.

The interest is compounded annually. So, [tex]n=1[/tex].

Substituting [tex]P=120000, r=0.053, n=1, t=8[/tex] in the above formula, we get

[tex]A=120000\left(1+\dfrac{0.053}{1}\right)^{1(8)}[/tex]

[tex]A=120000\left(1.053\right)^{8}[/tex]

[tex]A=181387.85936[/tex]

[tex]A\approx 181387.86[/tex]

Therefore, the value of the investment after 8 years is $181,387.86.

Which expression is equivalent to 3/x5y?

Answers

Answer:

option B

Step-by-step explanation:

[tex]\sqrt[3]{x^5 \ y} = (x^5 \ y )^\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ [ \ \sqrt[n]{x} = x^\frac{1}{n} \ \ , \ (xy)^a = x^a y^a]\\\\[/tex]

        [tex]= x^{ (5 \times \frac{1}{3} )} \ y ^{\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ ( x^a )^b = x^{ab} \ ]\\\\\\[/tex]

        [tex]= x^{\frac{5}{3} }\ y^{\frac{1}{3}}[/tex]

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