3. The t test for two independent samples - Two-tailed example
“Bullying,” according to noted expert Dan Olweus, “poisons the educational environment and affects the learning of every child.” Bullying and victimization are evident as early as preschool, with the problem peaking in middle school. Suppose you are interested in the emotional well-being of not only the victims but also bystanders, bullies, and those who bully but who are also victims (bully-victims). You decide to measure depression in a group of victims and a group of bully-victims using a 26-item, 3-point depression scale. Assume scores on the depression scale are normally distributed and that the variances of the depression scores are the same among victims and bully-victims.
The group of 30 victims scored an average of 21.5 with a sample standard deviation of 10 on the depression scale. The group of 27 bully-victims scored an average of 25.8 with a sample standard deviation of 9 on the same scale. You do not have any presupposed assumptions about whether victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:
H0
: μvictims
– μbully-victims
= 0
H1
: μvictims
– μbully-victims
≠ 0
You conduct an independent-measures t test. Given your null and alternative hypotheses, this is a test. To use the Distributions tool to find the rejection region, you first need to set the degrees of freedom. The degrees of freedom is .

The critical t-scores that form the boundaries of the rejection region for α = 0.01 are ± .
In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the null hypothesis is true. In order to calculate the standard error, you first need to calculate the pooled variance. The pooled variance is s2p
= . The standard error is s(M1 – M2)
= .
The t statistic is .
The t statistic in the rejection region. Therefore, the null hypothesis is . You conclude that victims have a different mean depression score than bully-victims. Thus, it can be said that these two means are different from one another.

Answer:27.5 i hope you really like this answer i hope its right too

Answer:

  46

Step-by-step explanation:

You want to know the number of regular pentagonal prism marshmallows that can be covered with 1.5 L of chocolate if each cm² takes 0.5 mL. The base area is 7 cm², and each rectangular face is 2 cm by 5 cm.

The area of each marshmallow is the sum of the areas of the 2 bases and 5 faces. Each face is a 2 cm by 5 cm rectangle, so has an area of ...

  A = LW

  A = (5 cm)(2 cm) = 10 cm²

The bases each have an area of 7 cm², so the total area is ...

  total area = base area + face area

  total area = 2 × 7 cm² + 5 × 10 cm² = 64 cm²

Each cm² takes 0.5 mL of chocolate to cover it, so the chocolate required for one marshmallow is ...

  (0.5 mL/cm²)(64 cm²) = 32 mL

1.5 L of chocolate is 1500 mL, so the number that can be covered is ...

  (1500 mL)/(32 mL/marshmallow) = 46 7/8

Kaitlyn can completely cover 46 marshmallows with the chocolate she has.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]

The values of x and y for the right triangle are 4 and 7.21

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

by Pythagoras, the hypotenuse for the bigger of the two triangles is calculated as;

√(6² + 9²) = 10.82

the angle opposite the side length 6 for triangle with hypotenuse 10.82 and the angle opposite the side length x for triangle with hypotenuse y are the same by proportion, so:

x/6 = 6/9 {opposite/adjacent}

x = 36/9 {cross multiplication}

x = 4

also;

4/y = 6/10.52 {opposite/hypotenuse}

y = 42.08/6

y = 7.21

Therefore, the values of x and y for the right triangle are 4 and 7.21

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Using a system of equations, the number of children and adults who attended the movies is as follows:

A system of equations is two or more equations solved concurrently.

A system of equations is also known as simultaneous equations.

The total number of people who went to the movies = 100

The unit cost of adult tickets = $4

The unit cost of children tickets = $2

The total sales = $276

Let the number of children who attended the movies = x

Let the number of adults who attended the movies = y

x + y = 100 ... Equation 1

2x + 4y = 276 ... Equation 2

Multiply Equation 1 by 2:

2x + 2y = 200 ... Equation 3

Subtraction Equation 3 from Equation 2:

2x + 4y = 276

-

2x + 2y = 200

2y = 76

y = 38

Substitute y = 19 in equation 1:

x + y = 100

x + 38 = 100

x = 62

Check in Equation 2:

2x + 4y = 276

2(62) + 4(38) = 276

124 + 152 = 276

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The writer can best improve their organization by reordering sentences to keep related ideas together.

Who is called writer?

Writers are individuals who use written words to communicate ideas, stories, or information to a particular audience. They may work in various fields such as journalism, creative writing, copywriting, technical writing, or academic writing. Writers can be novelists, poets, essayists, screenwriters, playwrights, and more, and their work can take many forms, such as books, articles, blogs, scripts, and speeches. Writing is a skill that can be developed and honed through practice, and good writers are able to engage and captivate their readers with their words.

Here,

The writer can best improve their organization by reordering sentences to keep related ideas together. Here's a possible reorganization of the text:

Ponies and horses have significant differences. Horses are considered to be over fifty-eight inches tall and usually live to be twenty-five to thirty years old. In contrast, ponies are generally shorter than horses, with a height of less than fifty-eight inches, and they tend to live longer, often up to thirty-five or even forty years.

This revision keeps the sentences that relate to each other together, creating a clear and logical progression of ideas. Additionally, it removes the redundant statement of defining ponies as a type of horse, which is already well-known information.

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The power emitted by the star's surface is much greater than the power generated by its interior.

a) The power generated by the star's interior can be calculated using the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(7x10^8)³ ≈ 1.41x10^27 cm³

Multiplying this volume by the power generated per cubic centimeter, we get:

P(interior) = 3x10^-7 watts/cm^3 x 1.41x10^27 cm^3 = 4.23x10^20 watts

The power emitted by the star's surface can be calculated using the formula for the surface area of a sphere:

A = 4πr²

Substituting r = 7x10^8 cm, we get:

A = 4π(7x10^8)^2 ≈ 6.16x10^18 cm^2

Multiplying this area by the power emitted per square centimeter, we get:

P(surface) = 6,000 watts/cm² x 6.16x10^18 cm^2 = 3.70x10^22 watts

We can see that the power emitted by the star's surface is much greater than the power generated by its interior.

b) Following the same process as in part (a), we get:

V = (4/3)π(5x10^12)³ = 5.24x10^38 cm³

P(interior) = 3x10^-7 watts/cm^3 x 5.24x10^38 cm^3 = 1.57x10^32 watts

A = 4π(5x10^12)^2 ≈ 3.14x10^26 cm²

P(surface) = 6,000 watts/cm^2 x 3.14x10^26 cm^2 = 1.88x10^30 watts

Again, we see that the power emitted by the star's surface is much greater than the power generated by its interior. However, the difference between the two quantities is much smaller in this case compared to the previous case.

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6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.

The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.

6. For a = 20, b = 99 using the Pythagoras Theorem we have:

x² = a² + b²

x² = 20² + 99²

x² = 9801

x = 99

7. For a = 60, b = 91 we have:

x² = 60² + 91²

x² = 10521

x ≈ 102.56

8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.

a = 20, b = 21, and c = 29

Here,

20² + 21² = 841

29² = 841

Hence, the triangle is right.

9. For a = 15, b = 19, and c = 24. We have:

15² + 19² = 556

24² = 576

The triangle is acute.

10. For a = 11, b = 23, and c = 26. We have:

11² + 23² = 650

26² = 676

The triangle is acute.

11. Using the Pythagoras Theorem we have:

x² = 53² - 45²

x² = 1044

x ≈ 32.28

The value of x is 32.28

12. x² = 41² - 9²

x² = 1600

x = 40

The value of x is 40.

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Answer:

Step-by-step explanation:

Answer:

63 answers

Hope this helps :p

The total number of questions to be answered correctly so that 75% of answers are correct is 63.

∵ To pass the assessment, the percentage of questions to be answered correctly = 75.

That means, for every 100 questions, the number of correct answers required = 75

∴ For 1 question, the number of correct answers required= 75/100

                                                                                         =3/4

But, the total number of questions in the assessment = 84

∴ For 84 questions, the number of correct answers required = 3/4×84

                                                                                                     = 63

Hence, the total number of questions to be answered correctly so that 75% of answers are correct is 63.

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As a result, Plan 4's $38.89 monthly premium is the lowest.

The monthly premium you pay for health insurance. You typically have to pay additional fees for your health care in addition to your premium, such as a deductible, copayments, and coinsurance.

(P + Simple Interest) / (500 + 58.33) / 14 = $42.02 is the formula for the monthly payment.

Plan 4: P = $500

t = 18/12 years, and r = 0.12

Simple interest equals $500 * 0.12/* (18/12) = $90.

(P + Simple Interest) / t = ($500 + $90) / 18 = $38.89 is the monthly payment.

Plan 5: P = $500

t = 12/12 years, and r = 0.14.

Simple interest is equal to $500 * 0.14 * (12/12) = $70.

(P + Simple Interest) / t = ($500 + $70) / 12 = $47.50 is the amount due each month.

As a result, Plan 4's $38.89 monthly premium is the lowest.

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Answer:

Step-by-step explanation:

To calculate how much you need to earn each month (January, February, and March) to be just over the gross income of $2495, you can divide that amount by 3 (since there are 3 months) and then add a small amount to ensure that you are over the limit. Here's how you can do that:

1) Divide the gross income by 3:

$2495 ÷ 3 = $831.67 (rounded to the nearest cent)

2) Add a small amount to each month's income to ensure that you are over the limit. You could add $1 or $5, for example. Let's say you add $5 to each month:

January: $831.67 + $5 = $836.67

February: $831.67 + $5 = $836.67

March: $831.67 + $5 = $836.67

So for each month, you should report an income of $836.67 (or whatever amount you calculated using the method above) to ensure that you are over the gross income limit of $2495.

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.

Given: Slope (m) = -2 and point (-2, -3)

Answer:

A watch manufacturer believes that 60% of men over the age of 50 wear watches. So, the manufacturer took a simple random sample of 275 men over the age of 50, and 170 of those men wore watches. Test the watch manufacturer's claim at α = 0.5 using PHANTOMS.

With regards to the above geometry problems the value of x are given below.

a) Here x = 15

b) here x = 28

These are solved using proportions.

Proportion helps to solve the above problems by setting two ratios equal to each other and cross-multiplying to solve for the unknown variable, which satisfies the ratio relationship between the two quantities.

a)

To solve for x, we can cross-multiply the fractions and simplify:

x/20 = 9/12

Cross-multiply:

12x = 9 * 20

Simplify:

12x = 180

x = 15

Therefore, the solution to the equation x/20 = 9/12 is x = 15.

b)
To solve for x, we can cross-multiply the fractions and simplify:

15/(x-3) = 18/(x+2)

Cross-multiply:

15(x+2) = 18(x-3)

Simplify:

15x + 30 = 18x - 54

Subtract 15x from both sides:

30 = 3x - 54

Add 54 to both sides:

84 = 3x

Divide both sides by 3:

x = 28

Therefore, the solution to the equation 15/(x-3) = 18/(x+2) is
x = 28.

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The expression can be said to be equivalent because they could be simplified to give the same result.

Equivalent expressions are two or more mathematical expressions that have the same value for all values of the variables involved. In other words, if you substitute the same values for the variables in two different expressions that are equivalent, you will get the same result.

Thus we can see that; 1/2x^3(8x + 10x^6) is equivalent to x^4(5x^4 + 4) as shown

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Answer:

300/65

Step-by-step explanation:

Answer:

3 65/100 then the simplified version is 13/20

Step-by-step explanation:

Answer:

320 would be the regular price

Step-by-step explanation:

The cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.

We need to use the vector cross product formula:

a × b = |a| |b| sin(θ) n

Where

Using the given values of ×, we have:

(+) × (5+4) = ⟨1, 1, 0⟩ × ⟨5, 4, 0⟩

= |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(θ) n

Where θ is the angle between ⟨1, 1, 0⟩ and ⟨5, 4, 0⟩. To find θ, we can use the dot product formula:

a · b = |a| |b| cos(θ)

⟨1, 1, 0⟩ · ⟨5, 4, 0⟩ = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| cos(θ)

1(5) + 1(4) + 0(0) = √2 √41 cos(θ)

9 = 2√41 cos(θ)

cos(θ) = 9/(2√41)

θ ≈ 20.11 degrees

Now we can plug in the values to find the cross product:

(+) × (5+4) = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(20.11) n

= √2 √41 sin(20.11) n

= (2/√41) ⟨-2sin(20.11), 3sin(20.11), 2√2cos(20.11)⟩

= ⟨-0.362, 0.536, 0.489⟩

Therefore, the cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.

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Answer:95

Step-by-step explanation: cause 320 - 225 = 95

Answer:

[tex]12\pi \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

r (radius) = 3 cm

h (height) = 4 cm

Find: A (lateral) - ?

[tex]a(lateral) = \pi \times r \times l[/tex]

[tex]a(lateral) = \pi \times 3 \times 4 = 12\pi \: {cm}^{2} [/tex]

The correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.

A statistical measure known as the standard deviation depicts how variable or dispersed a set of data is. It is determined by taking the square root of the variance, which is the sum of the squared deviations from the data set mean. While a large standard deviation suggests that the data points are more dispersed, a small standard deviation suggests that the data points tend to be close to the mean. It can be used to assess the variability between different data sets and is frequently used as a gauge of a data set's consistency or reliability.

Given, level of significance = 0.05.

n = 49 and sample > 30

Thus, using z-score we have:

z = 4.04 - 3.68 / (0.70/7) = 3.60

Now, p-value = 0.000318

Now, for P < 0.05 we have:

cohens D = 4.04 - 3.67 / 0.70 = 0.51

This shows a medium increase.

Hence, the correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.

The estimated Cohen’s d is given as:

Cohen’s d = (M - μ) / σ

The sample standard deviation is not given, so we cannot calculate the exact value of Cohen's d.

The sample standard deviation will determine the estimated Cohen's d in this situation, although if it is greater than 0.2, it might be regarded as having a small effect size.

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The two solutions of the quadratic equation x² + 11x - 26 = 0 are x = 2 and x = -13

Here we have the quadratic equation:

x² + 11x - 26 = 0

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

To solve it we need to use the quadratic formula, it will give:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}[/tex]

Now we can simplify that and we will get two solutions, these are:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}\\\\x = \frac{-11 \pm15}{2}[/tex]

Then the two solutions of the quadratic equation are:

x+ = (-11 + 15)/2 = 4/2 = 2

x- = (-11 - 15)/2 = -26/2 = -13

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Consequently, the loan's duration is roughly 0.6 years the loan's interest rate is roughly 22.5%And  the investment's principal is roughly $6,387.

An asset or thing is considered an investment if it is bought with the expectation that it may one day produce income or increase in value. A purchase of commodities that are not used right now but will be utilised to generate wealth down the road is referred to as an investment in the economic sense. Stocks, bonds, properties, and mutual funds are a few types of investments.

On the other hand, interest is the fee associated with the right to borrow money. Usually, it is stated as an annual percentage rate. (APR). The percentage of ownership a stockholder has in a firm is another definition of interest.

1. Using the formula below, we can determine the term (period) of a simple interest loan with a $450 principal, a 1.4% annual interest rate, and interest earnings of $37.80.

I = Prt

where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.

Inputting the values provided yields:

37.80 = 450 * 0.014 * t

Simplifying this equation, we get:

t = 37.80 / (450 * 0.014)

(t 0.6 years)

2. Using the formula below, we can determine the interest rate for a simple interest loan with a $425.00 principal amount and $286.88 in interest accrued over three years:

I = Prt

where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.

Inputting the values provided yields:

286.88 = 425 * r * 3

When we simplify this equation, we obtain:

r = 286.88 / (425 * 3)

r ≈ 0.225 or 22.5%

3. Using the technique below, we can determine the principal of an investment with simple interest that generated $25.81 in interest over the course of 8 months at an interest rate of 3.2%:

I = Prt

where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.

First, we must convert the seconds to years:

8 months equals 8/12 years.

Inputting the values provided yields:

25.81 = P * 0.032 * (8/12)

When we simplify this equation, we obtain:

P = 25.81 / (0.032 * (8/12))

P ≈ $6,387

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the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.

how to solve probability?

There are 38 possible outcomes for a single spin of the American roulette wheel. Out of these 38 slots, two are labeled 0 and 00, and half of the remaining 36 slots are red and half are black.

Therefore, the probability of the marble landing on a black slot is 18/38 or 9/19. This is because there are 18 black slots out of a total of 38 slots.

Similarly, the probability of the marble landing on a 00 slot is 1/38.

To find the probability of the marble landing on either a 00 or black slot, we can add the probabilities of these two events. That is,

P(00 or black) = P(00) + P(black)

= 1/38 + 9/19

= (1 + 18)/38

= 19/38

Therefore, the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.

It is important to note that while the probability of winning on a single bet in roulette may seem attractive, the game has a high house edge, meaning that the odds are in favor of the casino. Therefore, it is important to gamble responsibly and within one's means.

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f.  The height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm. g. when θ = 160 is -4.33 cm. h. g(θ) is 10. i. k = 150.

A function is a mathematical concept that describes the relationship between two sets of numbers or values, called the domain and the range. It assigns to each value in the domain a unique value in the range. The domain is the set of all possible input values, while the range is the set of all possible output values.

A function can be represented by an equation, a graph, or a table of values. The equation of a function typically has a variable, often denoted as x, that represents the input or independent variable, and a formula that expresses how the input is transformed to obtain the output or dependent variable, often denoted as y.

f. At 6:00 am, the minute hand is pointing directly up, so the angle rotated by the minute hand from 6:00 am is θ = 0. Plugging this into the function h(θ) = 10 cosθ + 13, we get:

h(0) = 10 cos(0) + 13 = 23

So, the height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm.

g. To find the height of the endpoint of the hour hand above the bookshelf when θ = 160, we need to convert θ to the angle rotated by the hour hand from 6:00 am. Since the hour hand rotates 30 degrees for every hour, or 0.5 degrees per minute, the angle rotated by the hour hand from 6:00 am is 30(5) + 0.5(0) = 150 degrees.

So, we need to find g(150), which is:

g(150) = -10 cos(150/12) + 13 = -4.33

Therefore, the height of the endpoint of the hour hand above the bookshelf when θ = 160 is -4.33 cm.

h. The amplitude of g(θ) is the absolute value of the coefficient of the cosine function, which is 10. So, the amplitude of g(θ) is 10.

i. The endpoints of the minute hand and hour hand meet when they are pointing in the same direction, so the angle rotated by the minute hand from 6:00 am must be a multiple of 30 degrees. To find the smallest possible value of k, we need to find the smallest multiple of 30 that is greater than or equal to 150 (the angle rotated by the hour hand from 6:00 am). This is 30(5) = 150.

So, the smallest possible value of k is when the minute hand has rotated 150 degrees from 6:00 am, which is at 5:00 am and 30 seconds. Therefore, k = 150.

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The expression which represents the model is (3 × 2/5). The Option C is correct.

A modeling refers to the process of creating a representation of a real-world scenario to make a prediction or provide insight.

In the given question, it can be observed that the model contains 10 parts in total with a division of 5 each into 2 parts.

Since the division of 2 is made thrice, it gives us:

3 × 2/5

Hence, this makes the third option (3 × 2/5) the correct one.

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H0 is the null hypothesis stating with that the population proportion of

puppies who are spotted is less than or equal to 0.25,

H0: p <= 0.25

H1: p > 0.25

In a scientific setting, a hypothesis (plural: hypotheses) is a tested

claim regarding the causal connection between two or more variables

or a suggested explanation for a phenomenon that has been

observed.

where H0 is the null hypothesis stating that the population proportion

of puppies who are spotted is less than or equal to 0.25, and H1 is the

alternative hypothesis stating that the population proportion of puppies

who are spotted is greater than 0.25.

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Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

The area of the rectangle is d. 54 square units.

A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.

The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.

From the given points, we can see that the length of one pair of parallel sides of the rectangle is:

4 - (-5) = 9 units

And the length of the other pair of parallel sides of the rectangle is:

2 - (-4) = 6 units

Therefore, the area of the rectangle is:

9 units × 6 units = 54 square units.

So the area of the rectangle is d. 54 square units.

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