Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 a. Find the mode. b. Find the median. c. Find the mean, to the nearest tenth. d. Find the midrange. e. Find the standard deviation, to the nearest hundredth. f. Determine the quartiles.

Answers

Answer 1

Answer: a. 43

b. 27

c.  34.8

d. 45

e. 17.72

f. First quartile = 23

Second quartile = 27

Third quartile =43

Step-by-step explanation:

The given set of data:  24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

Arrange in Ascending order:

12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25 , 29, 31, 43, 43 , 43 , 53 , 53, 65 , 78

Total data points: n= 18 ( even)

a. Mode= Most repeated data value = 43

i.e. mode =43

b. Median = [tex]\dfrac{(\frac{n}{2})^{th}\text{term}+(\frac{n}{2}+1)^{th}\text{term}}{2}[/tex]

[tex]=\dfrac{(\frac{18}{2})^{th}\text{term}+(\frac{18}{2}+1)^{th}\text{term}}{2}\\\\=\dfrac{9^{th}\text{term}+10^{th}\text{term}}{2}\\\\=\dfrac{25+29}{2}\\\\=27[/tex]

i.e. median = 27

c. Mean = (sum of data points)÷n

Sum =12+18+18 + 20 +23 +24 + 24 +25 + 25 + 29+ 31+ 43+ 43 + 43 + 53 + 53+ 65 + 78=627

Mean = 627 ÷ 18 ≈34.8

i.e. Mean = 34.8

d. Mid range = [tex]\dfrac{\text{Maximum value +Minimum value}}{2}[/tex]

[tex]=\dfrac{78+12}{2}\\\\=\dfrac{90}{2}\\\\=45[/tex]

e. Standard deviation =[tex]\sqrt{\dfrac{\sum (x-mean)^2}{n}}[/tex][tex]\sum (x-\mean)^2=(12-34.8)^2+(18-34.8)^2+(18 -34.8)^2+( 20 -34.8)^2+(23 -34.8)^2+(24 -34.8)^2+( 24 -34.8)^2+(25 -34.8)^2+2( 25 -34.8)^2+( 29-34.8)^2+( 31-34.8)^2+( 43-34.8)^2+( 43 -34.8)^2+( 43 -34.8)^2+( 53 -34.8)^2+( 53-34.8)^2+( 65 -34.8)^2+( 78-34.8)^2\\\\=5654.56[/tex]

[tex]\sqrt{\dfrac{5654.56}{18}}=\sqrt{314.1422}\approx17.72[/tex]

f. First quartile = Median of first half (12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25)

= 23  (middle most value)

Second quartile = Median = 27

Third quartile = Median of second half (29, 31, 43, 43 , 43 , 53 , 53, 65 , 78)

= 43 (middle most value)


Related Questions

Complete each ordered pair so that it is a solution of the given linear equation.

x - 4y = 4; (_,3), (4,_)

Answers

Answer: (16,3)  and (4,0)

Step-by-step explanation:

Using the equation x-4y=4  is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.

x-4(3)=4  multiply the left side

x - 12 = 4   add  12 to both sides

x= 16

You will now have the coordinates (16,3)  

In the second pair it gives the x coordinate which is 4 but we need to solve for y.  

4 - 4y=4  subtract 4 from both sides

-4        -4

 -4y = 0  Divide both sides by 4

    y = 0

The ordered pair will be (4,0)

∠3 and ∠6 can be classified as:

Answers

Answer:

Alternate Interior Angles

Step-by-step explanation:

Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.

Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.

Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.

Therefore, we are left with Alternate Interior Angles.

Answer:

angle 3 and angle 6 are

1) Alternate Angles

2) Interior Angles

Step-by-step explanation:

(see attached for reference)

What fraction of a ton is a pound?

Answers

Answer:

There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.

Answer:

5/100000 tons

Step-by-step explanation:

x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please

Answers

Answer:

  x = s, y = t, z = -6 -s -t

Step-by-step explanation:

These are dependent equations. For some values s and t, the solution is ...

  x = s, y = t, z = -6 -s -t

Find the sum of the first 12 terms of the sequence 512, 256, 128, …

Answers

Answer: 1023.75 (a)

Step-by-step explanation:

The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.

a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.

Now to calculate the sum, we consider two formula here and select the one that is most appropriate,

(1)  a( rⁿ - 1 )/r - 1, when r is greater than 1

(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.

In this question, formula 2 shall be appropriate because r is less than 1.

so,

S₁₂      =  512( 1 - 0.5¹² )/1 - 0.5

             512( 1 - 2.44 ₓ 10⁻⁴ )/0.5

          = 512( 0,9998 )/0.5

          = 511.875/0.5

          = 1023.75

The answer is a

Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.

Answers

Answer:

x ≈ 4.5

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

Here k = 76 and y = 17 , thus

17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )

17x = 76 ( divide both sides by 17 )

x ≈ 4.5 ( to the nearest tenth )

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.

Answers

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.

The calculation for total surface area:

Let the total surface of the rectangular box be expressed as:

S = 2xy + 2yz + 2xz

where,

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz .................(1)

Given:

Volume V = xyz = 8000 .............(2)

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since, Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20*20*20.

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Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.

Answers

Answer:

Solution : Third Option

Step-by-step explanation:

The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.

[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]

Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.

Therefore, the third option is a solution to the system.

Which expression is equivaleny to 0.7 + p + 0.86p?

A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p

Answers

Answer:

None of the above.

1.86p + 0.7

Step-by-step explanation:

Step 1: Write expression

0.7 + p + 0.86p

Step 2: Combine like terms

0.7 + 1.86p

None of those answer choices are correct unless you wrote the problem incorrectly.

wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of

Answers

Answer:

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Step-by-step explanation:

A test for the difference between two population means is to be performed.

As the population variances are known, the z-test will be used.

The hypothesis can be defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ

Assume that the significance level of the test is, α = 0.05.

The critical region can be defined as follows:

The critical value of z for α = 0.05 is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]

Use a z-table.

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

What is the x-intercept?

Answers

Answer: x-intercept = -94, -74, and -54

The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?

Answers

Answer:5

Step-by-step explanation:

A teacher shares sweets among 8 students so they get 6 each. How many sweets would they each have got if there had been 12 students? ​

Answers

Answer:

4 sweets

Step-by-step explanation:

we know that there is a total of 48 sweets being handed out, and we can tell that this is an example of inverse proportion:

when one increases the other decreases

So, we multiply 8 * 6 to get 48, and then divide that by 12 to get 4 which is how many each student gets

for some constant k -> xy/z=k

Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.

Answers

Answer:

A. The point that splits a line segment into two equal parts.

Step-by-step explanation:

A. The point that splits a line segment into two equal parts.

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.

Learn more about Midpoint:

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#SPJ5

please answer! I need these points for grade!

Answers

Answer:

∡NMO = 59°

Step-by-step explanation:

if MO bisect =>

=> ∡LMN = 2∡LMO =>

=> 5x - 22 = 2(x + 31)

5x - 22 = 2x + 62

5x - 2x = 62 + 22

3x = 84

x = 28°

∡LMO = ∡NMO => ∡NMO = x + 31

=> ∡NMO = 28 + 31 = 59°

The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in

Answers

Answer:

396 in^2

Step-by-step explanation:

The perimeter of a triangle is given by the formula:

● P = 2w+2L

L is the length and w is the width

■■■■■■■■■■■■■■■■■■■■■■■■■■

The width hereis 18 inches and the perimeter is 80 inches.

Replace w by 18 and P by 80 to find L.

● P= 2L+2w

● 80 = 2L + 2×18

● 80 = 2L + 36

Substrat 36 from both sides

● 80-36 = 2L+36-36

●44 = 2L

Divide both sides by 2

● 44/2 = 2L/2

● 22 = L

So the length is 22 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area of a rectangle is given by the formula:

● A= L×w

● A = 22×18

● A = 396 in^2

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.

Answers

Answer:

[tex]\large \boxed{\$10000.00}[/tex]

Step-by-step explanation:

We can use the formula for continuously compounded interest.

[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]

Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.

Answers

Mathematics can be tricky so precise definitions are important. Without them there can be confusion which more often then not will generate a wrong answer. With clear precise definitions it is easier to understand the topic. Therefore, it is easier to get the correct answer.

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

Answers

Answer:

Margin of Error = z∝/2 * Standard Error

Step-by-step explanation:

The formula for standard error is given by

SE = [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.

Now Margin of Error is given by

ME = z∝/2 * Standard Error

The confidence level is used to estimate the value of alpha.

For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96

Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0

Answers

Answer:

x=0 or x=2 or x=−4 or x= (7)(2)

Step-by-step explanation:

How much work is done in lifting a 1.4-kg book off the floor to put it on a desk that is 0.7 m high?

Use the fact that the acceleration due to gravity is g = 9.8 m/s^2. How much work is done in lifting a 21-lb weight 6 ft off the ground?

Answers

Answer:

Step-by-step explanation:

Work is said to be done when a force applied to an object cause the body to move in a specified direction.

Work-done = Force * Distance

Since Force = mass * acceleration due to gravity

Work-done =  mass * acceleration due to gravity * distance

Given mass = 1.4kg, distance = 0.7m and g = 9.8m/s²

Workdone in lifting the book off the floor = 1.4*0.7*9.8

Workdone = 9.604Joules

- Similarly, work done in lifting a 21-lb weight book 6 ft off the ground is expressed using the same formula as above;

Given mass = 21-lb, g = 32ft/s² and distance = 6ft

Workdone = 21 * 32 * 6

Workdone = 4,032 lb-ft²/s²

Hence, work-done in lifting a 21-lb weight book 6 ft off the ground is  4,032 lb-ft²/s²

The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.

Answers

Answer:

d. 25.25.

Step-by-step explanation:

A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.

32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:

A. x = 0, −5, 1.7i, −1.7i

B. x = 0,−5, 1.7i

C. x = −5, 1.7i, −1.7i

D. x = 0,−3, −5

Answers

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

|5x|=3 please help me

Answers

Answer: see below

Explanation:

|5x| = 3

5x = 3
x = 3/5

5x = -3
x = -3/5

12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state

Answers

Answer:

0.8343

Step-by-step explanation:

From the question, we have the following values:

Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75

Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25

P = 0.25

n = number of random variables = 9

The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:

P < 4 = P ≤ 3

n = 9

P(x) = n!/(n - x)! x! × p^x × q^(n - x)

x = 3

p = 0.25

q = 0.75

P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)

P(x) =0.8343

The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.

Given information:

75% of the vehicles passing through a checkpoint are from within the state.

So, the probability that the vehicle is from within the state is 0.75.

The probability that the vehicle is from outside the state will be 1-0.75=0.25.

Now, let x be the random variable. So, the value of n=9. and x<4

It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.

So, [tex]x< 4[/tex], p=0.25 and q=0.75.

So, the required probability can be calculated as,

[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]

Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.

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NEED HELP ASAP trig question!! Need to find y!!

Answers

Answer:

Hey there!

Tangent 70=12/y

Tangent 70y=12

y=12/Tangent 70

y=4.37 cm

Let me know if this helps :)

find the derivative of f(x)=3x^2✓x​

Answers

Answer:

  [tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]

Step-by-step explanation:

The power rule applies.

  d(x^n)/dx = nx^(n-1)

__

  [tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]

Use the gradient to find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye^z, P(2, 4, 0), Q(0, 0, 0)

Answers

Answer: Find answer in the attached files

Step-by-step explanation:

PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.

Answers

Answer:

The answer is

15x - y = - 126

Step-by-step explanation:

To find the equation of the line we must first find the slope (m)

[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]

So the slope of the line using points

(-8,6) (-9,-9) is

[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]

So the equation of the line using point (-8,6) and slope 15 is

y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form

Ax+By=C

We have

15x - y = -120-6

The final answer is

15x - y = - 126

Hope this helps you

Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05

Answers

Answer:

Calculated χ² = 13.425

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

Step-by-step explanation:

Color             Blue      Orange     Green    Red   Yellow    Brown

Frequency     30         48              55        66         70         131

Expected      40           40              40        80          80        120

H0:  The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown

Ha: The color distribution is not equal to  the distribution stated in the null hypothesis.

Calculate chi square

χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120

χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425

The critical region for χ²  for 5 degrees of freedom with ∝= 0.05 is

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

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