A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food rewards were equal in appeal. Thus, a pilot study was designed in which participants were asked which of the rewards they preferred. The observed frequencies are as follows:

Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.

1. The appropriate statistical test for this problem is (be specific): ________.

2. What are the expected frequencies for this question?

3. What is the cutoff on the comparison distribution (step 3)?

4. What is the correct calculation for chi-square (step 4)?

Answers

Answer 1

Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

1.

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

2.

To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]

[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]

[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]

3.

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]

The rejection region is then X²₂ ≥ 7.378

4.

[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]

I hope this helps!


Related Questions

Distance between (-1,0) and (8,6)

Answers

Answer:

3 √ 13

Step-by-step explanation:

Answer:

3√13

Step-by-step explanation:

We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]

Thus, the answer is 3√13.

~ an aesthetics lover

Which of the following are perfect squares? Check all that apply.

Answers

Answer: 16, 64, and 49

Step-by-step explanation: Perfect squares are products made by squaring or multiplying a whole number by itself twice.

11 is not a perfect square since nothing can

be multiplied by itself to give us 11.

The same is true for 62 and 15.

16 is a perfect square since it's possible to find a whole number that can be multiplied by itself to give us 16.

That number is 4 since 4 × 4 = 16.

64 is also one since 8 can be multiplied by itself twice to give us 64.

49 is also one since 7² or 7 × 7 is 49.

Answer:D,E and F

Step-by-step explanation:

Perfect squares are numbers in which their square roots are whole numbers.

From the options

√16 =4

√64 =8

√49 =7

Fifteen mothers were asked how many months old their babies were when they cut their first tooth. The results are shown below.

8, 8, 6, 8, 9, 10, 5, 7, 9, 5, 9, 7, 6, 8, 7

Find the range and the outlier(s), if any, of the data set.

Answers

range 5
there are no outliers

Solve |6k + 12| + 9=9 for k

Answers

|6k+12|=0
6k+12=0
K=12/6= -2 or 2

Answer:

k= -2

Step-by-step explanation:

Solve for a,b,and/or c
Help solve ASAP!

Answers

Answer:

a=90-67=23°

.................

50 POINTS!!!!!!! WILL MARK BRAINLIEST! NO COPY/PASTE! TWO TO THREE SENTENCES AND EXPLAIN! WILL REPORT STUPID ANSWERS! According to Nikita Khrushchev, Premier of the Soviet Union, which of the three events had the potential to advance Soviet interests the most? The three events are the Cuban Missile Crisis, The Space Race, and The Berlin Wall.

Answers

Answer: Soviet leader Nikita Khrushchev had gambled on sending the missiles to Cuba with the specific goal of increasing his nation's nuclear strike capability.

Step-by-step explanation:

The Soviet Union signed a treaty with Hitler, the U.S. kept the atomic bomb a secret, and the U.S. took a long time to attack Hitler. France, Britain, and the United States wanted to reunify Germany, so they combined their areas into West Germany. Soviets cut off transportation to West Berlin. This lead to the United States and Britain using the Berlin airlift to bring food/supplies into the isolated part of Soviet occupied West Berlin.

12 divided by 9 tenths and hundredths

Answers

1.333 the answer I hope help

How to find the area of the seating area

Answers

Parallelogram area is base times height.  Base of 14, height of 10,

Answer: A = (14 ft)(10 ft)    second choice

Answer:

choice B

Step-by-step explanation:

How to add or subtract this polynomial

Answers

Answer:

18x^2 + 9x - 5

Step-by-step explanation:

Combine like terms:

(9x^2-8) + (9x^2+9x+3)

= 9x^2 + 9x^2 + 9x - 8 + 3

= 18x^2 + 9x - 5

Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?

Answers

Answer:

6.44 m2                                                                      

Step-by-step explanation:

1.] What is the probability of choosing a king
from a standard deck of playing cards?

Answers

Answer:

1/13

Step-by-step explanation:

there are 4 kings in a deck of 52 cards.

4/52 = 1/13

Look at recent question

Answers

Answer:

ok was it college math if so the I don't know

Factorise 2y^2 + y + 6xy + 9x - 3​

Answers

Answer: (2y+3)(3x+y-1)

Step-by-step explanation:

First regroup the terms.

6xy+9x+2y^2+y-3

Second factor 3x out of 6xy+9x

3x(2y)+9x+2y^2+y-3

3x(2y)+3x(3)+2y^2+y-3

And you get

3x(2y+3)+2y^2+y-3

Third factor by grouping


Two part-time employees share one full-time job. A girl works Mondays. Thursday, Wednesdays, and Fridays, and a boy works Tuesdays. The job pays an annual salary of $28,612. What annual salary does each employee earn?
The girls salary is______

Answers

One year is 52 week, days of work is 5, 5*52 week is 260 days. One year salary is 28,612, use 28,612/ 260 =110.05 a day. If the boy works only one day a week the he only work 52 day in a year, so is 52*110.05=5722.4 for the boys.
Then use 28612-5722.4= 22889.60 is the girls salary

Which of the following statements is FALSE? The correlation coefficient equals the proportion of data points that lie on a straight line. The correlation coefficient will be +1.0 only if all the data lie on an upward-tilting straight line. The correlation coefficient is undefined if all the data lie on a perfectly horizontal straight line. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.

Answers

Answer:

The first one is False.

Step-by-step explanation:

If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.

-3b+7=13 solve for b

Answers

Answer:

b = -2

Step-by-step explanation:

Start with your given:

-3b + 7 = 13

Subtract 7 on both sides:

-3b = 6

Then, divide -3 on both sides and solve:

b = -2

Answer:

b = -2

Step-by-step explanation:

You start by subtracting the 7 on the left and move it to the other side. Then you have 6 on the right and -3b on the left. Then you divide the -3 on each side and that gives you b= -2.

Hope this helps.


What percentage of students who take honors English are taking a non-honors math class?

Answers

Answer:

B

Step-by-step explanation:

Took quiz GL

Answer:

the answer is not B

Step-by-step explanation:

the answer is A I actually took the quiz

A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?

Answers

Answer:

  about 76.2°

Step-by-step explanation:

The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.

  Tan = Opposite/Adjacent

  tan(angle) = (33,500/8,200)

  angle = arctan (335/82) ≈ 76.246°

The angle of elevation is about 76.2°.

PLS HELP ME!
Um doing venn digrams so u have to set one up for it to work... TWENTY POINTS

Answers

Answer:

Creating a diagram..

Step-by-step explanation:

Alrighty, I've made a diagram. I've even uploaded it so everyone can see how good at drawing I am (not)

a. 7 do not own anything.

b. the probability that someone owns a bone or a stick is 50%.

c. the probability that someone owns a rock and a bone is 14%.

d. the probability that someone owns at least 2 items is 42%.

e. the probability that someone owns only 1 of these items is 51%.

Please tell me if im wrong! im only a student .m.

find the value of p in the following equation: 6 * 2/4 = p * 1/4

Answers

Answer: [tex]p=12[/tex]

Step-by-step explanation:

[tex]6*\frac{2}{4}=p*\frac{1}{4}[/tex]

Solve the multiplication on the left side.

6 and 4 can be simplified.

6/2=3

4/2=2

Leaving it like;

[tex]3*\frac{2}{2}=p*\frac{1}{4}[/tex]

2 and 2 is 1 and 3 times 1 is 3.

[tex]3=p*\frac{1}{4}[/tex]

Multiply by 4 to eliminate the fraction and isolate p.

[tex]4*3=p*\frac{1}{4}*4\\12=p[/tex]

Solve for x - y = -3

Answers

Answer:

0-3=-3

Step-by-step explanation:

What is x:
1. X-y= -3
2. Add y to both sides
3. X= -3+y

What is y:
1. X-y= -3
2. Subtract x from both sides
3. -y=-3-x
4. Divide both sides by negative 1
5. y=3+x

Solution;
-3+y, 3+x

Hope this helps!!

A 6-sided die is rolled three times. What is the probability of rolling a 4 each time?
A 0.00463
B. 0.99537
C 0.16667
D. 0.00231

Answers

Answer:

a

Step-by-step explanation:

math

The formula A=12(b+c)h. Write the equation in term of c?

Answers

Answer:

[tex]c = \frac{A}{12h} - b[/tex]

Step-by-step explanation:

Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!

Hope this helped! :)

The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDEF)?

Answers

Answer:

D,E

Step-by-step explanation:

hope I helped

Round 0.378 to the place underlined digit 3

Answers

Answer:

0.38

Step-by-step explanation:

7 is the 3rd digit, so 8 is greater then 5, so you round up, if it is correct, can you give brainiest

Answer:

0.40

Step-by-step explanation:

this is because the number before it is up to five and even more than 5 so we round it up by adding one to the next number and the remaining digit to zero

The table shows the number of cups of water required when cooking different amounts of rice.

Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.

The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation

Answers

Answer:

The amount of water is the dependent value.The amount of rice is the independent value.

Step-by-step explanation:

The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.

That makes "water" the dependent variable, and "rice" the independent variable.

  The amount of water is the dependent value.

  The amount of rice is the independent value.

Answer:

The amount of water is the dependent value.

The amount of rice is the independent value.

Step-by-step explanation:

Two forces are acting on an object at the same point. Determine the angle between the two forces. (-2,7) and (3,-1)

Answers

The answer is 56 degree

Answer:

It is 124 degrees.

Step-by-step explanation:

You square each coordinate like this:

sqrt(x^2+y^2 )

You will end up getting sqrt(53 and sqrt(10.

Then find the dot product which is -6+-7=-13.

Then cos^-1(-13/sqrt53*sqrt10)

=124 degrees

One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V. Which function can be used to find the number of ounces of coffee in the can based on its radius? C(V(r)) = 32.768πr3 C(V(r)) = 3.2πr3

Answers

Answer:

C(V(r)) = 3.2πr3

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

[tex]C(V(r))=3.2(\pi r^{3} )[/tex]

Therefore, the right answer is the last choice.


A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies does the bookstore have left?

Answers

Answer:

30

Step-by-step explanation:

1/3 of 60 is 20

40 would be left

1/4 of 40 is 10 so 30 would be left

A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.

Answers

Hey there! I'm happy to help out!

As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.

However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:

[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]

So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!

[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512

However, we want to find how much he has done in total! So, let's find how much he did on the other squares!

[tex]2^8[/tex]= 256

[tex]2^7[/tex]=128

[tex]2^6[/tex]=64

[tex]2^5[/tex]=32

[tex]2^4[/tex]=16

2³=8

2²=4

[tex]2^1[/tex]=2

[tex]2^0[/tex]=1

Now, we add these all up to find the total grains of rice!

512+256+64+32+16+8+4+2+1=895

Therefore, George has placed a total of 895 grains of rice on the chess board.

I hope that this helps! Have a wonderful day!

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

What is a geometric sequence?

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

On the first square, George placed 1 grain of rice.

On the second square, he placed 2 grains.

On the third square, he placed 4 grains.

On the fourth square, he placed 8 grains.

In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.

So,

On the first 10 squares,

1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]

This is a geometric series with a first term of 1 and a common ratio of 2.

The sum of the first n terms of a geometric series.

[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Substituting the values,

[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)

    = 1(1 - 1024) / (-1)

    = 1023

Therefore,

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

Learn more about geometric sequence here:

https://brainly.com/question/2321576

#SPJ7

Other Questions
By years end, what is the total amount Whitney paid for the fund sharesHow many shares does Whitney own at the end of the year?What is the value of Whitneys fund on December 5What is the average price Whitney paid per share?Using the costs shown, what is the overall average cost per share for the 12-month period What has an ionised atom lost or gained?ProtonsGamma RaysElectronsNeutrons Please help, its a math question On a coordinate plane, a circle has a center at (4, 5) and a radius of 3 units.Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?(x 4)2 + (y 5)2 = 2(x 4)2 + (y 5)2 = 4(x 5)2 + (y 4)2 = 2(x 5)2 + (y 4)2 = 4 Which sentence uses a active verb?A. Julie is studied by motivational speakers all the time.B. Wallace will never finish studying for his test.C. Julie was known as a woman on a mission.D. Wallace inhaled his lunch since he needed to study for a test. Which of the following groups of parrots is most likely in Hardy-Weinberg equilibrium? A. A group with 50 DD parrots, 30 Dd parrots, and 20 dd parrots. B. A group with 30 DD parrots, 40 Dd parrots, and 30 dd parrots. C. A group with 25 DD parrots, 50 Dd parrots, and 25 dd parrots. D. A group with 50 DD parrots, 25 Dd parrots, and 25 dd parrots. Outsiders: Pony boys values and beliefs ? A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube. PLEASE HURRY!!IM BEING TIMED!WILL NAME BRAINLIEST!!The table and graph show that each cracker in a package has 7 calories.Crackers and Caloriescrackers(X) calories(Y)1 72 143 214 28Which statement about the graph is true?A.)The number of crackers is the dependent variable, and the number of calories is the independent variable.B.)The point (42, 6) is on the line.C.)The number of crackers are graphed on the y-axis, and calories are graphed on the x-axis.D.)The two variables are the number of crackers and the number of calories.(Picture not option!just a graph!) A bedroom wall is to be painted around a window as shown below. A rectangle with length 11 feet and width 10 feet. A smaller rectangle with length 3 feet and width 2 feet is cut out of the larger rectangle.What is the area of the wall that will be painted?A.6 feet squaredB.104 feet squaredC.110 feet squaredD.116 feet squared Red squirrels and gray squirrels have been the native species on an island for many years. A few years ago, black squirrels entered this island. The black squirrel is an invasive species. Invasive species aren't native to the ecosystem. They move into an ecosystem because of natural changes or human intervention. Red squirrels and black squirrels have identical food requirements, but gray squirrels have a different diet. What three effects will these events have on the island's squirrel population? can someone help with this please,, also explain if you can.. hey can anyone pls help me out in dis!!!!!!!!! Which choice is equivalent to the quotient shown here for acceptable values of x? Select the correct answer.Which transitional word correctly begins the second sentence in this paragraph?Like many realist writers, Tolstoy uses a simple writing style in his novella The Death of Ivan Ilych. much of what the author tellsreaders about Ivan Ilych's state of mind is not matter-of-fact description. Tolstoy is in effect conveying his protagonist's despair at hisapproaching death.OAMoreoverOBHoweverC. AlthoughD. ThereforeResetNextstum. All rights reservedGood Writing Versu...10:38 PMD# de 5/14/2020Which is the correct answer Crane Corporation had the following 2020 income statement. Sales revenue $197,000 Cost of goods sold 124,000 Gross profit 73,000 Operating expenses (includes depreciation of $19,000) 48,000 Net income $25,000 The following accounts increased during 2020: Accounts Receivable $10,000, Inventory $10,000, and Accounts Payable $11,000. Prepare the cash flows from operating activities section of Cranes 2020 statement of cash flows using the direct method. Comparing the skeletons of which of the following fish wouldbest show the evolution of a fish species?a male fish and a female fish that could produce offspringthe same fish just before it received a cut and after it healeda fish that lived recently and a fish that lived a long time agothe same fish just after it hatched and when it was full-grown Find the area. The figure is not drawn to scale.1.36 in.40 in.33 in.- You can repair your furnace for $500 and it will last 5 more years, but your heating bills will cost you about $1500 per year. Alternatively, a new furnace can be installed for $3000 that will reduce your annual heating bill to $1200. Suppose you sell the house in 5 years and receive an additional $1000 in the sales price of your home (salvage value) because of having a fairly new furnace. Should you replace it? Use a 5-year analysis period and a MARR of 5% 71. When making decisions that are ethical under either profit maximization or corporate citizenship theories, a business should include all of the following steps except a. recognize that there is an ethical issue in the decision. b. apply ethical theories to reasonable alternatives. c. publicize the options you rejected with your reasons. d. reflect on the outcome of the decision once it is made