. Suppose you wish to find out the answer to the questions "Do Americans prefer Coke or Pepsi?" You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. Results of your taste test indicate that 53 of 100 individuals prefer Pepsi. Conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to coca cola. Use the ???? = 0.05 level of significance.

Answer:

The common difference is 0.38

Step-by-step explanation:

If you look at the data, you can find that the y-value is getting 0.38 added to it. 24 + 0.38 is 24.38. 24.38 + 0.38 is 24.76. 24.76 + 0.38 = 25.14. Therefore, the common difference is 0.38.

Answer:

0.38

Step-by-step explanation:

It was right when I did it on flvs.

(1) 132.67 square meters

(2) 379.94 square meters

Step-by-step explanation:

A barn is in the shape of a rectangle with each corner angle a right angle.

[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]

Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.

Area of field grazed by goat = area of sector of circle

[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]

[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]

Answer:

Jelly Bean price per pound = $3.25, Trail Mix price per pound = $1.25

Step-by-step explanation:

Let jb = price per pound of jelly beans

Let tm = price per pound of trail mix

equation 1 -> 6*jb + 2*tm = 22

equation 2 -> 3*jb + 5*tm = 16

simplify equation 1

6*jb + 2tm = 22

2*tm = 22 - 6*jb

divide by 2

tm = 11 - 3*jb

plug this into equation 2

3*jb + 5*tm = 16

3*jb + 5*(11-3*jb) = 16

3*jb + 55 - 15*jb = 16

-12*jb + 55 = 16

-12*jb = 16 - 55

-12*jb = -39

jb = -39/-12

jb = 3.25

then, plug the cost per pound of jelly beans back into the simplified equation 1

tm = 11 - 3*jb

tm = 11 - 3*3.25

tm = 1.25

Answer:

the answer is 80%

Step-by-step explanation:

4/5 = 80%

Answer:

in fraction form that is 4/5   or .8 chance of getting a blue marble

Step-by-step explanation:

because you divide  the number of possible  winning out comes 4 marbles  by the total  event 5 marbles

Answer:

Answer: A

Step-by-step explanation:

The scenario best correlates with the principle of 'Acceptability' in money characteristics, where the Magic cards are accepted in place of traditional currency for trades on IMagicCards.com.

Magic Cards as Currency

The scenario you've described involves the trading of Magic: The Gathering cards on IMagicCards.com. This website uses the cards themselves as a form of currency instead of traditional money. Assessing the relation to characteristics of money, this system best correlates with Acceptability. Acceptability is a key attribute of money, signifying that it must be widely accepted for the purchase of goods and services. In this context, the acceptance of Magic cards for trades is equivalent to the principle of acceptability in currency.

The other options do not seem to fit as appropriately in this case. Portability involves the ease with which units of currency can be transported for use in purchasing or trade. Divisibility refers to the ability of money to be divided into smaller units without loss of value. Durability means the currency must withstand the physical wear and tear. Stability pertains to the value of the money remaining relatively stable over time.

https://brainly.com/question/32409590

#SPJ12

Answer:

x=13

Step-by-step explanation: (8x-44)+(8x-44)+(8x-44)=180

24x-132=180

24x=312

312/24

x=13

Showing Proof

8(13)-44=60

60+60+60=180

Therefore the answer is x=13

In the triangle in the given diagram, the value of x is 13

In the diagram, the value of ∠C = (8x -44)°.

To determine the value of x, we will first determine the measure of ∠C.

From the question,

Triangle ABC is equilateral

Recall that, each interior angle of an equilateral triangle equals 60°.

∴ m ∠C = 60°

Since the measure of ∠C = 60°

Then, we can write that

(8x - 44)° = 60°

Now, we will solve the above equation for x

8x° - 44° = 60°

First, add 44° to both sides

8x° - 44° + 44° = 60° + 44°

8x° = 104°

∴ x = 104° ÷ 8°

x = 13

Hence, in the given triangle, the value of x is 13

Learn more here: https://brainly.com/question/23421311

Answer:

59 cups

Step-by-step explanation:

We need to convert these into the same units first. Remember that 1 pint = 2 cups. This means that 30 pints is equal to 2 * 30 = 60 cups.

Now, we just subtract 1 cup from 60 cups: 60 - 1 = 59 cups.

Thus, the answer is 59 cups.

Hope this helps!

Answer:

29½ pints

Step-by-step explanation:

1 pint = 2 cups

1 cup = ½ pint

30 pints - 1 cup

30 pints - ½ pint

29.5 pints

Answer:

(C). ​(Probability of state A*Value in state A)+(Probability of state B*Value in state B)

Step-by-step explanation:

The expected value of a probability distribution, E(X) is defined as:

[tex]E(x)=\sum_{i=1} ^{k} x_{i} \cdot P(x_{i})\\$Where x=An Outcome\\P(x)=Probability of that Outcome[/tex]

Given Outcome A and B, the Expected Value  therefore is:

Expected Value = ​(Probability of state A*Value in state A)+(Probability of state B*Value in state B)

Final answer:

The expected value for two mutually exclusive events A and B is calculated as the sum of the products of the probabilities of each event and their corresponding values, thus option c is the correct answer.

Explanation:

The concept of expected value in probability is a fundamental idea in mathematics, particularly in probability theory and statistics. The expected value is calculated as the sum of all possible values, each multiplied by the probability of its occurrence. In the context of two mutually exclusive events A and B, the expected value is computed using the formula:

Expected value = (Probability of state A * Value in state A) + (Probability of state B * Value in state B).

Thus, the correct answer to the student’s question is option c.

Answer:

The answer is C) $197,263.70

Step-by-step explanation:

It's losing 6% PER year for the last 3 year.

You can do what I did and take $237,500 and times it 0.06. Which should give you 14,250, that is how much is lost in year one.

So subtract 14,250 from 237,500, you should have $223,250 now.

Repeat the first step with $223,250 now, you times it by 0.06 again and you should get 13,395, you subtract that from $223,250.

You have $209,855 now, once again times that by 0.06 and you get 12,591.30. Subtract 12,591.30 from 209,855 and you should end up with $197,263.70

It's a long, simple method and I'm sure there is another method of solving this question, but this is an easy way to get the answer.

Answer:

c

Step-by-step explanation:

because simple answer

Answer:

wdym

Step-by-step explanation:

The equation 7/8 + 0 = 7/8 demonstrates the Identity Property of Addition, which states adding zero to any number leaves it unchanged. This property highlights zero's role as the addition identity element.

The property illustrated by the equation 7/8 + 0 = 7/8 is known as the Identity Property of Addition. This property states that adding zero to any number or fraction does not change its value. It's an essential property in mathematics, underlining the concept that zero is the identity element for addition. This implies that adding zero to a number does not contribute any new value, essentially leaving the original number unchanged.

In broader mathematical contexts, understanding such properties helps in simplifying expressions and solving equations more efficiently. The identity property, similar to the concept of identity in multiplication (where multiplying by 1 leaves a number unchanged), plays a crucial role in developing more complex algebraic concepts and operations.

Answer:

The central line of the p-chart is 0.05.

Step-by-step explanation:

In statistical quality control, the p-chart is a form of control chart used to observe the proportion of non-conforming or defective components in a random sample, where the sample proportion of defective items is defined as the fraction of the number of defective units to the size of the sample, n.

The central line of the p-chart is given by:

[tex]CL=\frac{\sum np}{\sum n}[/tex]

It is provided that:

The sample selected from a shipment for inspection every day is of size, n = 50.

The average percentage of incorrect shipments is 5%, i.e. p = 0.05.

Compute the number defective units in the sample as follows:

[tex]np=50\times \frac{5}{100}[/tex]

Compute the central line of the p-chart as follows:

[tex]CL=\frac{\sum np}{\sum n}[/tex]

      [tex]=\frac{5\times 50}{100\times 50}\\[/tex]

      [tex]=0.05[/tex]

Thus, the central line of the p-chart is 0.05.

The center line for a p-chart is calculated as the average percentage of defects across all samples, which in this case is 5%.

The center line for a p-chart is calculated as the average percentage of defects across all samples.

In this case, the average percentage of incorrect shipments is 5%.

Hence, the center line for the p-chart in this scenario would be 5%.

Answer:

D) 4

Step-by-step explanation:

[tex]|3| + |-1| = 3 + 1 = 4 \\ [/tex]

Final answer:

To find the probability of selecting two male students from a class with 8 male and 7 female students, we multiply the individual probabilities. Hence, the answer is 4/15.

Explanation:

Probability of getting a male student in the first selection: 8/15

Probability of getting a male student in the second selection given the first is male: 7/14

Probability both selections are male students: (8/15) * (7/14) = 8/30 = 4/15

Answer:

51.0264 units squared

Step-by-step explanation:

1) convert the fractions into decimals.

5/7+6=6.714 and 3/5+7=7.6

2) Use the formula A=lw to find the area of the rectangle

[tex]6.714*7.6=51.0264[/tex]

Given:

Given that the side of the regular polygon is 16 feet.

We need to determine the area of the polygon.

Area of the polygon:

The area of the polygon can be determined using the formula,

[tex]Area =\frac{s^2 n}{4 \ tan \frac{180}{n}}[/tex]

where n is the number of sides,

s is the side length.

Substituting n = 3 and s = 16, we get;

[tex]Area =\frac{16^2 (3)}{4 \ tan \frac{180}{3}}[/tex]

Simplifying, we get;

[tex]Area =\frac{(256) (3)}{4 \ tan \ 60}[/tex]

[tex]Area = \frac{768}{6.928}[/tex]

Dividing, we get;

[tex]Area = 110.85[/tex]

Rounding off to the nearest tenth, we have;

[tex]Area = 110.9[/tex]

Thus, the area of the regular polygon is 110.9 square units.

Answer:

Step-by-step explanation:

We assume you want your model to be ...

  p = c·e^(kt)

Filling in (t, p) values of (3, 484) and (5, 1135), we have two equations in the two unknowns:

  484 = c·e^(3k)

  1135 = c·e^(5k)

Taking logs makes these linear equations:

  ln(484) = ln(c) +3k

  ln(1135) = ln(c) +5k

Subtracting the first equation from the second, we have ...

  ln(1135) -ln(484) = 2k

  k = ln(1135/484)/2 ≈ 0.42615

Using that value in the first equation, we find ...

  ln(484) = ln(c) +3(ln(1135/484)/2)

  ln(c) = ln(484) -(3/2)ln(1135/484)

  c = e^(ln(484) -(3/2)ln(1135/484)) ≈ 134.8

The initial number in the culture was 135, and the k-value is about 0.42615.

_____

I prefer to start with the model ...

  p = 484·(1135/484)^((t-3)/2)

Then the initial value is that obtained when t=0:

  c = 484·(1135/484)^(-3/2) = 134.778 ≈ 135

The value of k the log of the base for exponent t. It is ...

  ln((1135/484)^(1/2)) = 0.426152

This starting model matches the given numbers exactly. The transformation to c·e^(kt) requires approximations that make it difficult to match the given numbers.

__

For this model, the base of the exponent is the ratio of the two given population values. The exponent is horizontally offset by the number of days for the first count, and scaled by the number of days between counts. The multiplier of the exponential term is the first count. The model can be written directly from the given data, with no computation required.

We want to find the number of dollars Chi makes for every hour he cuts lawns. This proportion would be dollars/hour.

329.12 / 34 = 9.68

Chi's hourly wage is $9.68 per hour.

Hope this helps!! :)

Answer:

pic not their put plz so i can answer

Step-by-step explanation:

Prism B has larger volume than Volume of prims A.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

Given that;

Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.

Since, The volume of the rectangular prism is given as,

V = length × height × width

Put length as 2 unit cubes, height as 7 unit cubes, and width as 1 unit cubes.

For prism A;

V = 2 x 7 x 1 = 14 units³.

Put length as 3 unit cubes, height as 2 unit cubes, and width as 3 unit cubes.

For prism B;

V = 3 x 2 x 3 = 18 units³.

Hence, Prism B has larger volume than Volume of prims A.

To learn more about volume,

brainly.com/question/1578538

#SPJ3

Answer:

[tex]n=\frac{0.005(1-0.005)}{(\frac{0.001}{1.96})^2}=19111.96[/tex]  

And rounded up we have that n=19112

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.001[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.005(1-0.005)}{(\frac{0.001}{1.96})^2}=19111.96[/tex]  

And rounded up we have that n=19112

Answer:

We need a mailing list of at least 191112 people.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

[tex]\pi = 0.005[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

To be within a tenth of a percentage point (0.001) of the true rate with 95% confidence, how big does the test mailing have to be?

They need at least n people

n is found when [tex]M = 0.001[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.001 = 1.96\sqrt{\frac{0.005*0.995}{n}}[/tex]

[tex]0.001\sqrt{n} = 1.96\sqrt{0.005*0.995}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.005*0.995}}{0.001}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.005*0.995}}{0.001})^{2}[/tex]

[tex]n = 19111.96[/tex]

We need a mailing list of at least 191112 people.

Answer:

Because our p-value of .023 is lower than the alpha-level of .05, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of subjects who have the necessary qualities is less than .2. Our test provided a statistically significant result.

Answer:

The null hypothesis is represented as

H₀: p ≤ (3/4)

The alternative hypothesis is represented as

Hₐ: p > (3/4)

z = 1.65

p-value = 0.049471

The obtained p-value is less than the significance level at which the test was performed at. Hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is significant evidence to conclude that more than (3/4) of the voting population would vote for the Democrat.

Step-by-step explanation:

The complete question is presented in the attached image to this answer.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing.

For this question, the null hypothesis would be that there isn't significant evidence that that more than (3/4) of the entire voting population would vote for the Democrat. That is, the proportion of the entire voting population that would vote for the democrat is less than or equal to (3/4).

While the alternative hypothesis is that there is significant evidence that more than (3/4) of the voting population would vote for the Democrat.

Mathematically,

The null hypothesis is represented as

H₀: p ≤ (3/4)

The alternative hypothesis is represented as

Hₐ: p > (3/4)

To do this test, we will use the z-distribution because the sample size (1200) is large enough for the p-value for z-test statistic and the t-test statistic to approximately be equal.

So, we compute the z-test statistic

z = (x - μ)/σₓ

x = sample proportion of the surveyed registered voters that would vote for the democrat = (925/1200) = 0.77

μ = p₀ = The standard proportion that we're comparing against = (3/4) = 0.75

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 1200

σₓ = √[0.77×0.23/1200] = 0.01215

z = (0.77 - 0.75) ÷ 0.01215

z = 1.65

checking the tables for the p-value of this t-statistic

Significance level = 0.05

The hypothesis test uses a one-tailed condition because we're testing only in one direction (whether the proportion is greater than 0.75)

p-value (for z = 1.65, at 0.05 significance level, with a one tailed condition) = 0.049471

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.049471

0.171485 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is significant evidence to conclude that more than (3/4) of the voting population would vote for the Democrat.

Hope this Helps!!!

Answer:

At t=1, Rate of Change=-36.86

At t=10 hours, Rate of Change =-0.0088

Step-by-step explanation:

The function which describes the number of facts of a certain type which are remembered after t hours is given as:

[TeX]f(t)=\frac{85t}{99t-85}[/TeX]

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]

At t=1

[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]

=-36.86

At t=10 hours

[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]

=-0.0088

The rate of change of the function is calculated by finding its derivative and evaluated by substituting the respective hours (1 hour and 10 hours). The rate of change after 1 hour is approximately -106.25, implying a decline per hour, and after 10 hours is approximately -0.918, indicating a slower rate of decline per hour.

The rate of change of a function is calculated by finding the derivative of the function. The derivative of a function gives the rate of change of the function at any given point. Let's calculate the derivative of the function f(t) = 85 t / (99 t - 85).

We get f'(t) = (85*(99 t - 85) - (85 t)*99) / (99 t -85)² = (-850)/ (99 t - 85)². This is the rate of change of the function f(t).

To find the rate of change after 1 hour and 10 hours, substitute t = 1 and t = 10 into f'(t).

https://brainly.com/question/20816247

#SPJ3

Answer: the probability that this whole shipment will be​ accepted is 0.673

Step-by-step explanation:

This is a binomial distribution because the probabilities are either that of success or failure

The probability that a particular shipment of thousands of aspirin tablets actually has defects is 4% = 0.04. Then the probability that there would be no defect is 1 - 0.04 = 0.96

Since the shipment is accepted with at most even when there is defect, then the probability of success is 0.04 and that of failure is 0.96

The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 0.04

q = 0.96

n = 14

Since entire shipment is accepted if at most 2 tablets do not meet the required specifications, then the probability is

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x = 0) = 14C0 × 0.04^0 × 0.96^(14 - 0) = 0.56

P(x = 1) = 14C1 × 0.04^1 × 0.96^(14 - 1) = 0.024

P(x = 2) = 14C2 × 0.04^2 × 0.96^(14 - 2) = 0.089

P(x ≤ 2) = 0.56 + 0.024 + 0.089 = 0.673

Answer:

  35 minutes

Step-by-step explanation:

The total amount of water is 200 +60 = 260 gallons. The two tanks will have equal amounts when each has half that, or 130 gallons.

If the volume in tank 2 is increasing at 2 gallons per minute, it will increase by 70 gallons from 60 gallons to 130 gallons in 70/2 = 35 minutes.

Answer:

[tex] {9}^{15} [/tex]

Step-by-step explanation:

[tex]( {9}^{3} ) \times ( {9}^{12} ) = 9 {}^{3 + 12} = {9}^{15} \\ [/tex]

Answer:

The degrees of freedom associated with the critical value is 25.

Step-by-step explanation:

The number of values in the final calculation of a statistic that are free to vary is referred to as the degrees of freedom. That is, it is the number of independent ways by which a dynamic system can move, without disrupting any constraint imposed on it.

The degrees of freedom for the t-distribution is obtained by substituting the values of n1​ and n2​ in the degrees of freedom formula.

Degrees of freedom, df = n1​+n2​−2

                                       = 15+12−2=27−2=25​

Therefore, the degrees of freedom associated with the critical value is 25.

Answer:

6.79

Step-by-step explanation:

-Let X denote the total amount of the job.

-The job has to be done in 5 hrs, therefore the portion done every hour is:

[tex]Rate=\frac{Total}{Time}\\\\=\frac{X}{5}\\\\=\frac{1}{5}X=0.2X[/tex]

Therefore, the rate of Bill and Ted working jointly must equal the rate calculated above:

[tex]R_{Bill}=\frac{X}{19}\\\\=\frac{1}{19}X\\\\R_{Bill}+R_{Ted}=R_{required}\\\\\frac{1}{19}X+R_{Ted}=\frac{1}{5}X\\\\R_{Ted}=\frac{1}{5}X-\frac{1}{19}X\\\\=\frac{14}{95}X\\\\\therefore \frac{14}{95}X=1\ hr\\\\X=1\div \frac{14}{95}\\\\=6.7857\approx 6.79[/tex][tex]hrs[/tex]

Hence, Bill working alone should complete the house in 6.79 hrs

Answer:

If the proportion of female rats that show compassion = p₁

And

If the proportion of male rats that show compassion = p₂

And the difference between them is given as

μ₀ = p₁ - p₂

The null hypothesis and alternative hypothesis can be expressed as:

The null hypothesis that there is no significant evidence to conclude that there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

That is, there is no significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

H₀: μ₀ = 0

or

H₀: p₁ = p₂

And the alternative hypothesis that there is evidence that the proportion of female rats that show compassion is significantly different from the proportion of male rats that show compassion.

That is, there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

Hₐ: μ₀ ≠ 0

or

Hₐ: p₁ ≠ p₂

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is usually about the absence of significant difference between two proportions being compared. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It proposes that there is indeed a significant difference between two proportions being compared. It usually confirms the theory being tested by the experimental setup.

It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to check whether there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

If the proportion of female rats that show compassion = p₁

And

If the proportion of male rats that show compassion = p₂

And the difference between them is given as

μ₀ = p₁ - p₂

The null hypothesis and alternative hypothesis can be expressed as:

The null hypothesis that there is no significant evidence to conclude that there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

That is, there is no significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

H₀: μ₀ = 0

or

H₀: p₁ = p₂

And the alternative hypothesis that there is evidence that the proportion of female rats that show compassion is significantly different from the proportion of male rats that show compassion.

That is, there is a significant difference in the proportion of female rats that show compassion and the proportion of male rats that show compassion.

Hₐ: μ₀ ≠ 0

or

Hₐ: p₁ ≠ p₂

Hope this Helps!!!

The null hypothesis, denoted as \( H_0 \), states that there is no difference in the proportion of female rats and male rats that show compassion by freeing a trapped rat. In mathematical terms, this can be expressed as:

[tex]\[ H_0: p_f - p_m = 0 \][/tex]

where [tex]\( p_f \)[/tex] is the proportion of female rats showing compassion and [tex]\( p_m \)[/tex] is the proportion of male rats showing compassion.

The alternative hypothesis, denoted as [tex]\( H_1 \) or \( H_a \)[/tex], states that there is a difference in the proportion of female rats and male rats that show compassion. This can be expressed as:

[tex]\[ H_1: p_f - p_m \neq 0 \][/tex]

This is a two-tailed test because the alternative hypothesis does not specify the direction of the difference, only that a difference exists.

Given the confidence interval for the difference in proportions is 0.104 to 0.480, we can see that the interval does not include zero. This suggests that at the 95% confidence level, there is evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating that there is a statistically significant difference between the proportions of female and male rats showing compassion