The stockholders' equity section of Waterway Corporation consists of common stock ($10 par) $2,050,000 and retained earnings $520,000. A 10% stock dividend (20,500 shares) is declared when the market price per share is $14. The before-and-after effects of the dividend are as follows...
Explanation:(a) Before the stock dividend, the components of stockholders' equity in Waterway Corporation are common stock ($10 par) $2,050,000 and retained earnings $520,000. After the stock dividend, the common stock would increase by 20,500 shares ($10 x 20,500 = $205,000) and retained earnings would decrease by the same amount since it is used to finance the dividend. So, the new components of stockholders' equity would be common stock ($10 par) $2,255,000 and retained earnings $315,000.
(b) Before the stock dividend, the shares outstanding in Waterway Corporation are not provided in the question. After the stock dividend, the number of shares outstanding would increase by 20,500 shares.
(c) The par value per share of the common stock remains the same before and after the stock dividend, which is $10 per share.
Final answer:
A 10% stock dividend for Waterway Corporation, with a par value of $10 and a market price of $14 per share, results in an increase in common stock by $205,000, a decrease in retained earnings by the same amount, an increase of 20,500 shares, while the par value per share remains at $10.
Explanation:
When a stock dividend is declared, it affects the stockholders' equity section of a corporation. In the case of Waterway Corporation, a 10% stock dividend is declared when each share has a market price of $14. Since the par value is $10 and there are 20,500 new shares being issued, the total value at par is $205,000 (20,500 shares x $10 par value). This amount is transferred from retained earnings to common stock. No additional capital is generated since it's a stock dividend, not a cash dividend.
Here's the before-and-after effects of the dividend:
(a) Components of stockholders' equity:
Before the dividend:
Common stock: $2,050,000
Retained earnings: $520,000
After the dividend:
Common stock: $2,255,000 (original $2,050,000 + $205,000 from the stock dividend)
Retained earnings: $315,000 (original $520,000 - $205,000 transferred to common stock)
(b) Shares outstanding:
Before the dividend: Assuming each common stock's par value aligns with one share, the company has 205,000 shares ($2,050,000 / $10 par value).
After the dividend: 225,500 shares (205,000 original shares + 20,500 new shares issued)
(c) Par value per share:
The par value per share remains unchanged at $10, as the stock dividend does not affect the par value.
Which of the following is not a way to determine if a relation is a function
Solve for x: x^2 = 3x + 10
2.The mean area of several thousand apartments in a new development is advertised to be 1,100 square feet. A consumer advocate has received numerous complaints that the apartments are smaller than advertised. A state building inspector is sent out to measure a sample of apartments. State the null and the alternative hypothesis to test this claim.
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1,100 square feet
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1,100 square feet
Step-by-step explanation:
We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.
A consumer advocate has received numerous complaints that the apartments are smaller than advertised.
Let [tex]\mu[/tex] = mean area of several apartments.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1,100 square feet
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1,100 square feet
Here, null hypothesis states that the mean area of apartments are same as advertised.
On the other hand, alternate hypothesis states that the mean area of apartments are smaller than advertised.
So, this would be the appropriate null and the alternative hypothesis to test this claim.
A set simbols that expresses a mathematical rule is called a?
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An estimated regression equation was developed relating the percentage of games won by a team in the National Football League for the 2011 season given the average number of passing yards obtained per game on offense and the average number of yards given up per game on defense (ESPN website, November 3, 2012). a. Predict the percentage of games won for a particular team that averages 225 passing yards per game on offense and gives up an average of 300 yards per game on defense. b. Develop a 95% prediction interval for the percentage of games won for a particular team that averages 225 passing yards per game on offense and gives up an average of 300 yards per game on defense.
The predicted percentage of games won for a team with these statistics is approximately 60.025%.
To address the given questions, we'll use the provided estimated regression equation:
[tex]\[ \hat{y} = 60.5 + 0.319x_1 - 0.241x_2 \][/tex]
where:
- [tex]\( \hat{y} \)[/tex] is the predicted percentage of games won,
- [tex]\( x_1 \)[/tex] is the average number of passing yards obtained per game on offense,
- [tex]\( x_2 \)[/tex] is the average number of yards given up per game on defense.
a. To predict the percentage of games won for a team that averages 225 passing yards per game on offense [tex](\( x_1 = 225 \))[/tex] and gives up an average of 300 yards per game on defense [tex](\( x_2 = 300 \))[/tex], we'll substitute these values into the regression equation:
[tex]\[ \hat{y} = 60.5 + 0.319(225) - 0.241(300) \][/tex]
[tex]\[ \hat{y} = 60.5 + 71.775 - 72.3 \][/tex]
[tex]\[ \hat{y} = 60.5 - 0.525 \][/tex]
[tex]\[ \hat{y} = 60.025 \][/tex]
Therefore, the predicted percentage of games won for a team with these statistics is approximately 60.025%.
Complete question:
In exercise 24, an estimated regression equation was developed relating the percentage of games won by a team in the National Football League for the 2011 season (y) given the average number of passing yards obtained per game on offense (x1) and the average number of yards given up per game on defense (x2). The estimated regression equation was y = 60.5 + 0.319x1 - 0.241x2.
Predict the percentage of games won for a particular team that averages 225 passing yards per game on offense and gives up an average of 300 yards per game on defense.
Calculate the divergence of the following radial field. Express the result in terms of the position vector r and its length StartAbsoluteValue Bold r EndAbsoluteValue. FequalsStartFraction left angle x comma y comma z right angle Over x squared plus y squared plus z squared EndFraction equalsStartFraction Bold r Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction Choose the correct answer below. A. The divergence of F is 0. B. The divergence of F is StartFraction negative 2 Over StartAbsoluteValue Bold r EndAbsoluteValue Superscript 4 EndFraction . C. The divergence of F is StartFraction 1 Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction . D. The divergence of F is StartFraction negative 1 Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction
Answer:
C. The divergence of F is StartFraction 1 Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction
∇•F = 1/|r|²
Step-by-step explanation:
The position vector r = (x, y, z)
r = xi+yj+zk
|r| = √x²+y²+z²
|r|² = x²+y²+z²
Given the radial field F = r/|r|²
Divergence of the radial field is expressed as:
∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {(r/|r|²)
∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {xi/|r|² + yj/|r|² + zk/|r|²}
∇•F = δ/δx(x/|r|²) + δ/δy(y/|r|²)+δ/δz(z/|r|²)
Check the attachment for the complete solution.
The double number line shows that a water park allows 18 people to go down a giant water slide in three minutes. Select the double number line that correctly label the number of people that can go down the slide in one, two, and four minutes.
Answer: B
Step-by-step explanation:
Firstly, we identify the number of people that can use the slide per minute, which is 6. Using this, we find that for 1 minute it's 6 people, for 2 minutes it's 12 people and for 4 minutes it's 24 people.
Explanation:The question provides us that 18 people can go down the water slide in 3 minutes. This suggests that every minute, 18 ÷ 3 = 6 people can go down the slide. So, for the double number line, we would show:
1 minute: 6 people 2 minutes: 6 x 2 = 12 people 4 minutes: 6 x 4 = 24 people
This 'per minute' basis helps in understanding and calculating the number of people going down the slide at different time intervals.
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You are the manager of a monopoly. A typical consumer's inverse demand function for your firm's product is P = 250- 4Q, and your cost function is TC = 10Q. A. MC is fixed and is equal to $10 (MC=AC=S). MR=250-8Q.
(P=price, Q=quantity of output, TC=total cost, MC=marginal cost, MR=marginal revenue, S=supply)
1)What price the company should choose to get maximum profit if the company will use ordinary pricing strategy?
2)Now suppose the company is thinking about using price discrimination for lower income group of customers. If the company will offer discount of $30 in price to the lower income groups how much additional profit will the company earn? Illustrate graphically.
3)Explain the conditions needed to apply the price discrimination strategy?
Answer:
(1) 240-8Q=0240−8Q=0 (2) 225 (3) it is very necessary that the direct elasticity of demand for a product at a price from several buyers be different significantly; so that customers are easily known, that further goods resale by buyers is not possible
Step-by-step explanation:
Solution
Given that:
(1) TR=∫MR=250Q−4Q
Pr=TR-TC=250Q-4Q² - 10Q=240Q−4Q²
Thus,
Pr =240−8Q
240-8Q=0240−8Q=0
(2) Q=30
Now,
p=250-4 * 30=130
p=100
so.
100=250−4Q
Q=37.5
Pr=240×37.5−4×37.5²
=3375
Hence,
ΔPr=3600−3375=225
(3) For the execution of price discrimination by a monopolist, it is very important that the direct elasticity of demand for a product at a price from different buyers be remarkably different; so that customers are easily known, that further goods resale by buyers is not done.
Determine the intercepts of the line. y = − 7 x + 3 y=−7x+3
Answer:
x intercept (3/7, 0) or (0.429, 0)
y intercept (0, -3)
Step-by-step explanation:
1. Find the area of the shaded sector.
- 12m
74
Answer:
888
Step-by-step explanation:
Im pretty sure this is the answer, if helpful please mark me as brainiest :>
I need help ASAP what do I put for what I already know
Valerie is taking a road trip over spring break. At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph. Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph. When was she moving exactly 50 mph?Select one:a. 4:30 p.m.b. 4:35 p.m.c. 4:40 p.m.d. Cannot be determined
Answer:
b. 4:35 p.m
Step-by-step explanation:
Her speed in t minutes after 4:30 p.m. is modeled by the following equation:
[tex]v(t) = v(0) + at[/tex]
In which v(0) is her speed at 4:30 pm and a is the acceleration.
At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.
This means that [tex]v(0) = 45[/tex]
Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.
This means that [tex]v(10) = 55[/tex]
So
[tex]v(t) = v(0) + at[/tex]
[tex]55 = 45 + 10a[/tex]
[tex]10a = 10[/tex]
[tex]a = 1[/tex]
So
[tex]v(t) = 45 + t[/tex]
When was she moving exactly 50 mph?
This is t minutes after 4:30 p.m.
t is found when v(t) = 50. So
[tex]v(t) = 45 + t[/tex]
[tex]50 = 45 + t[/tex]
[tex]t = 5[/tex]
5 minutes after 4:30 p.m. is 4:35 p.m.
So the correct answer is:
b. 4:35 p.m
There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 2?
Answer:
There is a 11/14 chance that the result is a multiple of 3 or a multiple of 2.
Step-by-step explanation:
Since the spinner is from 1 to 14, find all of the multiples of 3 and multiples of 2.
There are 4/14 multiples of 3 and 7/14 multiples of 2.
Add both of these numbers together 4/14 + 7/14 = 11/14
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The probability of landing on a multiple of 2 or 3 when spinning a spinner numbered 1 through 14 is 4/7.
The student asked about the probability of getting a multiple of 3 or a multiple of 2 when spinning a spinner numbered 1 through 14. To determine this, we first list the multiples of 3 and 2 within the range of numbers on the spinner.
Multiples of 3: 3, 6, 9, 12
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Note that 6 and 12 are multiples of both 2 and 3, so we should not count them twice.
The total number of distinct multiples of 2 or 3 is 3 (multiples of 3) + 7 (multiples of 2) - 2 (common multiples) = 8 unique numbers. Since there are 14 possible outcomes on the spinner, the probability of landing on a multiple of 3 or 2 is 8 (favorable outcomes) divided by 14 (total possible outcomes).
The probability calculation is: 8/14, which simplifies to 4/7.
According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of n equals 350 adults is obtained from the city. Describe the sampling distribution of ModifyingAbove p with caret, the sample proportion of adults who have credit card debts of more than $2000. Round to three decimal places when necessary. A. Approximately normal; mu Subscript pequals0.34, sigma Subscript pequals0.001 B. Binomial; mu Subscript pequals119, sigma Subscript pequals8.862 C. Approximately normal; mu Subscript pequals0.34, sigma Subscript pequals0.025 D. Exactly normal; mu Subscript pequals0.34, sigma Subscript pequals0.025
Answer:
2000*24%=680\
Step-by-step explanation:
At a local community college, 62% of all freshmen take both Statistics and English. What percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics?
(1) 18% (3) 82%
(2) 62% (4) 94%
Answer:
(3) 82%
Step-by-step explanation:
.62/.76=.8157894737 which when rounded is 82%.
If 76 percent of freshmen take Statistics, the percentage of freshmen who take English is 82 percent. Option B is correct.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics is found as;
The percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics is found as;
[tex]\rm \% S=\frac{.62}{.76} \times 100 \\\\ \% S=82\%[/tex][tex]% STATICS = \frac{.62}{.76} \times 100 \\\\ % STATICS = 81.5 \%[/tex]
Sixty-two percent of all freshmen at a nearby community college take both Statistics and English. If 76 percent of freshmen take Statistics,
Hence, the percentage of freshmen who take English is 82 percent.
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X^2-4/x-8 help please
Answer:
-3
Step-by-step explanation:
Put 4 where x is, and do the arithmetic.
(4^2 -4)/(4 -8) = (16 -4)/(-4) = 12/-4 = -3
The value of the expression is -3 for x=4.
Consider the quadratic equation x2 = 4x - 5. How many solutions does the equation have?
Answer:
no real solutions2 complex solutionsStep-by-step explanation:
The equation can be rearranged to vertex form:
x^2 -4x = -5 . . . . . . . . . subtract 4x
x^2 -4x +4 = -5 +4 . . . . add 4
(x -2)^2 = -1 . . . . . . . . . show the left side as a square
x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary
x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.
_____
Comment on the question
Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.
[tex] \sqrt{4 - {x}^{2}dx } [/tex]
Answer:
do you know what x or dx =
Step-by-step explanation:
Click the prime number cards to build composite numbers to 50. Click the blank card to add a new prime number
Answer:
See Explanation
Step-by-step explanation:
A prime number is a number that is only divisible by by 1 and itself.Composite numbers on the other hand is any number which is not prime.To determine the number of prime cards needed to build a composite number, we simply express the number as a product of its prime factors.
These are:
4=2X2
6=2X3
8=2X2X2
9=3X3
10=2X5
12=2X2X3
14=2X7
15=3X5
16=2X2X2X2
18=2X3X3
20=2X2X5
21=3X7
22=2X11
24=2X2X2X3
26=2X13
27=3X3X3
28=2X2X7
30=2X3X5
32=2X2X2X2X2
33=3X11
34=2X17
35=5X7
36=2X2X3X3
38=2X19
39=3X13
40=2X2X2X5
42=2X3X7
44=2X2X11
45=3X3X5
46=2X2X13
48=2X2X2X2X3
49=7X7
50=2X5X5
Therefore for each of the numbers, those are the prime number cards to be used.
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The set {5, 6, 8, 9, 10} is part of a solution set for which inequality?
A. c+14<24
B. c+18≥24
C. c+18>24
D. c+14≤24
please help
Answer:
D. c+14≤24
Step-by-step explanation:
A. c+14<24 is c<10 (subtract 14)
B. c+18≥24 is c≥6 (subtract 18)
C. c+18>24 is c>6 (subtract 18)
D. c+14≤24 is c≤10 (subtract 14)
The set is {5, 6, 8, 9, 10}, so it should include each one of those numbers. C and A don't include 6 and 10 respectively, so they can't be the answer. B contains all numbers 6 and above, which doesn't include 5. The remaining letter is D, so that's the final answer.
A sphere has a diameter of 30 meters. What is the volume of the sphere.
Answer:
V≈14,137.17m³ or 4500π
Step-by-step explanation:
Formula: V=(1 /6)πd³
V=(1/6)π(30³)= 14137.16694115406957308189522475776297888726229718797619438.....
Answer:
14137.17 meters cubed
Step-by-step explanation:
volume = 14137.17 meters cubed
What is the volume of a sphere with a radius of 4 units?
The formula is (4*pi/3)*r^3, so 256*pi/3 cubic units = 268.08 cubic units. {whatever units r is in}
Answer:
(256/3)pi
Step-by-step explanation:
(4/3)(pi)(r^3) =
(4/3)(pi)(4^3) =
(4/3)(pi)(64) =
(256/3)pi
From a boat on the lake, the angle of elevation to the top of a cliff is 24 degrees 19'. If the base of the cliff is 2994 feet from the boat, how high is the cliff (to the nearest foot)?
Answer:
1353 ft
Step-by-step explanation:
The cliff height and the distance from its base to the boat form the legs of a right triangle. The cliff height is the leg opposite the elevation angle, and the distance to the boat is the leg adjacent. Given these two legs of the triangle, the tangent relation seems useful:
Tan = Opposite/Adjacent
We want to find the cliff height (opposite), so we can multiply this equation by Adjacent:
Opposite = Adjacent×Tan
cliff height = (2994 ft)(tan(24°19')) ≈ 1353 ft
The cliff is about 1353 feet high.
Insert three geometric means between 2 and 81/8
Answer:
The three geometric means are 3, 9/2 and 27/4Step-by-step explanation:
The nth term of a geometric sequence is expressed as Tn = [tex]ar^{n-1}[/tex] where;
a is the first term
r is the common ratio
n is the number of terms
Since we are to insert three geometric means between 2 and 81/8, the total number of terms in the sequence will be 5 terms as shown;
2, a, b, c, 81/8
a, b, and c are the 3 geometric mean to be inserted
T1 = [tex]ar^{1-1}[/tex] = 2
T1 = a = 2....(1)
T5= [tex]ar^{5-1}[/tex]
T5 = [tex]ar^{4}[/tex] = 81/8... (2)
Dividing equation 1 by 2 we have;
[tex]\frac{ar^{4} }{a}= \frac{\frac{81}{8} }{2}[/tex]
[tex]r^{4} = \frac{81}{16}\\\\r = \sqrt[4]{\frac{81}{16} } \\r = 3/2[/tex]
Given a =2 and r = 3/2;
[tex]T2=ar\\T2 = 2*3/2\\T2 = 3\\\\T3 = ar^{2} \\T3 = 2*\frac{3}{2} ^{2} \\T3 = 2*9/4\\T3 = 9/2\\\\T4 = ar^{3}\\T4 = 2*\frac{3}{2} ^{3} \\T4 = 2*27/8\\T4 = 27/4\\[/tex]
Therefore the three geometric means are 3, 9/2 and 27/4
In a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:
[tex]\mathbf{T_2 =3 }[/tex]
[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]
Recall:
nth term of a geometric sequence is given as: [tex]\mathbf{T_n = ar^{n - 1}}[/tex]a = the first term; r = the common ratio; n = the number of termsGiven a geometric sequence, 2 . . . 81/8, with three other terms in the middle, first, find the value of r.
Thus:
First Term:
a = 2Fifth Term:
[tex]T_5 = ar^{n - 1}[/tex]
a = 2
n = 5
r = ?
T5 = 81/8
Plug in the value of a, n, and T5[tex]\frac{81}{8} = 2r^{5 - 1}\\\\\frac{81}{8} = 2r^4\\\\[/tex]
Multiply both sides by 8[tex]\frac{81}{8} \times 8 = 2r^4 \times 8\\\\81 = 16r^4\\\\[/tex]
Divide both sides by 16[tex]\frac{81}{16} = \frac{16r^4}{16} \\\\\frac{81}{16} = r^4\\\\[/tex]
Take the fourth root of both sides[tex]\sqrt[4]{\frac{81}{16}} = r\\\\\frac{3}{2} = r\\\\\mathbf{r = \frac{3}{2}}[/tex]
Find the three geometric means [tex]T_2, T_3, $ and $ T_4[/tex] between 2 and 81/8.
[tex]\mathbf{T_n = ar^{n - 1}}[/tex]
a = 2
r = 3/2
Thus:[tex]T_2 = 2 \times (\frac{3}{2}) ^{2 - 1}\\\\T_2 = 2 \times (\frac{3}{2}) ^{1}\\\\\mathbf{T_2 = 3}[/tex]
[tex]T_3 = 2 \times \frac{3}{2} ^{3 - 1}\\\\T_3 = 2 \times (\frac{3}{2}) ^{2}\\\\T_3 = 2 \times \frac{9}{4}\\\\\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]T_4 = 2 \times \frac{3}{2} ^{4 - 1}\\\\T_4 = 2 \times (\frac{3}{2}) ^{3}\\\\T_4 = 2 \times \frac{27}{8}\\\\\mathbf{T_4 =\frac{27}{4} }[/tex]
Therefore, in a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:
[tex]\mathbf{T_2 =3 }[/tex]
[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]
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what is the sum of 5/13 + 10/13
Answer:15/13
Step-by-step explanation:
Dale says the ratios 3:5 and 2:10 are equivalent. Is he correct?
Answer:
Dale says the ratios 3:5 and 2:10 are equivalent.
He is wrong.
Let's compare the two ratios by converting them into the new forms which have the same denominator.
3/5 = 6/10
2/10 = 2/10
6/10 > 2/10 => 3/5 > 2/10
Hope this helps!
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"Her eyes shone as bright as the sun" is an example of
Is it a simile of idiom
Answer:
Similie
Step-by-step explanation:
A similie is a comparison using like or as
An idiom however is a group of words established by usage as having a meaning not deducible from those of the individual words
reading this statement, its saying "Her eyes shone as bright as the sun"
the caparison is between her eyes and the bright sun
therefore making this a similie
Hope this helps
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Based on the information given, the expression is a simile.
A simile simply means a figure of speech that is used in comparing something with another thing.In this case, "Her eyes shone as bright as the sun" is an example of a simile. The eyes were compared to the sun.
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Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than .03 is _______.
Answer:
The correct answer to the following question will be "0.0367".
Step-by-step explanation:
The given values are:
[tex]p1=p2=0.06[/tex]
[tex]q1=q2=1-p1=0.94[/tex]
[tex]n1=n2=400[/tex]
As we know,
[tex]E(p1-p2)=p1-p2=0\\[/tex]
[tex]SE(p1-p2)=\sqrt{\frac{p1q1}{n1}+\frac{p2q2}{n2}}[/tex]
On putting the given values in the above expression, we get
[tex]= \sqrt{p1q1(\frac{1}{400}+\frac{1}{400})}[/tex]
[tex]=0.0168[/tex]
Now, consider
[tex]P(p1-p2>0.03)=P[\frac{(p1-p2)-E(p1-p2)}{SE(p1-p2)}>\frac{0.03-0}{0.0168}][/tex]
[tex]=P(Z>1.7857)[/tex]
[tex]=P(Z>1-79)[/tex]
[tex]=0.036727[/tex]
Therefore, "0.0367" is the right answer.
Calculating the probability of the difference between two sample proportions being more than 0.03 involves executing a hypothesis test via a z-test due to our large sample size. We formulate and employ a formula to get the z-score and then determine the associated p-value using a statistical tool.
Explanation:This question falls within the area of statistics, particularly dealing with hypothesis testing and comparison of two independent population proportions. Given that 0.06 of each population possess a certain characteristic and samples of size 400 are drawn from each, we are required to calculate the probability that the difference between the sample proportions exceeds 0.03.
First, we establish the null hypothesis (H0) and alternative hypothesis (Ha) for the test. H0: P1 = P2 and Ha: P1 ≠ P2. Here, P1 and P2 represent the populations respectively. Given a sufficiently large sample size (n > 30), we use a z-test for comparing the proportions.
In computing the z-score, we use the following formula: z = (P1 - P2) / √ ((P*(1 - P*) / n1) + (P*(1 - P*) / n2)). Here, P* = (x1 + x2) / (n1 + n2), where x is the number of successes in each sample (0.06*400 = 24 per population logistically).
The p-value associated with the calculated z-score, which represents the probability that the difference between the first sample proportion and the second sample proportion being more than 0.03, can be found using a statistical calculator or statistical software. The precise numerical value for p will depend on the computed z-score.
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In a previous year, 58% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 600 females aged 15 and older and finds that 339 are living alone. Is there sufficient evidence at the alphaequals0.01 level of significance to conclude the proportion has changed?
Answer:
[tex]z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744[/tex]
Since is a bilateral test the p value would be given by:
[tex]p_v =2*P(z<-0.744)=0.4569[/tex]
And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58
Step-by-step explanation:
Information given
n=600 represent the random sample selcted
X=339 represent the number of females aged 15 and older that living alone
[tex]\hat p=\frac{339}{600}=0.565[/tex] estimated proportion of females aged 15 and older that living alone
[tex]p_o=0.58[/tex] is the value that we want to check
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic
[tex]p_[/tex] represent the p value
Sytem of hypothesis
We want to check if the true proportion females aged 15 and older that living alone is significantly different from 0.58.:
Null hypothesis:[tex]p=0.58[/tex]
Alternative hypothesis:[tex]p \neq 0.58[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744[/tex]
Since is a bilateral test the p value would be given by:
[tex]p_v =2*P(z<-0.744)=0.4569[/tex]
And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58
Which triangle can be solved using the law of sines?
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for AAS triangles or SSA
Step-by-step explanation:
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ny triangle whose two sides and 1 angle is known or 2 angles are known and 1 side is known
Step-by-step explanation: