Answer:
[tex]\displaystyle \frac{7}{8}[/tex].
Step-by-step explanation:
If two events are complements, then the sum of their probabilities should be [tex]1[/tex].
This question suggests that the following two events are complements:
At least one child is female.All three children are male.As a result:
[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male})\end{aligned}[/tex].
According to the question,
[tex]\displaystyle P(\text{all three children are male}) = \frac{1}{8}[/tex].
Therefore,
[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male}) \\ &= 1 -\frac{1}{8} \\ &= \frac{7}{8}\end{aligned}[/tex].
In this Mathematics problem of probability, the calculation required was for the probability of 'at least one child being female'. This is a complementary event to 'all three children being male', enabling us to solve it by using the formula P(at least one child is female) = 1 - P(all three children are male). Hence, the answer equals 7/8.
Explanation:The subject of the question is probability, which is a branch of Mathematics. Looking at the question, the probability of having all three children as males has been given as 1/8. We are required to find the probability of having 'at least one female child'. This event is complementary to having 'all three children as males', so we can find the solution using the formula you stated. As P(all three children are male) = 1/8, therefore P(at least one child is female) = 1 - 1/8 = 7/8.
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You and a friend go to the movies. You each buy a ticket for x dollars and a popcorn-and-drink combo for $5.25. Use the distributive property to find the total amount of money you and your friend spent using the following expression 2(x + 5.25)
Answer:
2x + 10.5.
Step-by-step explanation:
Multiply 2 by x and 5.25.
Answer:
.
Step-by-step explanation:
A researcher wants to study exercise as a way of reducing anger expression. He plans to throw water balloons at participants, measure their anger using behavioral cues (e.g., number of swear words, redness of face, etc.), make them do 20 pushups, then measure their anger again. He wants to see if there are differences before and after 20 pushups. Which t-test should he use? a. Single sample b. Paired samples c. Independent samples
Answer:
Option B: Paired sample t-test, since there is a "before 20 push ups" and "after 20 push up " score for each participant.
Step-by-step explanation:
In this question, we have a case where each participant undergoes different exercises to see differences before and after 20 push ups.
Now, it's obvious that the same condition applies to all participants i.e. differences before and after 20 push ups.
Thus, this will be a case of paired sample t-test or dependent t test because conditions for all participants in both tests are dependent or same.
So, the only option that corresponds with my explanation to use paired sample is option B
The sum of the digits of a 2-digit number is 11. If the digits are reversed, the number formed is 45 more than the original number. Find the original number
Step-by-step explanation:
Let the two-digit number be 10t+u where t is the tens digit and u the units digit.
-------------------
EQUATION:
t+u = 11
10u+t = 10t+u + 45
-------------
Rearrange the equations:
t+u = 11
9t-9u = -45
-------------
Simplify:
t+u = 11
t-u = -5
---------
Add the equations to solve for "t":
2t = 6
t = 3
--------
Substitute to solve for "u":
3+u = 11
u = 8
The demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.
p = −0.01x2 − 0.1x + 32
Determine the consumers' surplus if the market price is set at $2/cartridge. (Round your answer to two decimal places.)
Demand function: p = -0.01x^2-0.2x+13 (1).
The equation (2) is: CS = ∫ D(p) dp, where D is the demand curve expressed in terms of the price. The bottom limit of the integrand is the market price given as $5 and the top limit is $13 found by setting x = 0 in (1) above. Equation (2) above requires we solve the original equation, (1) above, for x in terms of p. The first step is (a) to multiply both sides of equation by -100 to clear decimals, then (b) place equation in standard quadratic form, namely, x^2 + 20x + 100p – 1300 = 0. Step (c): Solve for x by applying quadratic formula, namely, x = (-b +- √(b^2 – 4ac)) / 2a to solve for x. Use a = 1, b = 20, c = 100p – 1300. The new demand equation is: x = -10 + 10√(14 – p). Now calculate ∫ (-10 + 10(14 – p)^(1/2)) dp and evaluate at 5 and 13. This gives: -10(13 – 5) – (2/3) (10) ((14 - 13)^(3/2) – (14 – 5)^(3/2)) . This evaluates to: -80 – (20/3) + 180. So, CS = $93.33.
The consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.
What do you mean by domain and range of a function?For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.
Given is the demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where [p] is the unit price in dollars and [x] is the quantity demanded each week, measured in units of a thousand.
The demand function is -
p = − 0.01x² − 0.1x + 32
For p = 2, we can write -
− 0.01x² − 0.1x + 32 = 2
− 0.01x² − 0.1x + 30 = 0
Graph the equation and note the [x] intercepts. Taking the positive value of [x] intercept, we get 50.
Hence, the consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.
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A pair of snow boots at an equipment store in Big Bear that originally cost $60 is on sale for 40% off. Then, you have a coupon for 10% off. What is the final cost?
Answer:
$30 i think
Step-by-step explanation:
because %40+%10=%50
and %50 is half of %100 so 60-(60×(50%)=30
sorry is its wrong
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.The owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.There is sufficient evidence to support the claim that the mean attendance is greater than than 694.There is sufficient evidence to support the claim that the mean attendance is less than 694.There is not sufficient evidence to support the claim that the mean attendance is less than 694.There is not sufficient evidence to support the claim that the mean attendance is greater than 694.
Answer:
Option D is correct.
Failure to reject the null hypothesis means that there is not sufficient evidence to support the claim that the mean attendance is greater than 694.
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 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 owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium.
So, the null hypothesis would be that there isn't enough evidence to support the claim that the mean attendance is greater than 694.
That is, the mean isn't greater than 694; the mean is less than or equal to 694.
While the alternative hypothesis would be that there is sufficient evidence to support the claim that the mean attendance is greater than 694.
Mathematically,
The null hypothesis is represented as
H₀: μ₀ ≤ 694
The alternative hypothesis is represented as
Hₐ: μ₀ > 694
Failure to reject the null hypothesis means that the null hypothesis is true. Hence, the answer choice picked is the obvious correct answer.
Hope this Helps!!!
How many centimeter cubes will fill a box 20cm by 6cm by 3cm
Answer:
360
Step-by-step explanation:
formula is L x B x H so first layer would be 6 rows of 20 cubes which is 120cubes
H is 3cm so 120x3 = 360
or find out the volume of the box, 20x6x3 = 360
g Exercise 6. Let X be a Gaussian random variable with X ∼ N (0, σ2 ) and let U be a Bernoulli random variable with U ∼ Bern(?) independent of X. Define V as V = XU. (a) Find the characteristic function of V , ϕV = E(e jsV ) = RfV (v)e jsv. Hint: use iterated expectation. (b) Find the mean and variance of V .
Answer:
Step-by-step explanation
question solved below
Kendra makes $8 per hour mowing lawns in the summer. Gas for the mower
costs $16 and will last all summer. How many hours must she mow to earn at
least $200?
Answer:
27 hours
Step-by-step explanation:
So t is going to represent time. $8t is equivalent to how much she makes for t amount of time. Being she is already down $16 for the gas, we have to take that into consideration that she must earn that back. Set up:
$8t - $16 = $200
Add like terms to get:
$8t = $216
Now solve for t by dividing both sides by $8.
t = 27 hours
What is 3 to the 3rd power
Answer:
27
Step-by-step explanation:
3 x 3 x 3=27
Answer:
27
Step-by-step explanation:
you can just do 3x3x3 or 3^3 to figure it out.. 3x3=9 and 9x3= 27.. hope this helped..
A 2010 estimate of Australia's population is 21,515,754.
Which is the best estimate of the number of Australians with type A blood in 2010?
Blood Types in Australia
Answer:
[tex]\mathrm{Number\:of\:Australians\:with\:type\:A\:Blood\:Group\:in\:2010}\:\approx\:8175987[/tex]
Step-by-step explanation:
[tex]\mathrm{Percent}:\\\\\mathrm{A\:ratio\:expressed\:as\:a\:fraction\:out\:of\:a\:hundred.}\\\\\mathrm{In\:order\:to\:convert\:a\:percent\:to\:a\:ratio,\:divide\:it\:by\:100}:\\\\38\%\:=\frac{38}{100}\\\\\mathrm{Percentage\:of\:population\:with\:A\:Blood\:Type}\:=\frac{38}{100}\times 21515754\\\\\approx8175987[/tex]
An estimated 8,175,987 Australians have Type A blood.
There were 21,515,754 in Australia in 2010. In the same year, it was estimated that 38% of people had Type A blood.
This means that the best estimate of people in Australia with Type A blood is:
= Percentage of people with type A blood x Number of people in Australia
= 38% x 21,515,754
= 8,175,986.52
= 8,175,987 people
In conclusion, approximately 8,175,987 Australians have Type A blood.
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Write the word sentence as an inequality. A number h is at least −12.
Answer:
h ≥ -12
Step-by-step explanation:
at least means greater than or equal to
h ≥ -12
Answer:
h>-12
Step-by-step explanation:
multiply 3/4 x 16/19
To multiply fractions, multiply the numerators and denominators separately. For [tex]\frac{3}{4} \times \frac{16}{19}[/tex], the result is [tex]\frac{12 }{ 19}[/tex] after simplifying.
To multiply fractions, you simply multiply the numerators together and the denominators together. In this case, [tex]\frac{3}{4} \times \frac{16}{19}[/tex] would be calculated as: [tex]\frac{3 \times 16}{4 \times 19} = \frac{48 }{ 76}[/tex] This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which in this case is 4: [tex]\frac{48 \div 4 }{ 76 \div 4 }= \frac{12 }{ 19}[/tex].
A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school. (7 points) What is the proportion of semester students returning to summer school
Answer:
The proportion of semester students returning to summer school
p = 0.35
Step-by-step explanation:
Explanation:-
Given data A university planner is interested in determining the percentage of spring semester students who will attend summer school.
She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school
Given the sample size 'n' = 160
let 'x' = 56
Sample proportion of semester students returning to summer school
[tex]p = \frac{x}{n} = \frac{56}{160}[/tex]
p = 0.35
Ali is riding his bicycle. He rides at a Speed of 12.8 kilometers per hour for 2 hours how many kilometers did he ride
Answer:
25.6 kilometers
Step-by-step explanation:
12.8 km in an hour
he is riding for 2 hours
12.8 x 2 = 25.6
Using the formula 'Distance equals Speed times Time', we find that Ali rode a distance of 25.6 kilometers given that he rode his bicycle at a speed of 12.8 kilometers per hour for 2 hours.
Explanation:To answer this question, you can use the formula to calculate distance, which is Speed multiplied by Time. In Ali's case, he's riding his bicycle at a speed of 12.8 kilometers per hour and for 2 hours. Using the formula, you'll multiply 12.8(km/h) by 2(h). Thus, Ali's distance covered would be 25.6 kilometers.
Here's how it works in a step-by step format:
Use the formula: Distance = Speed x TimePlug in the given values: Distance = 12.8 km/h x 2 hCompute: Distance = 25.6 kmTherefore, Ali rode his bicycle for a distance of 25.6 kilometers.
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The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes". Suppose that 150 women and 200 men were interviewed.
a) What are the null and alternative hypotheses that The Wall Street Journal should test in order to show that its claim is true?
b) For a 0.01 level of significance, what is the critical value for the rejection region?
c) What is the value of the test statistic? (hint: you need to find pbar)
d) What is the p-value of the test?
e) What conclusion should be reached?
Answer:
(a) H₀: P₂ - P₁ = 0 vs. Hₐ: P₂ - P₁ > 0.
(b) The critical value for the rejection region is 2.33.
(c) The calculated z-statistic value is, z = 7.17.
(d) The p-value of the test is 0.
(e) The proportion of women who view sexual harassment on the job is more than that for men.
Step-by-step explanation:
Here we need to test whether the proportion of women who view sexual harassment on the job is more than that for men.
(a)
Our hypothesis will be:
H₀: The difference between the proportions of men and women who view sexual harassment on the job as a problem is same, i.e. P₂ - P₁ = 0
Hₐ: The difference between the proportions of men and women who view sexual harassment on the job as a problem is more than 0, i.e. P₂ - P₁ > 0.
(b)
The significance level of the test is:
α = 0.01
The rejection region is defined as:
If test statistic value, z[tex]_{t}[/tex] > z₀.₀₁ then then null hypothesis will be rejected.
Compute the critical value of the test as follows:
[tex]z_{\alpha}=z_{0.01}=2.33[/tex]
*Use z-table.
Thus, the critical value for the rejection region is 2.33.
(c)
The z-statistic for difference of proportions is,
[tex]z=\frac{\hat p_{2}-\hat p_{1}}{\sqrt{P(1-P)\times (\frac{1}{n_{2}}+\frac{1}{n_{1}})}}[/tex]
[tex]\hat p_{i}[/tex] = ith sample proportion,
P = population proportion
[tex]n_{i}[/tex] = ith sample size.
The given information is:
[tex]n_{1}=200\\n_{2}=150\\\hat p_{1}=0.24\\\hat p_{2}=0.62[/tex]
Since, there is no data about the population proportion the unbiased estimate of P is given by,
[tex]P=\frac{n_{1}\hat p_{1}+n_{2}\hat p_{2}}{n_{1}+n_{2}}=\frac{200\times 0.24+150\times 0.62}{200+150}=0.4029[/tex]
Using the given data we compute the z-statistic as:
[tex]z=\frac{\hat p_{2}-\hat p_{1}}{\sqrt{P(1-P)\times (\frac{1}{n_{2}}+\frac{1}{n_{1}})}}[/tex]
[tex]=\frac{0.62-0.24}{\sqrt{0.4029(1-0.4029)\times (\frac{1}{150}+\frac{1}{200})}}[/tex]
[tex]=7.17[/tex]
Thus, the calculated z-statistic value is, z = 7.17.
(d)
Compute the p-value of the test as follows:
[tex]p-value=P(Z>z_{t})[/tex]
[tex]=P(Z>7.17)\\=1-P(Z<7.17)\\=1 -(\approx1)\\=0[/tex]
Thus, the p-value of the test is 0.
(e)
As stated in part (b), if z₀.₀₁ > z[tex]_{t}[/tex] then then null hypothesis will be rejected.
z[tex]_{t}[/tex] = 7.17 > z₀.₀₁ = 2.33
Thus, the null hypothesis will be rejected at 1% level of significance.
Conclusion:
The proportion of women who view sexual harassment on the job is more than that for men.
Write the equation for g(x)
Answer:
g-x=3
Step-by-step explanation:
Josh wants to download music online. He must buy a membership for $14.
Then he can download songs for 99 cents each. Josh has $20. How many
songs can Josh buy without spending more money than he has?
Answer:
6 songs
Step-by-step explanation:
It's best to start by setting up an equation equal to $20.
$14 + $.99s = $20
s being songs in this case.
First we add like terms by subtracting $14 from both sides.
$.99s = $6
Now we solve for s by dividing both sides by $.99
s = $6.06
Therefore, Josh can by 6 songs.
Final answer:
Josh can buy 6 songs with his remaining $6 after purchasing a $14 membership, since each song costs 99 cents.
Explanation:
Josh wants to download music online. With $20 to spend, he first needs to buy a membership for $14, leaving him with $6 to spend on songs. Each song costs 99 cents, so to determine how many songs Josh can purchase without exceeding his budget, we have to divide the remaining money by the cost per song.
Step 1: Calculate the remaining budget after membership: $20 - $14 = $6.
Step 2: Divide the remaining budget by the cost per song: $6 \(\div\) $0.99 ≈ 6 songs.
Thus, Josh can buy 6 songs without spending more than he has.
Let X and Y denote the values of two stocks at the end of a five-year period. X is uniformly distributed on the interval (0, 12). Given X = x, Y is uniformly distributed on the interval (0, x). Determine Cov(X, Y) according to this model.
Answer:
Cov (X,Y) = 6
Step-by-step explanation:
hello,
Cov(X,Y) = E(XY) - E(X)E(Y)
we must first find E(XY), E(X), and E(Y).
since X is uniformly distributed on the interval (0,12), then E(X) = 6.
next we find the joint density f(x,y) using the formula
[tex]f(x,y) = g(y|x)f_{X}(x)[/tex]
[tex]f_{X} (x) = \frac{1}{12} \ $for$\ 0<x<12[/tex] this is because f is uniformly distributed on the the interval (0,12)
also since the conditional probability density of Y given X=x, is uniformly distributed on the interval [0,x], then
[tex]g(y|x)=\frac{1}{x}[/tex] for 0≤y≤x≤12
thus
[tex]f(x,y)=\frac{1}{12x}[/tex].
hence,
[tex]E(X,Y)= \int\limits^{12}_{x=0} \int\limits^x_{y=o} xy\frac{1}{12x} \,dy dx[/tex]
[tex]E(X,Y)=\frac{!}{24} \int\limits^{12}_{x=0} x^2 \, dx = 24[/tex]
also,
[tex]E(Y) = \int\limits^{12}_{x=0} \int\limits^x_{y=0} y\frac{1}{12x} \, dydx[/tex]
[tex]E(Y)=\frac{1}{24}\int\limits^{12}_{x=0} {x} \, dx =3[/tex]
thus Cov(X,Y) = E(XY) - E(X)E(Y)
= 24 - (6)(3)
= 6
Practice
Active
Write the ordered pair that represents yz. Then find the magnitude of yz
Y(3, 1), z{0, 4)
Answer:
[tex](y,z)=(3,5)\\\\ |(y,z)|=\sqrt{34}[/tex]
Step-by-step explanation:
Given y(3, 1), z(0, 4)
-The ordered pair is written by summing their corresponding coordanates as below:
[tex](y,z)=y(3,1)+z(0,4)\\\\=(3+0,1+4)\\\\=(3,5)[/tex]
-We then calculate the magnitude of this ordered pair as following:
[tex]|y,z|=\sqrt{y^2+z^2}\\\\=\sqrt{3^2+5^2}\\\\=\sqrt{34}\\\\\therefore |(y,z)|=\sqrt{34}[/tex]
Hence, the magnitude of the ordered pair is [tex]\sqrt{34}[/tex]
The plot shows the temperatures (in ºF) for a group of children who visited a doctor’s office. A plot shows the temperature of children at a doctor's office. 1 child had a temperature of 96 degrees; 2, 97 degrees; 5, 98 degrees; 2, 99 degrees; 1, 100 degrees. What conclusions can be drawn from the data set? Check all that apply.
Answer:
See below.
Step-by-step explanation:
1) the measure of center are the same
3) there is little variability in the data
4) the average temperature is 98
5) the data is clustered around the mean
The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. A simple random sample of 50 undergraduates at Johns Hopkins University will be obtained to estimate the proportion of all Johns Hopkins students who feel that drinking is a problem among college students. A simple random sample of 50 undergraduates at Ohio State University will be obtained to estimate the proportion of all Ohio State students who feel that drinking is a problem among college students. Answer Questions 4-5 below.
The remaining part of Question:
4) what can we conclude about sampling variability in the sample proportion calculated in the sample at John Hopkins as compared to that calculated in the sample at Ohio State.
5) The number of undergraduates at Johns Hopkins is approximately 2000 while the number at Ohio State is approximately 40000, suppose instead that at both schools, a simple random sample of about 3% of the undergraduates Will be taken.
Answer:
4) The sample proportion from Johns Hopkins will have about the same sampling variability as that from Ohio State
5) The sample proportion from John Hopkins will have more sampling variability than that from Ohio State
Step-by-step explanation:
Note: The sampling variability in the sample proportion decreases with increase in the sample size.
4) since the sample size at both Johns Hopkins and Ohio State is the same (i.e. n = 50), the sample variability of the sample proportion will be the same for both cases.
5) 3% of the population are selected for the observation in both cases.
At Johns Hopkins, sample size, n = 3% * 2000
n = 60
At Ohio State, sample size, n = 3% * 40000
n = 1200
Since sampling variability in the sample proportion decreases with increase in the sample size, the sampling variability in sample proportion will be higher at Johns Hopkins than at Ohio State.
Is 26, 31, 36, 41, 46 an arithmetic sequence?
Answer:
Yes, it is arithmetic sequence.
Step-by-step explanation:
31-26=5
36-31=5
41-36=5
46-41=5
Difference between consecutive numbers is the same, so we have arithmetic sequence.
Answer:
Yes it is an arithmetic sequence
26+5=31
31+5=36
36+5=41
41+5=46
Suppose samples of size 100 are drawn randomly from a population that has a mean of 20 and a standard deviation of 5. What are the values of the mean and the standard deviation of the distribution of the sample means
Answer:
a) The mean of the sampling distribution of means μₓ = μ = 20
b) The standard deviation of the sample σₓ⁻ = 0.5
Step-by-step explanation:
Explanation:-
Given sample size 'n' =100
Given mean of the Population 'μ' = 20
Given standard deviation of population 'σ' = 5
a) The mean of the sampling distribution of means μₓ = μ
μₓ = 20
b) The standard deviation of the sample σₓ⁻ = [tex]\frac{S.D}{\sqrt{n} }[/tex]
Given standard deviation of population 'σ' = 5
= [tex]\frac{5}{\sqrt{100} } = 0.5[/tex]
Final answer:
The mean of the distribution of the sample means drawn from a population with a mean of 20 and a standard deviation of 5, using samples of size 100, is 20. The standard deviation of this distribution, also known as the standard error, is 0.5.
Explanation:
The question involves understanding the concept of the distribution of sample means, also known as the sampling distribution. When samples of size 100 are drawn from a population with a mean (μ) of 20 and a standard deviation (σ) of 5, the mean of the distribution of the sample means will be the same as the population mean, which is 20. However, the standard deviation of the distribution of sample means, known as the standard error (SE), will be the population standard deviation divided by the square root of the sample size (√n), which in this case is 5/√100 = 0.5.
Therefore, the mean of the distribution of the sample means is 20 and the standard deviation (standard error) of this distribution is 0.5. This is based on the central limit theorem which states that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population’s distribution, with these exact parameters of mean and standard deviation.
How tall is a building that casts a 74-ft shadow when the angle of elevation of the sun is 36°?
Answer:
101.85ft
Step-by-step explanation:
We can use tan here
[tex]tan\theta=\frac{opp}{adj}\\adj = \frac{opp}{tan \theta} \\adj = \frac{74}{tan(36)} = 101.85[/tex]
The height should be 101.85 ft.
Calculation of the height:Since it casts a 74-ft shadow when the angle of elevation of the sun is 36°
So, the height should be
Here we can use tan
[tex]= 74\div tan\ 36[/tex]
= 101.85 ft
Therefore, we can conclude that The height should be 101.85 ft.
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The point (-3,1) is on the terminal side of the angle in standard position. What is tanθ
Answer:
[tex] \tan \theta = - \frac{1}{3}[/tex]
Step-by-step explanation:
Since, point (-3, 1) is on the terminal side of the angle in standard position.
[tex] \therefore \: ( - 3, \: 1) = (x, \: y) \\ \therefore \:x = - 3 \: \: and \: \: y = 1 \\ \because \tan \theta = \frac{y}{x} \\ \therefore \:\tan \theta = \frac{1}{ - 3} \\ \\ \huge \red{ \boxed{\therefore \:\tan \theta = - \frac{1}{3} }}[/tex]
A study was done on the timeliness of flights (on-time vs. delayed) of two major airlines: StatsAir and AirMedian. Data were collected over a period of time from five major cities and it was found that StatsAir does better overall (i.e., has a smaller percentage of delayed flights). However, in each of the five cities separately, AirMedian does better.
Which of the following is correct?
(a) This situation is mathematically impossible.
(b) This is an example of Simpson's Paradox.
(c) "City" is a lurking variable in this example.
(d) This is an example of a negative association between variables.
(e) Both (b) and (c) are correct.
Answer:
The answer is Option E; both B and C are correct
Step-by-step explanation:
Both (b) and (c) are correct. Simpson's paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data. This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration.
Now, this question is an example of Simpsons paradox because the groups of collected data over a period of time from five major cities showed a trend that StatsAir does better overall, but this trend is reversed when the groups are studied separately to show that air median does better.
So, option B is correct.
Also, City is a variable that influences both the dependent variable and independent variable, causing a spurious association. That is it is the cause of why the 2 results are biased. Thus, city is a lurking variable.
So, option C is also correct
The U.S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U.S. Department of Agriculture Center for Nutrition Policy and Promotion).
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 13120
For the alternative hypothesis,
µ ≠ 13120
This is a 2 tailed test
Since the population standard deviation is not given, the t test would be used to determine the test statistic. The formula is
t = (x - µ)/(s/√n)
Where
s = sample standard deviation
x = sample mean
µ = population mean
n = number of samples
From the information given,
µ = $13120
x = $12925
n = 500
s = $1745
t = (12925 - 13120)/(1745/√500) = - 2.5
Degree of freedom = n - 1 = 500 - 1 = 499
Using the t score calculator to find the probability value,
p = 0.012
Since α = 0.10 > p = 0.012, it means that there is enough evidence to reject the claim
A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether this distribution has changed, you randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the claimed or expected distribution? Use alpha = 0.10.
Response Old Survey % New Survey Frequency
Reward 27 112
Low rate 23 96
Cash back 21 109
Discount 9 48
Others 20 60
Answer:
See explanation
Step-by-step explanation:
Solution:-
- A survey was conducted among the College students for their motivations of using credit cards two years ago. A randomly selected group of sample size n = 425 college students were selected.
- The results of the survey test taken 2 years ago and recent study are as follows:
Old Survey ( % ) New survey ( Frequency )
Reward 27 112
Low rate 23 96
Cash back 21 109
Discount 9 48
Others 20 60
- We are to test the claim for any changes in the expected distribution.
We will state the hypothesis accordingly:
Null hypothesis: The expected distribution obtained 2 years ago for the motivation behind the use of credit cards are as follows: Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20%
Alternate Hypothesis: Any changes observed in the expected distribution of proportion of reasons for the use of credit cards by college students.
( We are to test this claim - Ha )
We apply the chi-square test for independence.
- A chi-square test for independence compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each other.
- We will compute the chi-square test statistics ( X^2 ) according to the following formula:
[tex]X^2 = Sum [ \frac{(O_i - E_i)^2}{Ei} ][/tex]
Where,
O_i : The observed value for ith data point
E_i : The expected value for ith data point.
- We have 5 data points.
So, Oi :Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20% from a group of n = 425.
Ei : Rewards = 112 , Low rate = 96, Cash back = 109, Discount = 48, Others = 60.
Therefore,
[tex]X^2 = [ \frac{(112 - 425*0.27)^2}{425*0.27} + \frac{(96 - 425*0.23)^2}{425*0.23} + \frac{(109 - 425*0.21)^2}{425*0.21} + \frac{(48 - 425*0.09)^2}{425*0.09} + \frac{(60 - 425*0.20)^2}{425*0.20}]\\\\X^2 = [ 0.06590 + 0.03132 + 4.37044 + 2.48529 + 7.35294]\\\\X^2 = 14.30589[/tex]
- Then we determine the chi-square critical value ( X^2- critical ). The two parameters for evaluating the X^2- critical are:
Significance Level ( α ) = 0.10
Degree of freedom ( v ) = Data points - 1 = 5 - 1 = 4
Therefore,
X^2-critical = X^2_α,v = X^2_0.1,4
X^2-critical = 7.779
- We see that X^2 test value = 14.30589 is greater than the X^2-critical value = 7.779. The test statistics value lies in the rejection region. Hence, the Null hypothesis is rejected.
Conclusion:-
This provides us enough evidence to conclude that there as been a change in the claimed/expected distribution of the motivations of college students to use credit cards.
Final answer:
To test for changes in credit card usage motivations among college students, calculate the expected frequencies from the old survey percentages, apply the chi-square goodness-of-fit test, and compare the statistic to the chi-square critical value at alpha = 0.10.
Explanation:
Understanding the Hypothesis Test for Changed Distribution
To determine whether there has been a shift in the distribution of college students' motivations for using credit cards since the previous survey, we conduct a hypothesis test for goodness of fit. The test will compare the observed frequencies from the new survey with the expected frequencies based on the old survey percentages.
First, calculate the expected frequency for each category using the formula: Expected Frequency = (Old Survey Percentage / 100) × Total Number of Students. Then, employ the chi-square goodness-of-fit test to analyze the data:
Reward: Expected = 0.27 × 425 = 114.75
Low rate: Expected = 0.23 × 425 = 97.75
Cash back: Expected = 0.21 × 425 = 89.25
Discount: Expected = 0.09 × 425 = 38.25
Others: Expected = 0.20 × 425 = 85.00
With the expected frequencies calculated, the chi-square statistic will be computed:
χ² = Σ((Observed - Expected) ² / Expected)
This statistic will be compared to a critical value from the chi-square distribution table with (n - 1) degrees of freedom, where n is the number of categories, at alpha = 0.10 to determine whether to reject the null hypothesis (no change in distribution).
Carmen needs $3560 for future project. She can invest $2000 now at annual rate of 7.8%, compound monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?
Answer:
7.42 years (7 years 5 months)
Step-by-step explanation:
The future value of Carmen's account can be modeled by
FV = P(1 +r/12)^(12t)
where P is the principal invested, r is the annual rate, and t is the number of years.
Solving for t, we have ...
FV/P = (1 +r/12)^(12t)
log(FV/P) = 12t·log(1 +r/12)
t = log(FV/P)/(12·log(1 +r/12))
For FV = 3560, P=2000, r = 0.078, the time required is ...
t = log(3560/2000)/(12·log(1 +.078/12))
t ≈ 7.42
It will take Carmen about 7 years 5 months to reach her savings goal.