This solution calculates the probability of different outcomes when rolling a fair die three times. The results are obtained by defining the successful outcomes versus the total possible outcomes for each specific event.
Explanation:This question is about probability. A fair die has 6 equally likely outcomes. Let's address each part:
You roll all 4's: There's 1 chance in 6 to roll a 4. Since you're rolling the die three times, the probability is (1/6) * (1/6) * (1/6) = 1/216. You roll all even numbers: There are 3 even numbers on a die (2, 4, 6), so the probability is (3/6) * (3/6) * (3/6) = 1/8. None of your rolls gets a number divisible by 2: This is the same as rolling all odd numbers. There are 3 odd numbers on a die (1, 3, 5), so the probability is (3/6) * (3/6) * (3/6) = 1/8. You roll at least one 2: The opposite of this are outcomes without any 2, i.e., combinations of 1, 3, 4, 5, and 6. Thus, subtract combinations without any 2 from total possible combinations: 1 - [(5/6) * (5/6) * (5/6)] = 91/216. The numbers you roll are not all 2's: The only case when this does not happen is when you roll a 2 three times. So, if we subtract the probability of rolling three 2's from 1, we get 1 - (1/6) * (1/6) * (1/6) = 215/216.Learn more about probability here:
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The probability of rolling all 4's is 1/64. The probability of rolling all even numbers is 7/64. The probability of not rolling all 2's is 63/64.
Explanation:a) The probability of rolling all 4's is ⅛3, or 1/64. There is only one way to roll a 4 on a fair die and a total of 6 possible outcomes on each roll, so the probability is 1/6. Since the rolls are independent, the probability of getting a 4 on all three rolls is (1/6)(1/6)(1/6) = 1/64.
b) The probability of rolling all even numbers is also 1/64. There are 3 even numbers on a die (2, 4, and 6), so the probability of rolling an even number on any single roll is 3/6 or 1/2. Since the rolls are independent, the probability of getting an even number on all three rolls is (1/2)(1/2)(1/2) = 1/8. However, we need to subtract the probability of rolling all 4's from this, which is also 1/64. So the final probability is 1/8 - 1/64 = 7/64.
c) The probability of none of the rolls getting a number divisible by 2 is 1 - (1/2)(1/2)(1/2) = 1 - 1/8 = 7/8. This is the complement of rolling all even numbers.
d) The probability of rolling at least one 2 is 1 - the probability of rolling no 2's. The probability of not rolling a 2 on any single roll is 5/6, so the probability of not rolling a 2 on all three rolls is (5/6)(5/6)(5/6) = 125/216. Therefore, the probability of rolling at least one 2 is 1 - 125/216 = 91/216.
e) The probability of rolling all 2's is 1/64. Therefore, the probability of not rolling all 2's is 1 - 1/64 = 63/64.
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When you sample the first individuals you can find, you call it a _____; it's cheap and easy to do, but statistically not a very strong method.
A.
cluster
B.
stratified random sample
C.
convenience sample
D.
cluster sample
E.
simple random sample
Answer:
C. convenience sample
Step-by-step explanation:
Convenience sampling is a type of non-probability sampling or non-random sampling which is any sampling method where some elements of the population have no chance of selection. The selection is left at the judgment of the interviewer or investigator and this non-randomness in the statistical sense implies that the interviewer or investigator do not fulfill some of the basic requirements or assumptions of the common standard methods for testing hypothesis and drawing inferences from the sample data to the target population
Two teams play a series of games, the first team to win 4 games is the winner overall. Suppose that one of the teams is stronger and has probability 0.6 to win each game, independent of any other games. What is the probability that the stronger team wins the series in exactly i games. Do it for i = 4,5,6,7. Compare the probability that the stronger team wins with the probability that it would win a 2 out of 3 series.
Answer:
Step-by-step explanation:
Figuring it out rn
Which of the following are true about the correlation coefficient r? Select one or more:
If the correlation coefficient is +1, then the slope of the regression line is also +1.
The correlation coefficient is always greater than 0.
If the correlation coefficient is close to 0, that means there is a strong linear relationship between the two variables.
The correlation coefficient will change if we change the units of measure.
The correlation coefficient is always between -1 and +1.
If the correlation coefficient is positive, the slope of the regression line will also be positive.
Answer:
Which is the output of the formula =AND(12>6;6>3;3>9)?
A.
TRUE
B.
FALSE
C.
12
D.
9
Step-by-step explanation:
Answer:
A correlation coefficient close to zero
Step-by-step explanation:
This makes linear regression unreasonable because the correlation coefficient shows how related the data points are, -1 and 1 being very strong and 0 being uncorrelated. So the line of best fit would not make sense because the data points are random in relation to one another.
Step-by-step explanation:
Find the error in the "proof" of the following "theorem." "Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive. "Proof ": Let a ∈ A. Take an element b ∈ A such that (a, b) ∈ R. Because R is symmetric, we also have (b, a) ∈R. Now using the transitive property, we can conclude that (a, a) ∈ R because (a, b) ∈ R and (b, a) ∈ R.
Answer:
The proof is wrong. The part that says 'take an element b ∈ A such that (a, b) ∈ R' is assuming that such an element b exists, and that may not be the case. We can give the 'theorem' validation by adding the hypothesis ' each element of A is related to any other element of A', otherwise the 'theorem' is false. An example for that is the following relation on the natural numbers:
'a R b if both numbers are even'
This relation if crearly symmetric and transitive, but it is not reflexive, an odd number does not relate with itself. In fact, odd numbers dont relate with any number.
Final answer:
The error in the given "proof" lies in the assumption that an element b ∈ A exists such that (a, b) ∈ R, which is not necessarily true for all a ∈ A. Symmetry and transitivity of a relation R do not inherently guarantee its reflexivity.
Explanation:
The error in the "proof" that a symmetric and transitive relation R on a set A is also reflexive lies in the initial assumption. The proof assumes the existence of an element b ∈ A such that (a, b) ∈ R for an arbitrary a ∈ A, but this is not guaranteed. Reflexivity requires that (a, a) ∈ R for all a ∈ A, independently of the existence of any such b. The proof fails because it assumes a specific relationship exists (between a and b) to demonstrate reflexivity, which is a general property that must hold without needing to reference any other elements.
The properties of reflexivity, symmetry, and transitivity define an equivalence relation. Symmetry and transitivity alone do not imply reflexivity. Therefore, the statement that a symmetric and transitive relation is reflexive is incorrect without additional assumptions about R.
obesity: The National Center for Health Statistics conducted the National Health Interview Survey (NHIS) for 27,787 U.S. civilian noninstitutionalized adults in January – September 2014. According to an early release report, an estimated 29.9% of U.S. adults aged 20 and over were obese. Obesity is defined as a body mass index (BMI) of 30 kg/m 2 or more. True or false? The 29.9% is a parameter representing a population of 27,787 adults.
Answer:
False.
Step-by-step explanation:
Hello!
29.9% is the proportion of adults aged 20 and over that were obese in January - September 2014.
This percentage was obtained from a sample of 27 787 adults, it's not a parameter but an estimation of the population proportion obtained from this sample.
I hope it helps!
False, the 29.9% does not represent a parameter for the specific population of 27,787 adults surveyed in the National Health Interview Survey (NHIS).
The 29.9% figure representing U.S. adults aged 20 and over who were estimated to be obese based on the NHIS data is a statistic, not a parameter of the surveyed 27,787 adults, as it aims to generalize the obesity rate to the broader U.S. adult population.
Instead, this percentage is a statistic representing an estimate of the entire U.S. adult population aged 20 and over, based on the sample surveyed.
In statistics, a parameter refers to a numerical measure that describes a characteristic of a population, whereas a statistic is a numerical measure that describes a characteristic of a sample from the population.
Therefore, since the 29.9% figure estimated from the NHIS sample aims to generalize to the broader U.S. adult population, it is classified as a statistic, and not a parameter of the 27,787 adults directly surveyed.
Write an equation of the line passing through the point (3, -1) and parallel to the line y=2/3x - 5. Show work
Answer:
The answer is: y = 2/3x - 3
Step-by-step explanation:
Given point: (3, -1)
Given equation: y = 2/3x - 5, which is in the form y = mx + b where m is the slope and b is the y intercept.
Parallel lines have the same slope. Use the point slope form of the equation with the point (3, -1) and substitute:
y - y1 = m(x - x1)
y - (-1) = 2/3(x - 3)
y + 1 = 2/3x - 6/3
y + 1 = 2/3x - 2
y = 2/3x - 3
Proof:
f(3) = 2/3(3) - 3
= 6/3 - 3
= 2 - 3
= -1, giving the point (3, -1)
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In the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated. Is it possible to claim that most of the seed will germinate? Consider a confidence level of 95%.
Answer:
More than 50% would germinate
Step-by-step explanation:
Given that in the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated
Let us check whether more than 50% will germinate using hypothesis test
[tex]H_0: p = 0.50\\H_a: p>0.50\\[/tex]
(right tailed test)
Sample proportion p =[tex]\frac{37}{60} =0.617\\q = 0.383\\Std error = \sqrt{\frac{pq}{n} } =0.0628[/tex]
p difference = 0.117
Test statistic Z = p difference/std error = 1.864
p value =0.0312
Since p value <0.05 our significance level of 5% we reject null hypothesis
It is possible to claim that most of the seed will germinate (i.e. more than 50%)
the height of woman ages 20-29 is normally distributed , with a mean of 64.4 inches. assuming the standard diviation = 2.3 inches. are you more likely to randomly select 1 woman with a height less than 64.9 inches or are you more likely to select a sample of 22 woman with a mean height less than 64.9 inches.(USING STANDARD NORMAL TABLE)A. what is the probability of randomly selecting 1 woman with a height less than 64.9 inches?B. what is the probability of selecting a sample of 22 woman with a mean height less then 64.9 inches?C. are you more likely to randomly select 1 woman with a height less than 64.9 inches or are you more likely to select a sample of 22 woman with a mean height of 64.9 inches?
We use the Z-score to determine the probability of selecting a single woman with a height less than 64.9 inches, and the concept of a sampling distribution (standard error) for a sample of 22 women. Generally, the larger the sample size, the closer the sample mean gets to the population mean, making it usually more probable to select one woman with a height of less than 64.9 inches than for a sample of 22 women.
Explanation:This question is about probability and statistics, and specifically about the Normal Distribution and its applications. We know that the height of women aged 20-29 is normally distributed with a mean of 64.4 inches and a standard deviation of 2.3 inches.
A. To find the probability of randomly selecting one woman with a height less than 64.9 inches, we need to convert 64.9 into a z-score using the formula Z = (X - μ) / σ. Here, X represents the given height (64.9 inches), μ is the mean (64.4 inches), and σ is the standard deviation (2.3 inches). The resulting Z score is then looked up in the standard normal table to determine the probability.B. The likelihood of selecting a sample of 22 women with a mean height less than 64.9 inches would involve using the concept of a sampling distribution. Here, the standard deviation is divided by the square root of the sample size (σ/√n) to calculate the standard error. This would then be used in a similar fashion as in part A, by calculating a z-score to find the probability.C. We can't definitively answer this without exact values but generally, the larger the sample size the closer the sample mean gets to the population mean due to the law of large numbers. Therefore, it would usually be more likely to select one woman with a height less than 64.9 inches than to select a sample of 22 women with a mean height less than 64.9 inches.Learn more about Normal Distribution / Probability here:https://brainly.com/question/30653447
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Calculate probabilities for selecting 1 woman and a sample of 22 women with heights less than 64.9 inches; Compare which selection is more likely.
Given:
Mean (μ) = 64.4 inches
Standard deviation (σ) = 2.3 inches
Probability for 1 Woman:Calculate the z-score:
z = (x - μ) / σ
= (64.9 - 64.4) / 2.3
= 0.5 / 2.3
= 0.2174
Now, we look up the probability corresponding to a z-score of 0.2174 in the standard normal table.
The probability for z = 0.2174 is approximately 0.5869.
So, the probability of randomly selecting 1 woman with a height less than 64.9 inches is approximately 0.5869.
Probability for 22 Women:Calculate standard error:
SE = σ / √n
= 2.3 / √(22)
≈ 0.489
Find the z-score for the sample mean:
z = ([tex]^-_x[/tex] - μ) / σ
= (64.9 - 64.4) / 0.489
= 0.5 / 0.489
≈ 1.021
Now, we look up the probability corresponding to a z-score of 1.021 in the standard normal table.
The probability for z = 1.021 is approximately 0.8451.
So, the probability of selecting a sample of 22 women with a mean height of less than 64.9 inches is approximately 0.8451.
Comparing the probabilities:→ Probability of randomly selecting 1 woman with a height less than 64.9 inches: 0.5869
→ Probability of selecting a sample of 22 women with a mean height less than 64.9 inches: 0.8451
Since 0.8451 is greater than 0.5869, it is more likely to select a sample of 22 women with a mean height of less than 64.9 inches.
Evaluate each of the following line integrals.
(a)
integral.gif
C
x dy − y dx, c(t) = (cos(t), sin(t)), 0 ≤ t ≤ 2π
(b)
integral.gif
C
x dy + y dx, c(t) = (2 cos(πt), 2 sin(πt)), 2 ≤ t ≤ 4
Answer:
a) 2π
b) 0
Step-by-step explanation:
Recall that for a parametrized differentiable curve C = (x(t), y(t)) with the parameter t varying on some interval [a, b]
[tex]\large \int_{C}[P(x,y)dx+Q(x,y)dy]=\int_{a}^{b}[P(x(t),y(t))x'(t)+Q(x(t),y(t))y'(t)]dt[/tex]
Where P, Q are scalar functions
a)
C(t) = (x(t), y(t)) = (cos(t), sin(t)), 0 ≤ t ≤ 2π
P(x,y) = -y ==> P(x(t),y(t)) = -y(t) = -sin(t)
Q(x,y) = x ==> Q(x(t),y(t)) = x(t) = cos(t)
x'(t) = -sin(t)
y'(t) = cos(t)
[tex]\large \int_{C}[-ydx+xdy]=\int_{0}^{2\pi}[(-sin(t))(-sin(t))+cos(t)cos(t)]dt=\\\\\int_{0}^{2\pi}[sin^2(t)+cos^2(t)]dt=\int_{0}^{2\pi}dt=2\pi[/tex]
b)
C(t) = (x(t), y(t)) = (2cos(πt), 2sin(πt)), 2 ≤ t ≤ 4
P(x,y) = y ==> P(x(t),y(t)) = y(t) = 2sin(πt)
Q(x,y) = x ==> Q(x(t),y(t)) = x(t) = 2cos(πt)
x'(t) = -2πsin(πt)
y'(t) = 2πcos(πt)
[tex]\large \int_{C}[ydx+xdy]=\int_{2}^{4}[(2sin(\pi t))(-2\pi sin(\pi t))+2cos(\pi t)2\pi cos(\pi t)]dt=\\\\4\int_{2}^{4}[cos^2(\pi t)-sin^2(\pi t)]dt=4\int_{2}^{4}cos(2\pi t)dt=\\\\4\left[\frac{sin(2\pi t)}{2\pi}\right]_2^4=\frac{2}{\pi}(sin(8 \pi)-sin(4\pi))=0[/tex]
A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on three numbers pays 11 to 1 (that is, if you bet $1 and one of the three numbers you bet comes up, you get back your $1 plus another $11). How much do you expect to win with a $1 bet on three numbers?
Answer:
You are expected to lose $0.05 (or win -$0.05)
Step-by-step explanation:
Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.
In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:
[tex]P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\[/tex]
The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:
[tex]EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525[/tex]
Therefore, with a $1 bet, you are expected to lose roughly $0.05
A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:
Answer:
77.53
Step-by-step explanation:
Sample size (n) = 15
Sample mean (μ) = 75
Sample variance (V) = 25
Sample standard deviation (σ) = 5
For a 95% confidence interval, z-score = 1.960
The upper limit of the confidence interval is defined as:
[tex]UL=\mu+z\frac{\sigma}{\sqrt{n}}\\UL=75+1.960\frac{5}{\sqrt{15}} \\UL = 77.53[/tex]
Therefore, the upper limit of the 95% confidence interval proposed is 77.53.
The upper limit of a 95% confidence interval for the population mean is approximately 76.98.
Explanation:The upper limit of a 95% confidence interval for the population mean can be calculated using the formula:
Upper Limit = Sample Mean + (Z-value)(Standard Error)
In this case, since the sample size is 15 and the sample variance is 25:
Standard Error = sqrt(sample variance/sample size)
Z-value can be obtained from the standard normal distribution table or calculator based on the desired confidence level. For a 95% confidence level, the Z-value is approximately 1.96.
Plugging in the values:
Upper Limit = 75 + (1.96)(sqrt(25/15))
Upper Limit ≈ 76.98
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What does the central nervous system use to determine the strength of a stimulus?
- origin of the stimulus
- frequency of action potentials
- size of action potentials
- type of stimulus receptor
Answer:
- frequency of action potentials
The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The intensity of the stimulus is interpreted not by the size, but by the frequency at which these potentials are produced.
Explanation:The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The central nervous system uses action potentials to transfer and process information. An action potential is a brief electrical charge that travels along an axon. The strength or intensity of the stimulus is interpreted not by the size of the action potentials, but by the frequency at which they are produced. For instance, a slightly warm temperature may produce action potentials at a lower frequency than a very hot temperature, which would produce action potentials at a high frequency. The central nervous system decodes this frequency to understand the intensity of the stimulus.
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How would you graph -x plus 2 thx
(1 point) Find the length traced out along the parametric curve x=cos(cos(4t))x=cos(cos(4t)), y=sin(cos(4t))y=sin(cos(4t)) as tt goes through the range 0≤t≤10≤t≤1. (Be sure you can explain why your answer is reasonable)
The length of a curve [tex]C[/tex] given parametrically by [tex](x(t),y(t))[/tex] over some domain [tex]t\in[a,b][/tex] is
[tex]\displaystyle\int_C\mathrm ds=\int_a^b\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
In this case,
[tex]x(t)=\cos(\cos4t)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\sin(\cos4t)(-\sin4t)(4)=4\sin4t\sin(\cos4t)[/tex]
[tex]y(t)=\sin(\cos4t)\implies\dfrac{\mathrm dy}{\mathrm dt}=\cos(\cos4t)(-\sin4t)(4)=-4\sin4t\cos(\cos4t)[/tex]
So we have
[tex]\displaystyle\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=16\sin^24t\sin^2(\cos4t)+16\sin^24t\cos^2(\cos4t)=16\sin^24t[/tex]
and the arc length is
[tex]\displaystyle\int_0^1\sqrt{16\sin^24t}\,\mathrm dt=4\int_0^1|\sin4t|\,\mathrm dt[/tex]
We have
[tex]\sin(4t)=0\implies4t=n\pi\implies t=\dfrac{n\pi}4[/tex]
where [tex]n[/tex] is any integer; this tells us [tex]\sin(4t)\ge0[/tex] on the interval [tex]\left[0,\frac\pi4\right][/tex] and [tex]\sin(4t)<0[/tex] on [tex]\left[\frac\pi4,1\right][/tex]. So the arc length is
[tex]=\displaystyle4\left(\int_0^{\pi/4}\sin4t\,\mathrm dt-\int_{\pi/4}^1\sin4t\,\mathrm dt\right)[/tex]
[tex]=-\cos(4t)\bigg_0^{\pi/4}-\left(-\cos(4t)\bigg_{\pi/4}^1\right)[/tex]
[tex]=(\cos0-\cos\pi)+(\cos4-\cos\pi)=\boxed{3+\cos4}[/tex]
In this exercise we have to use the knowledge of the integral to calculate the length of the arc:
The length of a curve is given by [tex]3+ cos( 4)[/tex]
The length of a curve given parametrically by [tex](x(t), y(t))[/tex] over some domain is [tex]t \in [a, b][/tex]
[tex]\int\limits_C \, ds = \int\limits^a_b {\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 } } \, dt[/tex]
Now performing the derivatives with respect to X and Y, we find that:
[tex]x(t) = cos(cos4t) \rightarrow \frac{dx}{dt} = -sin(cos4t)(-sin4t)(4)= 4sin4tsin(cos4t)\\y(t) = sin(cos4t) \rightarrow \frac{dy}{dt} = cos(cos4t)(-sin4t)(4)=-4sin4tcos(cos4t)[/tex]
So we have:
[tex](\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2= 16sin^24tsin^2(cos4t)+16sin^24tcos^2(cos4t)= 16sin^24t[/tex]
And the arc length is:
[tex]\int\limits^1_0 {\sqrt{16sin^24t} } \, dt= 4\int\limits^1_0 {sin4t} \, dt\\sin(4t)=0 \rightarrow 4t=n\pi \rightarrow t= \frac{n\pi }{4}[/tex]
where n is any integer; this tells us [tex]sin(4t)\geq 0[/tex] on the interval [tex][0,\pi/4][/tex] and [tex]sin(4t)<0[/tex] on [tex][\pi/4, 1][/tex]. So the arc length is:
[tex]=4(\int\limits^{\pi/4}_0 {sin(4t)} \, dt - \int\limits^1_{\pi/4} {sin(4t)} \, dt)\\=(cos(0)-cos(\pi))+(cos(4)-cos(\pi))= 3+cos(4)[/tex]
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Express the null hypothesis and the alternative hypothesis in symbolic form. The owner of a football team claims that the average attendance at games is over 63,500 , and he is therefore justified in moving the team to a city with a larger stadium.
Answer:
[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]
Step-by-step explanation:
We are given the following in the question:
The owner of a football team claims that the average attendance at games is over 63,500.
He wants to justify that the team needs to be moved to a larger stadium outside the city.
If the attendance is larger than 63,500 the team would be moved to a larger stadium and if it is less than or equal to 63,500 that it would not.
Thus, the null and alternate hypothesis will be designed as:
[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]
The null hypothesis says that the average attenders is equal to or less than 63,500 and alternate supports the claim that the attenders average is greater than 63,500.
In a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random, and each was asked if she eventually planned to have a child. One group was selected from among wives married less than two years and the other from among wives married five years. Suppose that 240 of the 300 wives married less than two years planned to have children some day compared to 288 of the 400 wives married five years. Can we conclude that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years? Make use of a P -value.
The P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.
To determine whether the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years, we can conduct a hypothesis test, following these steps:
1. Define the null and alternative hypotheses:
Null hypothesis (H0): The proportion of wives planning to have children is the same in both groups, regardless of the length of marriage.
Alternative hypothesis (H1): The proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.
2. Calculate the proportions and standard errors:
Proportion of wives planning children (<2 years): 240/300 = 0.8
Proportion of wives planning children (5 years): 288/400 = 0.72
Pooled standard error: sqrt((0.8*(1-0.8))/300 + (0.72*(1-0.72))/400) = 0.0298
3. Calculate the test statistic:
z = (0.8 - 0.72) / 0.0298 = 2.68
4. Find the P-value:
Using a z-score table or statistical software, look up the P-value associated with z = 2.68. This gives us a P-value of approximately 0.0072.
5. Make a decision:
Typically, we use a significance level of alpha (α) = 0.05. Since the P-value (0.0072) is less than alpha, we reject the null hypothesis.
This means there is statistically significant evidence to conclude that the proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.
Therefore, based on the P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 55 and a standard deviation of 4. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 43 and 55?
Answer:
50%
Step-by-step explanation:
68-95-99.7 rule
68% of all values lie within the 1 standard deviation from mean [tex](\mu-\sigma,\mu+\sigma)[/tex]
95% of all values lie within the 1 standard deviation from mean [tex](\mu-1\sigma,\mu+1\sigma)[/tex]
99.7% of all values lie within the 1 standard deviation from mean [tex](\mu-3\sigma,\mu+3\sigma)[/tex]
The distribution of the number of daily requests is bell-shaped and has a mean of 55 and a standard deviation of 4.
[tex]\mu = 55\\\sigma = 4[/tex]
68% of all values lie within the 1 standard deviation from mean [tex](\mu-\sigma,\mu+\sigma)[/tex] = [tex](55-4,55+4)[/tex]= [tex](51,59)[/tex]
95% of all values lie within the 2 standard deviation from mean [tex](\mu-1\sigma,\mu+1\sigma)[/tex]= [tex](55-2(4),55+2(4))[/tex]= [tex](47,63)[/tex]
99.7% of all values lie within the 3 standard deviation from mean [tex](\mu-3\sigma,\mu+3\sigma)[/tex]= [tex](55-3(4),55+3(4))[/tex]= [tex](43,67)[/tex]
Refer the attached figure
P(43<x<55)=2.5%+13.5%+34%=50%
Hence The approximate percentage of light bulb replacement requests numbering between 43 and 55 is 50%
I need help with this challenge question pls someone help asap
Answer:
Step-by-step explanation:
Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)
a. The line segment x=4 y=0 z=[0;4]
Find a scalar potential function f for F, such that
F=∇f.
The work done by F over the line segment is?
b. The helix r(t)= (4cost)i +(4sint)j +(2t/pi)k t=[0;2pi]
Find df/dt for F?
The Work done by F over the Helix?
c. The x axis from (4,0,0) to (0,0,0) followed by the line z=x, y=0 from (0,0,0) to (4,0,4)
What is the integral to comput the work done by F along the x-axis from followed by the line z=x?
What is the work done by F over the 2 curves
[tex]\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k[/tex]
We want to find [tex]f(x,y,z)[/tex] such that [tex]\nabla f=\vec F[/tex]. This means
[tex]\dfrac{\partial f}{\partial x}=x^2+y[/tex]
[tex]\dfrac{\partial f}{\partial y}=y^2+x[/tex]
[tex]\dfrac{\partial f}{\partial z}=ze^z[/tex]
Integrating both sides of the latter equation with respect to [tex]z[/tex] tells us
[tex]f(x,y,z)=e^z(z-1)+g(x,y)[/tex]
and differentiating with respect to [tex]x[/tex] gives
[tex]x^2+y=\dfrac{\partial g}{\partial x}[/tex]
Integrating both sides with respect to [tex]x[/tex] gives
[tex]g(x,y)=\dfrac{x^3}3+xy+h(y)[/tex]
Then
[tex]f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)[/tex]
and differentiating both sides with respect to [tex]y[/tex] gives
[tex]y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C[/tex]
So the scalar potential function is
[tex]\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}[/tex]
By the fundamental theorem of calculus, the work done by [tex]\vec F[/tex] along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it [tex]L[/tex]) in part (a) is
[tex]\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}[/tex]
and [tex]\vec F[/tex] does the same amount of work over both of the other paths.
In part (b), I don't know what is meant by "df/dt for F"...
In part (c), you're asked to find the work over the 2 parts (call them [tex]L_1[/tex] and [tex]L_2[/tex]) of the given path. Using the fundamental theorem makes this trivial:
[tex]\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3[/tex]
[tex]\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4[/tex]
An experiment consists of flipping a coin, rolling a 15 sided die, and spinning a roulette wheel. What is the probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17 ?
Answer:
There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.
Step-by-step explanation:
We have to find the probability of the three separate events, and then multiply them.
coin comes up heads
There is a [tex]\frac{1}{2}[/tex] probability that the coin comes up heads.
the die comes up less than 4
The are 15 sides on the die, from 0 to 14.
The values that satisfy us are 0,1,2,3.
So the probability is [tex]\frac{4}{15}[/tex].
the roulette wheel comes up with a number greater than 17
There roulette wheel can come from 1 to 36. There are 19 values greater than 17. So this probability is [tex]\frac{19}{36}[/tex]
What is the probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17 ?
[tex]P = \frac{1}{2}*\frac{4}{15}*\frac{19}{36} = 0.2639[/tex]
There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.
The combined probability of the coin landing on heads, the die rolling less than 4, and the roulette wheel landing on a number greater than 17 is found by multiplying the individual probabilities of each event.
Explanation:The question involves calculating the combined probability of independent events in a probability experiment: flipping a coin, rolling a 15-sided die, and spinning a roulette wheel. Each event's probability is calculated separately and then multiplied together to find the probability of all events occurring simultaneously.
The probability the coin comes up heads is 0.5, because a fair coin has two sides and the event has a theoretical probability of 1 in 2. When rolling a 15-sided die, the probability it comes up less than 4 (that is, obtaining a 1, 2, or 3) is 3 out of 15, as there are 3 favorable outcomes out of 15 possible outcomes. And for the roulette wheel, assuming it has numbers from 0 to 36, the probability of spinning a number greater than 17 is 19 out of 38, since there are 19 numbers from 18 to 36 (excluding 0 and 00 which might also be present).
To find the combined probability, you would multiply these probabilities together:
Combined Probability = Probability(Heads) * Probability(Die < 4) * Probability(Roulette > 17)
= 0.5 * (3/15) * (19/38)
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What is the value of X?
Answer:
x = 55°
Step-by-step explanation:
The sum of the angles in a triangle is 180°, so you have ...
x + 50° +75° = 180°
x = 55° . . . . . . . . . . . . subtract 125°
Felice knows that segment RS || segment QT. She wants to use the definition of a parallelogram to prove that the quadrilateral is a parallelogram. Which equation can she use?
Answer:
see below
Step-by-step explanation:
The definition of a parallelogram is that opposite sides of the quadrilateral are parallel. Felice already knows one pair of opposite sides is parallel. By showing the slope of RQ is the same as the slope of ST, she can show the other pair of opposite sides is parallel, hence the figure is a parallelogram.
__
The other answer choices are essentially nonsense.
Answer:
Top Right
Step-by-step explanation:
A newspaper article about an opinion poll says that "53% of Americans approve of the president's overall job performance." The poll is based on online survey interviews with 1,350 adults randomly chosen from a numbered list of one million responses from around the United States, excluding Alaska and Hawaii.
Part A: What is the population and sample in this poll? (3 points)
Part B: What type of sampling is used? (3 points)
Part C: Are there any sources of bias present? Explain. (4 points) (10 points)
Answer:
Part A: The population are the American adult citizens, excluding the ones from Alaska and Hawaii. The population is the people which the sample is trying to represent, as a hole.
The sample is a portion of this population, and in this case is represented by a randomly selected amount of people whose response to the interview has been selected.
Part B: The sample here has been selected in two steps. The first step is the one that we must pay attention to: the numbered list of one million responses from around the US (excluding Alaska and Hawaii). Because these responses were obtained by an online survey, the sample looks like a convenience sampling, as it depends on the availability and willingness from participants to take part of the study (is not compulsory for everyone, so not everyone is going to response, then there are people that is not going to be represented by). The second step is the random selection of a part of the previous responses. This last part will ensure that, the individuals that took part of the group that was interviewed, are well represented in the results.
Part C: As it was mentioned, there is a selection bias, because the information from the sample comes from a specific group of people that has certain features that may not represent all American adults citizens. For example, the opinion of those people who do not use internet, will not be considered (and they may be a large number of persons). This situations weaken the conclusions obtained in the study, as they are not representative of the hole population.
A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree. Round to the nearest thousandth.
Answer:
The 98% confidence interval would be given (0.616;0.686).
We are confident at 98% that the true proportion of people that they were planning to pursue a graduate degree is between (0.616;0.686).
Step-by-step explanation:
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".
Description in words of the parameter p
[tex]p[/tex] represent the real population proportion of people that they were planning to pursue a graduate degree
[tex]\hat p[/tex] represent the estimated proportion of people that they were planning to pursue a graduate degree
n=1010 is the sample size required
[tex]z_{\alpha/2}[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
Numerical estimate for p
In order to estimate a proportion we use this formula:
[tex]\hat p =\frac{X}{n}[/tex] where X represent the number of people with a characteristic and n the total sample size selected.
[tex]\hat p=\frac{658}{1010}=0.651[/tex] represent the estimated proportion of people that they were planning to pursue a graduate degree
Confidence interval
The confidence interval for a proportion is given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 98% confidence interval the value of [tex]\alpha=1-0.98=0.02[/tex] and [tex]\alpha/2=0.01[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=2.33[/tex]
And replacing into the confidence interval formula we got:
[tex]0.651 - 2.33 \sqrt{\frac{0.651(1-0.651)}{1010}}=0.616[/tex]
[tex]0.651 + 2.33 \sqrt{\frac{0.651(1-0.651)}{1010}}=0.686[/tex]
And the 98% confidence interval would be given (0.616;0.686).
We are confident at 98% that the true proportion of people that they were planning to pursue a graduate degree is between (0.616;0.686).
The government of Preon (a small island nation) was voted in at the last election with 68% of the votes. That was 2 years ago, and ever since then the government has assumed that their approval rating has been the same. Some recent events have affected public opinion and the government suspects that their approval rating might have changed. They decide to run a hypothesis test for the proportion of people who would still vote for them.The null and alternative hypotheses are:H0: Pi symbol = 0.68HA: Pi symbol ≠ 0.68The level of significance used in the test is α = 0.1. A random sample of 102 people are asked whether or not they would still vote for the government. The proportion of people that would is equal to 0.745. You may find this standard normal table useful throughout this question.Calculate the test statistic (z) for this hypothesis test.
Answer: 1.41
Step-by-step explanation:
Test statistic(z) for proportion is given by :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p=population proportion.
[tex]\hat{p}[/tex]= sample proportion
n= sample size.
As per given , we have
[tex]H_0:\mu=0.68\\\\ H_a: \mu\neq0.68[/tex]
n= 102
[tex]\hat{p}=0.745[/tex]
Then, the test statistic (z) for this hypothesis test will be :-
[tex]z=\dfrac{0.745-0.68}{\sqrt{\dfrac{0.68(1-0.68)}{102}}}\\\\=\dfrac{0.065}{\sqrt{\dfrac{0.2176}{102}}}\\\\=\dfrac{0.065}{\sqrt{0.0021333}}\\\\=\dfrac{0.065}{0.04618802}=1.40729132792\approx1.41[/tex]
[Rounded to the two decimal places]
Hence, the test statistic (z) for this hypothesis test = 1.41
g A university computer breaks down on average 2.1 times a month. Find the probability that during the next month this computer will break down at least six times. Use the Poisson probability formula. (Round to 4 digits, ex. 0.1234)
Answer:
Step-by-step explanation:
Suppose that two populations have the same mean. A researcher draws a sample of size 35 from each population and calculates the difference in sample means. He then repeats this process 99 more times, resulting in 100 calculated differences in sample means. The researcher finds the standard error of the difference in sample means to be 1.78. Which of the following statements is true regarding the distribution of the differences in sample means? The center of the distribution will be approximately 0, with about 68 percent of the differences in means between -3.56 and 3.56
Answer:
Step-by-step explanation:
Hello!
You have the difference between two sample means. Remember the sample means are variables with certain distribution, let's say, in this case, both sample means have a normal distribution. X[bar] = sample mean
X₁[bar]~N(μ₁;σ₁²/n₁)
X₂[bar]~N(μ₂;σ₂²/n₂)
Then the difference between these two variables results in a third variable that will also have a normal distribution:
X₁[bar]-X₂[bar]~N(μ₁-μ₂;σ₁²/n₁+σ₂²/n₂)
These are some of the properties of the normal distribution
Centered in μ
Symmetrical
Bell-shaped
[μ - σ; μ + σ]= 68% of the distribution
[μ - 2σ; μ+ 2σ]= 95% of the distribution
[μ - 3σ; μ+ 3σ]= 99.7% of the distribution
Check attachment.
Taking these properties into account, if you where to draw the results of the 100 trials, where μ₁-μ₂=0 would be its center and the standard deviation of the difference is 1.78.
68% of the information will be between (μ₁-μ₂) ± [(σ₁/√n₁)+(σ₂/√n₂)], this is 0 ± 1.78
I hope it helps!
Pela has 5 3/4 feet of string to make necklaces. She wants to make 4 necklaces that are the same length. How long should each necklace be?
Answer: 1.4375
Step-by-step explanation:
Pela has 5 3/4 feet of string to make necklaces. We would convert 5 3/4 feet to improper fraction. It becomes 23/4 feet. So Pela has 23/4 feet of string to make necklaces.
She wants to make 4 necklaces that are the same length. To determine how long should each necklace be,
We would divide the total length of the string by the number of necklaces to be made. It becomes
23/4 ÷ 4 = 23/4 × 1/4 = 23/16
The length of each string is 23/16 or 1.4375 feet
. A manager has just received the expense checks for six of her employees. She randomly distributes the checks to the six employees. What is the probability that exactly five of them will receive the correct checks (checks with the correct names)?
Answer:
13,8%
Step-by-step explanation:
There are six employees and six cheks, so there are 36 (6x6) possible combinations so if we need to measure the probability that five of them receive the exact check is only one for each one of them over the 36 possibilities, so 1/36 for one plus 1/36 the second and so on. 5/36 = 13,8%.
Answer:
0
Step-by-step explanation:
If 5 of them are correct, then the 6th one will also be correct. Thus, it is impossible to have exactly 5 correct, therefore 0
A regression and correlation analysis resulted in the following information regarding a dependent variable ( y) and an independent variable ( x). Σx = 90 Σ(y - )(x - ) = 466 Σy = 170 Σ(x - )2 = 234 n = 10 Σ(y - )2 = 1434 SSE = 505.98 The sum of squares due to regression (SSR) is
Answer:
The sum of squares due to regression(SSR)=928.02
Step-by-step explanation:
We are given that
Dependent variable=y
Independent variable=x
[tex]\sum x=90[/tex]
[tex]\sum(y-\bar y)(x-\bar x)=466[/tex]
[tex]\sum y=170[/tex]
[tex]\sum(x-\bar x)^2=234[/tex]
n=10
[tex]\sum(y-\bar y)^2=1434[/tex]
SSE=505.98
We have to find the sum of squares due to regression.
It means we have to find SSR.
SST=[tex]\sum(y-\bar y)^2=1434[/tex]
[tex]SSR=SST-SSE=1434-505.98=928.02[/tex]
Hence, the sum of squares due to regression(SSR)=928.02