Answer:
there is no any number to caculate social security tax.
Step-by-step explanation:
Social Security taxes are calculated using a deduction rate of 6.2% and 1.45% for Medicare from an employee's gross annual income. Employers also contribute matching amounts. However, the economic impact of employers' contributions often invariably impact employees indirectly.
Explanation:To calculate social security taxes, you need to consider a standard deduction rate of 6.2% for the Social Security and 1.45% from Medicare. These deductions are generally taken directly out of the employee's gross annual income. Employers also contribute matching percentages. However, it is important to note that in reality, the burden of the employer's contribution may in effect fall on the employee as it can result in lower wages. For instance, for those considered as independent contractors or members of the 'gig economy' receiving a 1099 tax statement, the individual must pay both the employer and employee portion of the social security and Medicare taxes.
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Use the value of the first integral I to evaluate the two given integrals. IequalsIntegral from 0 to 1 (x cubed minus 5 x )dxequalsnegative nine fourths a. Integral from 0 to 1 (10 x minus 2 x cubed )dx b. Integral from 1 to 0 (5 x minus x cubed )dx
Answer:
a) (9/2)
b) (9/4)
Step-by-step explanation:
I = ∫¹₀ (x³ - 5x) dx = -(9/4)
a) ∫¹₀ (10x - 2x³) dx = -2 ∫¹₀ (x³ - 5x) dx
∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I
-2 ∫¹₀ (x³ - 5x) dx = -2 × (-9/4) = (9/2)
b) ∫¹₀ (5x - x³) dx = -1 ∫¹₀ (x³ - 5x) dx
∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I
-1 ∫¹₀ (x³ - 5x) dx = -1 × (-9/4) = (9/4)
Hope this Helps!!!
Answer:
a.
[tex]\int\limits_{0}^{1} 10x - 2x^3 \,dx = -2(\int\limits_{0}^{1} x^3 -5x\,dx) = -2*(-9/4) = 9/2[/tex]
b.
[tex]\int\limits_{0}^{1} 5x - x^3 \,dx = -1*(\int\limits_{0}^{1} x^3 -5x\,dx) = -1*(-9/4) = 9/4[/tex]
Step-by-step explanation:
According to the information given.
[tex]\int\limits_{0}^{1} x^3 - 5x \,dx = -9/4\\[/tex]
Now.
a.
[tex]\int\limits_{0}^{1} 10x - 2x^3 \,dx = -2(\int\limits_{0}^{1} x^3 -5x\,dx) = -2*(-9/4) = 9/2[/tex]
b.
[tex]\int\limits_{0}^{1} 5x - x^3 \,dx = -1*(\int\limits_{0}^{1} x^3 -5x\,dx) = -1*(-9/4) = 9/4[/tex]
Concert marketing: The college’s performing arts center wanted to investigate why ticket sales for the upcoming season significantly decreased from last year’s sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail. Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail? Check all that apply. Group of answer choices The sample needs to be random, but we don’t know if it is. The actual count of community residents who received the concert brochure by mail is too small. The actual count of students who community residents who didn’t receive the concert brochure by mail is too small. n(p‐hat) is not greater than 10. n(1 minus p‐hat) is not greater than 10.
Answer:
Correct options are A,B,D:
The sample needs to be random, but we don't know if it is. The actual count of community residents who received the concert brochure by mail is too small. n(1 minus p‐hat) is not greater than 10.Step-by-step explanation:
Concert marketing: The college’s performing arts center wanted to investigate why ticket sales for the upcoming season significantly decreased from last year’s sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail.
The college's performing arts center should not calculate a confidence interval for the proportion of community residents who received the concert brochure by mail because there is no information on the randomness of the sample, and both n(p-hat) and n(1 minus p-hat) are less than 10.
Explanation:The college's performing arts center should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail based on the collected survey data for a few reasons. First, the sample needs to be random to provide a representative subset of the population, and there is no information provided to confirm that the sample used was random. Secondly, n(p-hat) is not greater than 10, which refers to the number of successes (7 residents received the brochure) not meeting the minimum requirement for the normal approximation to be valid. Lastly, n(1 minus p-hat) is also not greater than 10, indicating that the number of 'failures' (103 residents did not receive the brochure) also does not meet the condition for the central limit theorem to apply. Both the latter points touch upon the requirements for constructing a confidence interval for a proportion which is that np-hat as well as n(1-p-hat) should both be greater than 10 to approximate the binomial distribution with the normal distribution.
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During a recent drought, a water utility in a certain town sampled 100 residential water bills and found that 73 of the residences had reduced their water consumption over that of the previous year. f) If 95% confidence intervals are computed for 200 towns, what is the probability that more than 192 of the confidence intervals cover the true proportions
Final answer:
The probability of more than 192 confidence intervals containing the true proportion when constructing 95% confidence intervals across 200 towns, which follows a binomial distribution.
Explanation:
When constructing confidence intervals for a proportion, if we state that we have 95% confidence, this means that if we were to take many samples and build a confidence interval from each sample, we would expect 95% of those intervals to contain the population proportion. In the case with 200 towns, 95% confidence suggests that approximately 190 out of 200 intervals would contain the true population proportion, as 95% of 200 is 190.
To find the probability that more than 192 of these intervals contain the true proportion, we would use the binomial distribution, where each interval has a 0.95 probability of containing the true proportion (success), and we are looking for the sum of the probabilities of 193, 194, ..., 200 successes out of 200 trials.
The vertices of triangle ABC are as
follows:
A: (0, 6)
B: (0, -3)
C: (-3, 4)
What is the length of side AB?
Solution:
Answer:
The length of side AB is 9 units.
Step-by-step explanation:
In order to find this answer, you must use the distance formula.
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
x2 = 0
x1 = 0
y2 = -3
y1 = 6
Since both x values are equal to zero, we do not need to plug these into our formula. It will just cancel out. Therefore, just plug in the y values.
[tex]\sqrt{(-3-6)^2}[/tex]
-3 - 6 = -9
(-9)^2 = 81
sqrt(81) = 9 units
what is the value of the 2 in 7,239,103
Answer:
(2x100,000) 200,000,00
Step-by-step explanation:
200,000
Answer: 2 hundred thousands
Explanation: To determine what the digit 2 means in 7,239,103, if we put 7,239,103 into the place value chart, we can recognize that the digit 2 is in the hundreds column of the thousands period.
So in this problem, 2 refers to 2 hundred thousands.
Place value chart is attached
in the image provided.
Suppose that A and B each randomly, and independently, choose 3 of 10 objects. Find the expected number of objects (a) chosen by both A and B; (b) not chosen by either A or B; (c) chosen by exactly one of A and B.
Answer:
a) N(A∩B) = 0.9
b) N(A∩B) = 4.9
c) N(A or B) = 4.2
Step-by-step explanation:
Given that A and B each randomly, and independently, choose 3 of 10 objects;
P(A) = P(B) = 3/10 = 0.3
P(A') = P(B') = 1 - 0.3 = 0.7
a) chosen by both;
Probability of being chosen by both;
P(A∩B) = 0.3 × 0.3 = 0.09
Expected Number of objects being chosen by both;
N(A∩B) = P(A∩B) × N(total) = 0.09×10
N(A∩B) = 0.9
b) not chosen by either A or B;
Probability of not being chosen by either A or B;
P(A'∩B') = 0.7 × 0.7 = 0.49
Expected Number of objects being chosen by both;
N(A'∩B') = P(A'∩B') × N(total) = 0.49×10
N(A∩B) = 4.9
c) chosen by exactly one of A and B.
Probability of being chosen by exactly one of A and B
P(A∩B') + P(A'∩B) = 0.3×0.7 + 0.7 × 0.3 = 0.42
Expected Number of objects being chosen by both;
N(A or B) = 0.42 × 10
N(A or B) = 4.2
The expected number of objects chosen by both A and B is 0.9. The expected number of objects not chosen by either A or B is 9.1. The expected number of objects chosen by exactly one of A and B is 4.2.
Explanation:To find the expected number of objects chosen by both A and B, we can use the multiplication rule. Since A and B each independently choose 3 objects from a set of 10, the probability of choosing a specific object is 3/10 for both A and B. Therefore, the expected number of objects chosen by both A and B is (3/10)(3/10)(10) = 0.9.
To find the expected number of objects not chosen by either A or B, we can subtract the expected number of objects chosen by both A and B from the total number of objects. So, the expected number of objects not chosen by either A or B is 10 - 0.9 = 9.1.
To find the expected number of objects chosen by exactly one of A and B, we can use the addition rule. Since A and B each independently choose 3 objects, the probability of choosing a specific object is 3/10 for both A and B. Therefore, the expected number of objects chosen by exactly one of A and B is 2(3/10)(7/10)(10) = 4.2.
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Help me plz or I will fail
Answer:
D - Can't be determined
Step-by-step explanation:
10 * 2 *4 * 16 = 1280
1280/2 = 640
The population of ground squirrels in a public park is measured to be 100. The growth of the population over time can be modeled by P(t)=600/(1+5base e ^-0.5t), with P representing the number of squirrels and t cu d. in months after the infuriating population measurement. According to this model, what is the maximum bed of squirrels the park can support?
Answer:
600
Step-by-step explanation:
As t gets very large, the exponential term goes to zero, and the expression nears the value ...
P(∞) = 600/(1 +5·0) = 600
The maximum number of squirrels the park can support is modeled as being 600.
A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let pˆO represent the sample proportion of bags packaged on the old machine that are damaged, pˆN represent the sample proportion of bags packaged on the new machine that are damaged, pˆC represent the combined proportion of damaged bags from both machines, and nO and nN represent the respective sample sizes for the old machine and new machine. Have the conditions for statistical inference for testing a difference in population proportions been met?
A No, the condition for independence has not been met, because random samples were not selected.
B No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes.
C No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nN(pˆC) is not greater than or equal to 10.
D No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nO(1−pˆC) is not greater than or equal to 10.
E All conditions for making statistical inference have been met.
If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.
Step-by-step explanation:
We can test the claim and the assumptions about the population proportion under the following conditions
The method of random sampling should be adopted by the company so as to ensure that the observation conducted is independent and not biased The outcome data of the sampled unit must give rise to two outputs -On that is said to be successful and the other that is said to be a failure
Thus we can say that by studying the question we can say that the above mentioned condition have been met.Hence
If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.
The conditions for statistical inference for testing a difference in population proportions have not been met.
Explanation:In order to test for a difference in population proportions, certain conditions need to be met. Firstly, the condition for independence must be met, which means that random samples need to be selected. Secondly, the distribution of the difference in sample proportions needs to be approximately normal. This is determined by checking whether nO(pC) is greater than or equal to 10 and nO(1-pC) is greater than or equal to 10. In this case, the conditions for statistical inference have not been met because random samples were not selected (option A) and nN(pC) is not greater than or equal to 10 (option C).
Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and of this number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion.
Is there any reason to believe that the two polishing solutions differ? Use α = 0.05. What is the P-value for this test?
Answer:
[tex]z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358[/tex]
[tex]p_v =2*P(Z>5.358) = 4.2x10^{-8}[/tex]
Comparing the p value with the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.
Step-by-step explanation:
Data given and notation
[tex]X_{1}=253[/tex] represent the number with no defects in sample 1
[tex]X_{2}=196[/tex] represent the number with no defects in sample 1
[tex]n_{1}=300[/tex] sample 1
[tex]n_{2}=300[/tex] sample 2
[tex]p_{1}=\frac{253}{300}=0.843[/tex] represent the proportion of number with no defects in sample 1
[tex]p_{2}=\frac{196}{300}=0.653[/tex] represent the proportion of number with no defects in sample 2
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test (variable of interest)
[tex]\alpha=0.05[/tex] significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} - p_2}=0[/tex]
Alternative hypothesis:[tex]p_{1} - p_{2} \neq 0[/tex]
We need to apply a z test to compare proportions, and the statistic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748[/tex]
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
[tex]z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358[/tex]
Statistical decision
Since is a two sided test the p value would be:
[tex]p_v =2*P(Z>5.358) = 4.2x10^{-8}[/tex]
Comparing the p value with the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.
a data set has a lower quartile of 3 and an interquartile range of 5. Which box plot could represent this data set?
Answer:
Answer:
The first box plot.
Step-by-step explanation:
Step-by-step explanation:
In a box plot, the lower quartile is the right hand side of the box. In the first plot, this is 3.
The upper quartile is the left hand side of the box. In the first plot, this is 8.
The interquartile range is the difference between these two values:
8-3 = 5.
Look at the diagram.
Which term describes IG?
Answer: Angle Bisector
Step-by-step explanation: You divided into two equal angles, you bisected. You turned F, I, G and I, G, H into two separate triangles.
1
Find the surface area of the triangular
3 cm
4 cm
10 cm
5 cm
Step-by-step explanation:
you are going to have to be more specific... please let us know which ones are the legs
2. A spike train, commonly used to study neural activity, is a sequence of recorded times at which a neuron fires an action potential (spike). The time in between consecutive spikes is called the interspike interval (ISI). Answer the questions below for an experiment in which the firing rate for a neuron is 10 per second. (a) Let X represent a single interspike interval (ISI) having an exponential distribution. State the distribution of X and give its parameter value(s). (2 points) (b) Give the expected value and variance for an interspike interval (ISI). (4 points) (c) What is the probability that an ISI is less than 0.07 seconds
Answer:
a) X ~ exp ( 10 )
b) E(X) = 0.1 , Var (X) = 0.01
c) P ( X < 0.07 ) = 0.00698
Step-by-step explanation:
Solution:-
- The spike train, used to study neural activity, the given time in between consecutive spikes (ISI) where the firing rate = 10 neurons per seconds.
- Denote a random variable "X"represent a single interspike interval (ISI) having an exponential distribution.
- Where X follows exponential distribution defined by event rate parameter i.e λ.
X ~ Exp ( λ )
- The event rate (λ) is the number of times an event occurs per unit time. Since we are studying a single interspike interval (ISI) - which corresponds to the firing rate. So, event rate (λ) = firing rate = 10 neurons per second. Hence, the distribution is:
X ~ Exp ( 10 )
- The expected value E(X) denotes the amount of time in which a single an event occurs; hence, the time taken for a single neuron.
E(X) = 1 / λ
E(X) = 1 / 10
E(X) = 0.1 s per neuron.
- The variance is the variation in the time taken by a single neuron to be emitted. It is defined as:
Var (X) = 1 / λ^2
Var (X) = 1 / 10^2
Var (X) = 0.01 s^2
- The probability that ISI is less than t = 0.07 seconds: P ( X < t = 0.07 s):
- The cumulative distribution function for exponential variate "X" is:
P ( X < t ) = 1 - e^(-λ*t)
- Plug the values and the determine:
P ( X < 0.07 ) = 1 - e^(-0.1*0.07)
= 1 - 0.99302
= 0.00698
Please Help!
Look at the pattern.
What is the ratio of the area of the unshaded parts to the area of
the shaded parts in Figure 4? Express your answer as a ratio in its
simplest form.
Answer:
16:27
Step-by-step explanation:
16 white squares and 27 shaded squares
The ratio of the area of the unshaded parts to the area of the shaded parts is 4/5.
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
To find the ratio:
Required ratio = number of unshaded columns / total number of shaded columns
In the given figure 1,
Total no. of columns =3 x 3 = 9
Number of columns shaded = 9 -1 = 8
In the given figure 2,
Total no. of columns = 4 x 4 = 16
Number of columns shaded = 16 - 4 = 12
In the given figure 3,
Total no. of columns = 5 x 5 = 25
Number of columns shaded = 25 - 9 = 16
Similarly;
In the figure 4,
Total no. of columns = 6 x 6 = 36
Number of columns shaded = 36 - 16 = 20
Required ratio = number of unshaded columns / total number of shaded columns
Required ratio = 16 / 20
Required ratio = 4/5
Therefore, the ratio is 4/5.
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Bottles of purified water are assumed to contain 250 milliliters of water. There is some variation from bottle to bottle because the filling machine is not perfectly precise. Usually, the distribution of the contents is approximately Normal. An inspector measures the contents of eight randomly selected bottles from one day of production. The results are 249.3, 250.2, 251.0, 248.4, 249.7, 247.3, 249.4, and 251.5 milliliters. Do these data provide convincing evidence at α = 0.05 that the mean amount of water in all the bottles filled that day differs from the target value of 250 milliliters?
Answer:
We accept H₀ we don´t have evidence of differences between the information from the sample and the population mean
Step-by-step explanation:
From data and excel (or any statistics calculator) we get:
X = 249,6 ml and s 1,26 ml
Sample mean and sample standard deviation respectively.
Population mean μ₀ = 250 ml
We have a normal distribution but we dont know the standard deviation of the population. Furthermore we have a two tails test since we are finding if the sample give us evidence of differences ( in both senses ) when we compare them with the amount of water spec ( 250 ml )
Our test hypothesis are: null hypothesis H₀ X = μ₀
Alternative Hypothesis Hₐ X ≠ μ₀
We also know that sample size is 8 therefore df = 8 - 1 df = 7 , with this value and the fact that we are required to test at α = 0,05 ( two tails test)
t = 2,365
Then we evaluate our interval:
X ± t* (s/√n) ⇒ 249,6 ± 2,365 * ( 1,26/√8 )
249,6 ± 2,365 * (1,26/2,83) ⇒ 249,6 ± 2,365 *0,45
249,6 ± 1,052
P [ 250,652 ; 248,548]
Then the population mean 250 is inside the interval, therefore we must accept that the bottles have being fill withing the spec. We accept H₀
Answer:
Because the p-value of 0.4304 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of water in all the bottles filled that day does not differ from the target value of 250 milliliters.
Step-by-step explanation:
A peach pie is divided into eight equal slices
with 280 calories in each slice. How many
calories are in the entire peach pie?
The entire peach pie contains 2240 calories.
Explanation:To find the number of calories in the entire peach pie, we need to multiply the number of calories in each slice by the total number of slices. In this case, there are 8 equal slices in the peach pie, and each slice has 280 calories. Therefore, the total number of calories in the entire peach pie is 8 multiplied by 280, which equals 2240 calories.
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What is 10.9 as a fraction
Answer:
109/10 or 10 9/10
Step-by-step explanation:
Dividing something by 10 puts it one place after the decimal point.
so 9/10 becomes 0.9.
Answer:
10 9/10
Step-by-step explanation:
Help me plz i neEd answer
Answer:
C)[tex]64 feet^{2}[/tex]
Step-by-step explanation:
The formula for the area of a trapezium is :
[tex]\frac{a+b}{2} *height[/tex]
A is the top line
B is the bottom line
To work this out you would first add 6 to 10, which is 16. Then you would divide 16 by 2, which is 8. Then you would multiply 8 by 8, which is 64 [tex]feet^{2}[/tex]
1) Add 6 to 10.
[tex]6+10=16[/tex]
2) Divide 16 by 2.
[tex]16/2=8[/tex]
3) Multiply 8 by 8.
[tex]8*8=64 feet^{2}[/tex]
An article titled "Teen Boys Forget Whatever It Was" appeared in the Australian newspaper The Mercury (April 21, 1997). It described a study of academic perfor- mance and attention span and reported that the mean time to distraction for teenage boys working on an inde- pendent task was 4 minutes. Although the sample size was not given in the article, suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 minutes. Is there convincing evidence that the average attention span for teenage boys is less than 5 minutes? Test the relevant hypotheses using a .01.
Answer:
We conclude that the average attention span for teenage boys is less than 5 minutes.
Step-by-step explanation:
We are given that the mean time to distraction for teenage boys working on an independent task was 4 minutes.
Suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 minutes.
Let [tex]\mu[/tex] = average attention span for teenage boys
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 5 minutes {means that the average attention span for teenage boys is more than or equal to 5 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 5 minutes {means that the average attention span for teenage boys is less than 5 minutes}
The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean attention time span for teenage boys = 4 min
s = sample standard deviation = 1.4 min
n = sample of teenage boys = 50
So, the test statistics = [tex]\frac{4-5}{\frac{1.4}{\sqrt{50} } }[/tex] ~ [tex]t_4_9[/tex]
= -5.051
Now at 0.01 significance level, the t table gives critical value of -2.405 at 49 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -2.405 > -5.051, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the average attention span for teenage boys is less than 5 minutes.
In a survey of 468 registered voters, 152 of them wished to see Mayor Waffleskate lose her next election. The Waffleskate campaign claims that no more than 32% of registered voters wish to see her defeated. Does the 95% confidence interval for the proportion support this claim?
Answer:
The 95% confidence interval for the proportion is (0.2824, 0.3672). The upper limit of the interval is higher than 32% = 0.32, which means that the confidence interval does not support this claim.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 468, \pi = \frac{152}{468} = 0.3248[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3248 - 1.96\sqrt{\frac{0.3248*0.6752}{468}} = 0.2824[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3248 + 1.96\sqrt{\frac{0.3248*0.6752}{468}} = 0.3672[/tex]
The 95% confidence interval for the proportion is (0.2824, 0.3672). The upper limit of the interval is higher than 32% = 0.32, which means that the confidence interval does not support this claim.
In this problem, we apply mathematical concepts related to statistics to determine whether a campaign claim is supported by a survey. The calculation of a 95% confidence interval supports Mayor Waffleskate's claim that no more than 32% of voters want her defeated.
Explanation:The subject in question refers to confidence intervals and population proportions, both of which are topics in statistics. To answer it, we need to construct a 95% confidence interval for the proportion of voters who wish to see Mayor Waffleskate defeated in the election, based on a sample size of 468 voters, of which 152 express this sentiment.
The first step is to calculate the sample proportion (p), which is the number of 'successes' over the sample size, or in this case 152/468, which equals approximately 0.325.
Next, we apply the formula for the confidence interval for a population proportion, which i
Because the confidence interval (0.278, 0.372) includes the value of 0.32 stated by the Waffleskate campaign, it can be concluded that the claim that no more than 32% of registered voters wish to see her defeated is plausible or supported by this survey at the 95% confidence level.
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9. (12 pts) daniel is paying $600 for his auto insurance, and he is wondering if he is overpaying compared to his friends. he sent an email to all his friends in his contact list, and 9 of them replied with their paid amount. suppose the 9 friends who replied are a random sample, and the paid amount for auto insurance has approximately a normal distribution. (1) (2pts) what are the sample and population of the study? (2) (8 pts) use appropriate inference procedure to help daniel find out if he is overpaying compared to his friends. (3) (2pts) based on your conclusion in (2), what type of error is could you commit? explain the error using context words.
Answer:
Step-by-step explanation:
1) The sample and the population of this study is the friends who replied his email which includes in his contact list. then, the number of the replied to his email are 9 friends.
population: the whole friends include in his contact list.
3) Type I error occurs when one incorrectly rejects the null hypothesis
Here there is possibility of type I error
The mean of a population is 74 and the standard deviation is 16. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. Appendix A Statistical Tables a. A random sample of size 34 yielding a sample mean of 76 or more b. A random sample of size 120 yielding a sample mean of between 73 and 75 c. A random sample of size 218 yielding a sample mean of less than 74.8
Answer:
(a) P([tex]\bar X[/tex] [tex]\geq[/tex] 76) = 0.2327
(b) P(73 < [tex]\bar X[/tex] < 75) = 0.5035
(c) P([tex]\bar X[/tex] < 74.8) = 0.77035
Step-by-step explanation:
We are given that the mean of a population is 74 and the standard deviation is 16.
Assuming the data follows normal distribution.
Let [tex]\bar X[/tex] = sample mean
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 74
[tex]\sigma[/tex] = standard deviation = 16
n = sample size
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
(a) Probability that a random sample of size 34 yielding a sample mean of 76 or more is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 76)
P([tex]\bar X[/tex] [tex]\geq[/tex] 76) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{76-74}{\frac{16}{\sqrt{34} } }[/tex] ) = P(Z [tex]\geq[/tex] 0.73) = 1 - P(Z < 0.73)
= 1 - 0.7673 = 0.2327
The above probability is calculated by looking at the value of x = 0.73 in the z table which has an area of 0.7673.
(b) Probability that a random sample of size 120 yielding a sample mean of between 73 and 75 is given by = P(73 < [tex]\bar X[/tex] < 75) = P([tex]\bar X[/tex] < 75) - P([tex]\bar X[/tex] [tex]\leq[/tex] 73)
P([tex]\bar X[/tex] < 75) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{75-74}{\frac{16}{\sqrt{120} } }[/tex] ) = P(Z < 0.68) = 0.75175
P([tex]\bar X[/tex] [tex]\leq[/tex] 73) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{73-74}{\frac{16}{\sqrt{120} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.68) =1 - P(Z < 0.68)
= 1 - 0.75175 = 0.24825
Therefore, P(73 < [tex]\bar X[/tex] < 75) = 0.75175 - 0.24825 = 0.5035
The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.75175.
(c) Probability that a random sample of size 218 yielding a sample mean of less than 74.8 is given by = P([tex]\bar X[/tex] < 74.8)
P([tex]\bar X[/tex] < 74.8) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{74.8-74}{\frac{16}{\sqrt{218} } }[/tex] ) = P(Z < 0.74) = 0.77035
The above probability is calculated by looking at the value of x = 0.74 in the z table which has an area of 0.77035.
A racing car consumes a mean of 86 gallons of gas per race with a standard deviation of 7 gallons. If 41 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 3.1 gallons? Round your answer to four decimal places.
Answer:
0.0046 = 0.46% probability that the sample mean would differ from the population mean by more than 3.1 gallons
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 86, \sigma = 7, n = 41, s = \frac{7}{\sqrt{41}} = 1.0932[/tex]
If 41 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 3.1 gallons?
Less than 86 - 3.1 = 82.9 or more than 86 + 3.1 = 89.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.
Less than 82.9
pvalue of Z when X = 82.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{82.9 - 86}{1.0932}[/tex]
[tex]Z = -2.84[/tex]
[tex]Z = -2.84[/tex] has a pvalue of 0.0023
2*0.0023 = 0.0046
0.0046 = 0.46% probability that the sample mean would differ from the population mean by more than 3.1 gallons
Final answer:
The probability that the sample mean of 41 racing cars would differ from the population mean by more than 3.1 gallons is 0.0046 or 0.46%.
Explanation:
To calculate the probability that the sample mean of 41 racing cars would differ from the population mean by more than 3.1 gallons, you use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. In this case, 41 is usually considered large enough. The formula to calculate the z-score for a given sample mean difference is z = (X - µ) / (σ/√n), where X is the sample mean, µ is the population mean, σ is the standard deviation, and n is the sample size.
First, we calculate the standard error of the mean (SEM): SEM = σ/√n = 7/√41 ≈ 1.0934. Next, we calculate the z-score for a difference of 3.1 gallons: z = 3.1 / 1.0934 ≈ 2.8354.
Now, we look up the z-score in standard normal distribution tables or use a calculator to find the probability corresponding to a z-score of 2.8354, which gives us the probability of a sample mean being 3.1 gallons or more away from the population mean on one side. However, since the question asks for the probability of the sample mean differing by more than 3.1 gallons on either side, we have to multiply this probability by 2 to get the final answer.
To obtain the final probability, we use statistical software or tables, which typically provide the probability for the region beyond a certain z-score. If P(z > 2.8354) is the probability of being beyond 2.8354 standard deviations from the mean on one side, the probability of being more than 3.1 gallons away from the mean on either side is 2 * P(z > 2.8354). Assuming P(z > 2.8354) = 0.0023 (from a standard normal distribution table), the final probability would be 2 * 0.0023 = 0.0046 or rounded to four decimal places, 0.0046.
Amara was working on a report on Greek and Egyptian mathematicians. She decided to find a 98 percent confidence interval for the difference in mean age at the time of significant mathematics discoveries for Greek versus Egyptian mathematicians. She found the ages at the time of math discovery of all the members of both groups and found the 98 percent confidence interval based on a t-distribution using a calculator.
The procedure she used is not appropriate in this context becauseA. The sample sizes for the two groups are not equal.B. Age at the time of math discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same.C. Ages at the time of math discovery are likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid.D. Age at the time of math discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid.E. The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
Answer:
E. The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
Step-by-step explanation:
The entire population of Greek and Egyptian mathematicians was already measured by Amara. She can measure the actual difference in the mean. Therefore, she needn't use a confidence interval. It is mostly common for a researcher to be more interested in the difference between means than in the specific values of the means. The difference in sample means is used to compute the difference in population means.
Amara's sample is a random selection of Greek and Egyptian mathematicians. It is a smaller group drawn from the population that has the characteristics of the entire population. The observations and conclusions made against the sample data are attributed to the population. In this case, the entire position is measured.
A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups (Greek and Egyptian mathematicians) which may be related in certain features. It is mostly used when the data sets, like the data set recorded as the outcome from rolling a die 50 times, would follow a normal distribution and may have unknown variances. A t-test is used as a hypothesis testing tool, which allows testing of an assumption applicable to a population. Once the actual difference is known, a confidence interval should not be used.
pablo and greg both received gift cards for the same amount to a popular clothing store.Pablo bought 2 pairs of jeans and has $36 remaining on his gift card. greg bought 5 pairs of the same jeans and has no money left on his gift card. what is the cost of 1 pair of jeans.
Answer:
12
Step-by-step explanation:
let y be the value of the gift card and x be the cost of a pair of jeans
The equation for Pablo
y-2x=36 Add 2x to both sides
y=36+2x
The equation for Greg
y-5x=0 Add 5x to both sides
y=5x
Now that we have isolated y in both equations, lets set them equal to each other
36+2x=5x Subtract 2x from both sides
36=3x Divide both sides by 3
12=x x=12, which means that 1 pair of jeans costs $12
Final answer:
The cost of one pair of jeans is $12.
Explanation:
To find the cost of one pair of jeans, we can set up an equation using the information given.
Let's say the cost of one pair of jeans is x. Pablo bought 2 pairs of jeans, so he spent 2x.
He has $36 remaining on his gift card, which means the total amount he spent is the original amount on the gift card minus the remaining balance, which is 2x = original amount - $36.
Greg bought 5 pairs of jeans, so he spent 5x.
He has no money left on his gift card, so the total amount he spent is 5x = original amount.
We can write these two equations:
2x = original amount - $36 ... Equation 1
5x = original amount ... Equation 2
To solve this system of equations, we can substitute Equation 2 into Equation 1:
2x = 5x - $36
3x = $36
x = $12
Therefore, the cost of one pair of jeans is $12.
Please help me I’ve included a picture!
Answer:
257/2 degrees or 128.5 degrees
Step-by-step explanation:
radians to degrees is x radians * 180/π
[tex]\frac{257\pi }{360} * \frac{180}{\pi }= \frac{257}{2}[/tex]
it is 257/2 degrees or 128.5 degrees
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13 pls help
Answer:
infinite solutions
Step-by-step explanation:
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
Ditribute
-15x -10 -x +3 = -16x - 20+13
Combine like term
-16x -7 = -16x -7
Add 16x to each side
-16x+16x -7 = -16x+16x-7
-7 =-7
This is always true so we have infinite solutions.
answers
All real numbers are solutions
step by step
5(−3x−2)−(x−3)=−4(4x+5)+13
Step 1: Simplify both sides of the equation.
5(−3x−2)−(x−3)=−4(4x+5)+13
5(−3x−2)+−1(x−3)=−4(4x+5)+13(Distribute the Negative Sign)
5(−3x−2)+−1x+(−1)(−3)=−4(4x+5)+13
5(−3x−2)+−x+3=−4(4x+5)+13
(5)(−3x)+(5)(−2)+−x+3=(−4)(4x)+(−4)(5)+13(Distribute)
−15x+−10+−x+3=−16x+−20+13
(−15x+−x)+(−10+3)=(−16x)+(−20+13)(Combine Like Terms)
−16x+−7=−16x+−7
−16x−7=−16x−7
Step 2: Add 16x to both sides.
−16x−7+16x=−16x−7+16x
−7=−7
Step 3: Add 7 to both sides.
−7+7=−7+7
0=0
What is 6 yards 2 feet =
Answer:
20 feet
Step-by-step explanation:
A survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10. (a) Find and interpret the 95% confidence interval for the average spending. (b) Based on your answer in part (a), can you conclude statistically that the population mean is less than $30? Explain
Answer:
a) The 95% of confidence intervals for the average spending
(23.872 , 32.128)
b) The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.
The null hypothesis is accepted
A survey of 25 young professionals statistically that the population mean is less than $30
Step-by-step explanation:
Step:-(i)
Given data a survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10
The sample size 'n' = 25
The mean of the sample x⁻ = $28
The standard deviation of the sample (S) = $10.
Level of significance ∝=0.05
The degrees of freedom γ =n-1 =25-1=24
tabulated value t₀.₀₅ = 2.064
Step 2:-
The 95% of confidence intervals for the average spending
([tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha }\frac{S}{\sqrt{n} } )[/tex]
[tex](28 - 2.064 \frac{10}{\sqrt{25} } ,28 + 2.064\frac{10}{\sqrt{25} } )[/tex]
( 28 - 4.128 , 28 + 4.128)
(23.872 , 32.128)
a) The 95% of confidence intervals for the average spending
(23.872 , 32.128)
b)
Null hypothesis: H₀:μ<30
Alternative Hypothesis: H₁: μ>30
level of significance ∝ = 0.05
The test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{28-30 }{\frac{10}{\sqrt{25} } }[/tex]
t = |-1|
The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.
The null hypothesis is accepted
Conclusion:-
The null hypothesis is accepted
A survey of 25 young professionals statistically that the population mean is less than $30