.Personal Health Expenditures. Data made available through the Petersen-Kaiser Health System Tracker showed health expenditures were $12,531 per person in the United States for the year 2020. Use $12,531 as the population mean and suppose a survey research firm will take a sample of 100 people to investigate the nature of their health expenditures. Assume the population standard deviation is $2750. . What is the probability the sample mean will be within +$200 of the population mean? What is the probability the sample mean will be greater than $14,000? If the survey research firm reports a sample mean greater than $14,000, would you question whether the firm followed correct sampling procedures? Why or why not?

Answers

Answer 1

The firm must have taken an incorrect sample, made an error in measuring, or made some other mistake.The Central Limit Theorem is used to answer the three questions in this problem. The population is normal because it is based on data from a large number of individuals. The sampling distribution is normal due to the Central Limit Theorem's application.

To find the probability of the sample mean falling within +$200 of the population mean, we need to compute the z-score for the difference between the sample mean and the population mean. We have:$\mu = 12531, n = 100, \sigma = 2750,$ and the sampling distribution is normal.because the sample mean is within $200 of the population mean (+/-200). For a normal distribution, this probability is about 0.954.

As a result, the probability of the sample mean falling within +$200 of the population mean is about 0.954.2. What is the probability the sample mean will be greater than $14,000?To determine the probability of the sample mean being greater than $14,000, we must compute the z-score:$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}} = \frac{14000 - 12531}{\frac{2750}{\sqrt{100}}} = 5.327$We will use the standard normal distribution to find the probability of a z-score greater than 5.327. P(z > 5.327) is virtually zero since the standard normal distribution is nearly zero at 5.327. As a result, the probability of the sample mean being greater than $14,000 is virtually zero.3. If the survey research firm reports a sample mean greater than $14,000, would you question whether the firm followed correct sampling procedures? Why or why not?If the survey research firm reports a sample mean greater than $14,000, we would question whether the firm followed the proper sampling procedures since a sample mean of $14,000 or higher has a probability that is almost zero. Thus, the firm must have taken an incorrect sample, made an error in measuring, or made some other mistake.

To know more about Central Limit Theorem visit :-

https://brainly.com/question/898534

#SPJ11

Related Questions

Find the exact length of the curve z = 3+12t² y = 1+8t³ for 0 < t < 1

Answers

The exact length of the curve is √(238) units.

What is the square root of 238?

The given curve is defined by the parametric equations z = 3 + 12t² and y = 1 + 8t³, where 0 < t < 1. To find the length of the curve, we need to integrate the derivative of each component with respect to t and then evaluate the definite integral over the given interval.

Let's start by finding the derivatives:

dz/dt = 24t

dy/dt = 24t²

Using the formula for arc length, L = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt, we can calculate the length of the curve.

∫√(dz/dt)² + (dy/dt)² dt

= ∫√(24t)² + (24t²)² dt

= ∫√(576t² + 576t⁴) dt

To evaluate this integral, we need to find the antiderivative of the integrand and then substitute the limits of integration (0 and 1):

∫√(576t² + 576t⁴) dt = (1/48)∫√(576t² + 576t⁴) d(576t² + 576t⁴)

By making a substitution, u = 576t² + 576t⁴, the integral simplifies to:

(1/48)∫√u du

Integrating √u with respect to u gives us (2/3)u^(3/2):

(1/48) * (2/3)u^(3/2) + C

= (1/72)u^(3/2) + C

Now, we substitute the limits of integration:

(1/72)[(576 + 576)^(3/2) - (0 + 0)^(3/2)]

= (1/72)(1152^(3/2) - 0)

Simplifying further:

(1/72)(1152^(3/2))

= (1/72)(1152 * √1152)

= √(16 * 72 * 72)

= √(16 * 5184)

= √82944

= √(2 * 2 * 2 * 2 * 3 * 3 * 2 * 1152)

= √(2^4 * 3^2 * 2 * 1152)

= √(2^5 * 3^2 * 1152)

= √(2^5 * 3^2 * 2^7 * 9)

= √(2^12 * 3^3)

= √(4^6 * 3^3)

= 4^3 * √3

= 64√3

Therefore, the exact length of the curve is 64√3 units.

Learn more about parametric equations

brainly.com/question/29275326

#SPJ11

Solve (3x² +2y²)dx+(4xy -6y²)dy = 0 in two distinct ways. As in the previous problem, you are solving this equation twice: once using an applicable method, and again using another

Answers

The given equation can be solved using the method of exact differential equations and also by employing separation of variables.

How can the given equation be solved using different methods?

To solve the equation (3x² + 2y²)dx + (4xy - 6y²)dy = 0, we can approach it in two distinct ways. First, we can use the method of exact differential equations by checking if the equation satisfies the conditions for exactness and finding the integrating factor.

Alternatively, we can employ separation of variables by isolating the dx and dy terms on opposite sides of the equation and integrating each side separately. Both methods provide different approaches to solving the equation and yield distinct solutions.

Learn more about Exact differential equations

brainly.com/question/30351944

#SPJ11

From the 4380 Science students on campus, a random sample of 219 students are selected. Out of this sample, 177 was found to have a height over 1.80 m. Use a 95% left-sided confidence interval to estimate the true proportion of tall students. Are any of the conditions required for a valid interval violated? How many conditions are violated? (Only type the number) If it is possible to calculate a confidence interval, enter the confidence limits in the provided spaces (rounded to at least 3 decimal places). If it is not possible to calculate a confidence interval, then enter 0 for both limits. [ ] Is 63% a possible true percentage of tall Science students? Yes Or NO

Answers

The 95% left-sided confidence interval for the true proportion of tall students is approximately 0.825.If 63% is a possible true percentage of tall Science students. Since 63% is outside the interval is NO.

To determine if any conditions are violated and calculate a confidence interval for the true proportion of tall students, the formula for a confidence interval for a proportion:

p ± Z × √((p× q ) / n)

Where:

P is the sample proportion (177/219)

q is the complement of the sample proportion (1 - p)

n is the sample size (219)

Z is the Z-score corresponding to the desired confidence level (95% left-sided corresponds to a Z-score of -1.645)

calculate the confidence interval:

p = 177/219 =0.807

q = 1 - p = 1 - 0.807 =0.193

n = 219

Z = -1.645

Confidence interval formula:

0.807 ± -1.645 ×√((0.807 × 0.193) / 219)

Calculating the confidence interval:

0.807 ± -1.645 × √(0.156051 / 219)

0.807 ± -1.645 × 0.010941

0.807 ± -0.017989

0.789 to 0.825 (rounded to three decimal places)

To know more about percentage here

https://brainly.com/question/28998211

#SPJ4

use an addition or subtraction formula to write the expression as a trigonometric function of one number. cos(12°) cos(18°) − sin(12°) sin(18°)

Answers

By applying the subtraction formula for trigonometric function cosine, we can express the given expression as cos(6°).

To express the expression cos(12°) cos(18°) − sin(12°) sin(18°) as a trigonometric function of one number, we can use the subtraction formula for cosine. The subtraction formula states that cos(A - B) = cos(A) cos(B) + sin(A) sin(B). By applying this formula, we have:

cos(12°) cos(18°) − sin(12°) sin(18°)

= cos(12° - 18°) (using the subtraction formula)

= cos(-6°)

= cos(6°) (since the cosine function is an even function)

Thus, the expression cos(12°) cos(18°) − sin(12°) sin(18°) can be written as cos(6°), which is a trigonometric function of the single number 6°.

To know more about Trigonometric Functions refer-

https://brainly.com/question/29090818#

#SPJ11

The probability density function (PDF) of a sum of two independent continuous random variables X and Y is given by the convolution of the PDFs, fx and fy: fx+r(z) = Lf«(a)fy(2 – 2) ds. Show that a sum of two independent standard normal variables results in a normal variable. Find the PDF of such a sum. Give your solutions in two ways: 1) by using the convolution function above; 2) by using moment generating functions.

Answers

The given question discusses the probability density function (PDF) of the sum of two independent continuous random variables X and Y. It states that the PDF of the sum is obtained by convolving the individual PDFs of X and Y.

What is the task and purpose of the given question regarding the probability density function (PDF)?

The task is to show that the sum of two independent standard normal variables results in a normal variable and find its PDF using two different approaches: 1) using the convolution function provided in the question, and 2) using moment generating functions.

The question explores the mathematical concepts related to convolution, standard normal variables, and PDF derivation using different methods.

Learn more about probability density function

brainly.com/question/31039386

#SPJ11

6. [-15 Points) DETAILS The limit of the sequence 00 {( ) m 104 n + e-118 66n + tan (148 n) - -)} Is 1 Hint: Enter the limit as a logarithm of a number (could be a fraction). Submit Answer

Answers

Given the sequence {(-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)} and it is required to find its limit. The formula of the limit of sequence is: lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)n→∞To find the limit of the given sequence, it should be observed that the largest term that tends to infinity should be found.

Here, it is found that as n→∞, the term tan(148n) tends to infinity. As this term goes to infinity, this term and the constant term (-7) can be ignored. Now, let x = 148n.Let's find the limit of sequence in terms of logarithm of a number(lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)n→∞)lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)

= lim (-1)m(10^4n + e^-118 6^6n) (Ignoring the other two terms)lim (-1)m(10^4n + e^-118 6^6n) = lim(-1)m × lim(10^4n + e^-118 6^6n)lim(10^4n + e^-118 6^6n) = lim e^(-118 6^6n)/10^4nlim(10^4n + e^-118 6^6n) = lim [1/(10^4ne^(118 6^6n)] = 0Hence, lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7) = lim (-1)m × lim(10^4n + e^-118 6^6n + tan(148n) - 7)

= (-1)0 × 0 = 0Hence, lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)n→

∞ = ln1

= 0.

Limit of sequence is calculated as follows: lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)

= lim (-1)m(10^4n + e^-118 6^6n)lim (-1)m(10^4n + e^-118 6^6n)

= lim(-1)m × lim(10^4n + e^-118 6^6n)

= (-1)0 × 0

= 0Hence, lim (-1)m(10^4n + e^-118 6^6n + tan(148n) - 7)n→∞

= ln1

= 0.

To know more about sequence visit:-

https://brainly.com/question/30262438

#SPJ11

If A is a 2 x 4 matrix and the sum A + B can be computed, what is the dimension of B? X

Answers

The dimension of matrix B is 2 x 4, the same as matrix A.

If A is a 2 x 4 matrix and the sum A + B can be computed, the dimension of matrix B should also be 2 x 4.

The dimension of a matrix refers to the number of rows and columns it has. In this case, matrix A is given to be a 2 x 4 matrix, which means it has 2 rows and 4 columns. When we perform matrix addition, we add corresponding elements of matrices A and B. For this operation to be possible, both matrices must have the same dimensions, meaning B must also have 2 rows and 4 columns.

Learn more about matrix here : brainly.com/question/28180105

#SPJ11

Write the complex number in polar form with argument θ between 0 and 2π.
2 + 2 (sqrt 3)i

Answers

The required polar form is:

[tex]4(cos\frac{2\pi }{3}+i \,sin\frac{2\pi }{3} )[/tex]

Polar Form of Complex Number:

If we have been given a complex number then its is easy to convert it in polar form by finding its modulus and its argument. For example, if we have a complex number of the form a + ib then its modulus is denoted by r and its value :-

[tex]r=\sqrt{a^2+b^2}[/tex]

and its argument is :-

[tex]\theta=tan^-^1(\frac{b}{a} )[/tex]

To write from the complex number to polar coordinates w proceed as follows:

The given complex is:

[tex]z =2+2\sqrt{3i}[/tex]

Let its polar form be z = r(cosθ+isinθ).

r = |z| = [tex]\sqrt{2^2+(2\sqrt{3} )^2}[/tex] = 4

Let [tex]\alpha[/tex] be the acute angle , given by:

[tex]tan\alpha =|\frac{Im(z)}{Re(z)}|= |\frac{2\sqrt{3} }{2} |=\sqrt{3}[/tex]

=> [tex]\alpha =\frac{\pi }{3}[/tex]

Now, The point will be:

z = [tex](2,2\sqrt{3i} ),(2,2\sqrt{3} )[/tex] which lies in the second quadrant.

arg(z) = [tex]\theta=(\pi -\alpha )=(\pi -\frac{\pi }{3} )=\frac{2\pi }{3}[/tex]

Thus, |r| = 4 and [tex]\theta = \frac{2\pi }{3}[/tex]

Hence, The required polar form is:

[tex]4(cos\frac{2\pi }{3}+i \,sin\frac{2\pi }{3} )[/tex]

Learn more about Complex number at:

https://brainly.com/question/9786350

#SPJ4

A closed curve C in the x, y - plane is positively oriented if a point on the curve moves clockwise as the parameter describing C increases. Select one: OA. True OB. False

Answers

The given statement ''A closed curve C in the x, y - plane is positively oriented if a point on the curve moves clockwise as the parameter describing C increases'' is False.

We have to given that,

Statement is,

''A closed curve C in the x, y - plane is positively oriented if a point on the curve moves clockwise as the parameter describing C increases.''

Now, A closed curve is one that begins and ends at the same location in the x, y plane and does not cross itself. A circle is an illustration of a closed curve.

The direction of the tangent vector r'(t) at each point on the curve determines the orientation of the curve if we parameterize it using the function r(t) = x(t), y(t), where t is the parameter and indicates the location of a point on the curve.

The curve is considered to have a positive orientation if the tangent vector r'(t) spins counterclockwise as t grows. The curve is referred to as having a negative orientation if the tangent vector r'(t) spins in a clockwise direction as t grows.

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ4

Find the inverse of the given matrix, if it exists. Use the algorithm for finding A-by row reducing [A I]. A= 10 3 - 2 1 - 3 - 4 2 - 3 Set up the matrix [A I] 10 3 100 [A I] - -2 1-3 0 10 - 4 2 -3 0 0 1 (Type an integer or simplified fraction for each matrix element.) Find the inverse. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The inverse matrix is a (Type an integer or simplified fraction for each matrix element.) B. The matrix A does not have an inverse.

Answers

After considering the given data we conclude that the the answer is (A) the inverse matrix is [1 0 0.1455 -0.0675; 0 1 -0.35 0.675; 0 0 0.455 1.385;].

To evaluate the inverse of the given matrix A, we can applying the algorithm for finding A-by row reducing [A I],
Here I = identity matrix of the same size as A. The steps are as follows:
Set up the matrix [A I] by appending the identity matrix of the same size as A to the right of A:
10 3 -2 1 1 0 0
-3 -4 2 -3 0 1 0
Place row operations to transform the left side of the matrix into the identity matrix. The same row operations must be used on the right side of the matrix to obtain the inverse of A.
Apply divison of the first row by 10 to get a leading 1: 1 0 -0.2 0.1 0.1 0 0
Apply addition 3 times the first row to the second row: 0 -4 1.4 -2.7 0 1 0
Apply addition 2 times the first row to the third row: 0 3 0.6 0.2 0 0 1
Apply addition 3 times the second row to the first row: 1 -12 0 6.7 0 3 -0
Apply division by the second row by -4 to get a leading 1: 0 1 -0.35 0.675 0 -0.25 0
Apply addition 1.4 times the second row to the third row: 0 0 0.455 1.385 0 -0.35 1
Apply subtraction 0.6 times the third row from the second row: 0 1 -0.35 0.675 0 -0.25 0
Apply subtraction 0.455 times the third row from the first row: 1 -12 0 6.7 0 3 -1.455
The left side of the matrix is now the identity matrix, and the right side of the matrix is the inverse of A:
1 0 0.1455 -0.0675
0 1 -0.35 0.675
0 0 0.455 1.385
Hence , the inverse matrix is:
A⁻¹ = [1 0 0.1455 -0.0675; 0 1 -0.35 0.675; 0 0 0.455 1.385;]
To learn more about inverse matrix
https://brainly.com/question/27924478
#SPJ4

Which of the following definite integrals is equal to limn→[infinity]∑k=1n10kn(1+5kn−−−−−−√)(5n)limn→[infinity]∑k=1n10kn⁡(1+5kn)(5n) ?
∫6110x√ⅆx∫1610xⅆx
the integral from, 1 to 6, of, 10 times, the square root of x, end root, d x
A
∫612xx√ⅆx∫162xxⅆx
the integral from, 1 to 6, of, 2 x times, the square root of x, end root, d x
B
∫50101+x−−−−−√ⅆx∫0510⁡1+xⅆx
the integral from, 0 to 5, of, 10 times, the square root of 1 plus x, end root, d x
C
∫502x1+x−−−−−√ⅆx

Answers

lim(n→∞) ∑(k=1 to n) 10k * n * [tex](1 + 5k/n)^{-\sqrt{5n} ))[/tex] = ∫(0 to 5) 2x / [tex](1 + x^{-\sqrt{5} })[/tex] dx

is the definite integral

To determine which definite integral is equal to the given limit expression, let's evaluate the limit and compare it with the provided options.

Given:

lim(n→∞) ∑(k=1 to n) 10k * n * [tex](1 + 5k/n)^{-\sqrt{5n} ))[/tex]

To simplify the expression, let's rewrite it in integral notation:

lim(n→∞) ∑(k=1 to n) 10k * n * [tex](1 + 5k/n)^{-\sqrt{5n} ))[/tex]

= lim(n→∞) (1/n) * ∑(k=1 to n) 10k * (n/n) * [tex](1 + 5k/n)^{-\sqrt{5n} ))[/tex]

= lim(n→∞) (1/n) * ∑(k=1 to n) 10k * (1/n) * [tex](1 + 5k/n)^{-\sqrt{5n} ))[/tex] * n²

This limit can be interpreted as the integral:

∫(0 to 1) 10x * [tex](1 + 5k/n)^{-\sqrt{5} ))[/tex] dx

Comparing this integral with the given options, we find that the correct answer is:

Option D: ∫(0 to 5) 2x / [tex](1 + x^{-\sqrt{5} })[/tex] dx

Therefore, the definite integral that is equal to the given limit expression is option D.

Learn more about definite integral

brainly.com/question/28036871

#SPJ4

Find the domain of the vector function r(t)=t−2t+2i+sintj+ln(9−t2)k

Answers

The domain of the vector function r(t) = ti + sj + tk is (-∞, ∞) × (-∞, ∞) × (-3, 3), or in set-builder notation: {(t, s, k) : t ∈ ℝ, s ∈ ℝ, k ∈ ℝ, -3 < t < 3}.

To find the domain of a vector function r(t) = ti + sj + tk, we need to find the values of t that make each component of the vector function defined. Here, the given vector function is:

r(t) = (t - 2t + 2)i + sin(t)j + ln(9 - t²)k

Therefore, the x-component of the vector function is:

r₁(t) = t - 2t + 2 = -t + 2

We note that the x-component of the vector function is defined for all values of t.

Hence, the domain of the vector function with respect to the x-component is (-∞, ∞).

Similarly, the y-component of the vector function is:

r₂(t) = sin(t)

We note that the sine function is defined for all values of t.

Hence, the domain of the vector function with respect to the y-component is (-∞, ∞).

Finally, the z-component of the vector function is:

r₃(t) = ln(9 - t²)

For the natural logarithm function ln(x), the argument x must be positive. Hence, 9 - t² > 0.

Therefore, t must lie in the open interval (-3, 3).

Hence, the domain of the vector function with respect to the z-component is (-3, 3).

Therefore, the domain of the vector function

r(t) = ti + sj + tk is (-∞, ∞) × (-∞, ∞) × (-3, 3), or in set-builder notation:

{(t, s, k) : t ∈ ℝ, s ∈ ℝ, k ∈ ℝ, -3 < t < 3}

To know more about vector visit:

https://brainly.com/question/24256726

#SPJ11

Why does increasing the confidence level result in a larger margin of error?
Add Work Explain how a court trial is like hypothesis testing. Include the steps of a hypothesis test and why a verdict is "not guilty" instead of innocent.

Answers

Increasing the confidence level in statistical analysis results in a larger margin of error to provide a more conservative estimate with a wider range of values. A court trial is analogous to hypothesis testing, involving the formulation of hypotheses, collection and analysis of evidence, testing the evidence, and rendering a verdict based on the burden of proof.

Increasing the confidence level in a statistical analysis means that we want to be more certain or confident in our results. To achieve a higher confidence level, we need to widen the interval or range of values within which we estimate the population parameter. This wider range leads to a larger margin of error because we allow for more variability in the data and account for a greater degree of uncertainty. In other words, increasing the confidence level requires a larger margin of error to provide a more conservative estimate that captures a higher proportion of possible values.

Regarding a court trial and hypothesis testing, there are similarities in their logical structure. Both involve making a claim (hypothesis) and evaluating evidence to either support or reject that claim. The steps of a hypothesis test in a court trial can be seen as follows:

Formulation of hypotheses: The prosecution presents the alternative hypothesis (defendant is guilty), and the defense asserts the null hypothesis (defendant is not guilty).

Collection and analysis of evidence: Both sides present evidence and arguments to support their claims.

Test of evidence: The evidence is examined and evaluated using various methods such as witness testimony, forensic analysis, and cross-examination.

Decision: Based on the presented evidence, the jury or judge makes a decision, either rejecting the alternative hypothesis (verdict of "not guilty") or failing to reject the null hypothesis (insufficient evidence to prove guilt beyond a reasonable doubt).

The verdict of "not guilty" in a court trial does not imply the defendant is innocent but rather signifies that the evidence presented did not meet the burden of proof required to establish guilt beyond a reasonable doubt.

To know more about confidence level click here

brainly.com/question/22851322

#SPJ11

Estimate the final mark for a student that studied a total of 10 hours outside of class time for this subject. Please give your answer correctly rounded to two ...

Answers

The estimated final mark for a student who studied 10 hours outside of class time is 11.42, according to the given regression model with an intercept of 3.82 and a coefficient of 0.76 for the number of hours studied.

To estimate the final mark for a student who studied 10 hours outside of class time, we can use the simple linear regression model provided. The regression equation is y = 3.82 + 0.76x, where y represents the final mark and x represents the number of hours studied. We'll plug in x = 10 into the equation and calculate the estimated final mark.

According to the regression model, the intercept (b0) is 3.82 and the coefficient for the number of hours studied (b1) is 0.76. To estimate the final mark for a student who studied 10 hours, we substitute x = 10 into the regression equation:

Estimated final mark = 3.82 + 0.76 * 10 = 11.42

Therefore, the estimated final mark for a student who studied 10 hours outside of class time is 11.42 (rounded to two decimal places).

It's important to note that this estimation is based on the provided regression model and assumes a linear relationship between the number of hours studied and the final mark. The accuracy of the estimate depends on the validity and reliability of the regression model and the data used to create it.

Learn more about linear regression here: brainly.com/question/32178891

#SPJ11

Complete question is below and also in the image attached

A lecturer wanted to investigate the relationship between a student’s final mark (in points) for a subject and the number of hours the student studied in the trimester, outside of class time. They gathered a random sample of data and used EXCEL to create the following simple linear regression of marks on hours:

Estimate the final mark for a student that studied a total of 10 hours outside of class time for this subject. Please give your answer correctly rounded to two decimal places and do NOT include units.

Save A Solve the problem. A bottling company produces boitles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 49 bottles and finds the average amount of liquid held by the bottles is 9.9155 ounces with a standard deviation of 0.35 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion. O At a = 0.025, reject the null hypothesis. At a = 0.05, accept the null hypothesis. O At a = 0.10, fail to reject the null hypothesis. O At a = 0.05, reject the null hypothesis.

Answers

The average amount of liquid held in the bottles is significantly less than 10 ounces.

The p-value represents the probability of obtaining a sample mean as extreme as, or more extreme than, the observed value, assuming that the null hypothesis is true. In other words, it indicates how likely it is to observe a sample mean of 9.9155 ounces or less if the bottles do, in fact, hold at least 10 ounces on average.

Given that the p-value is calculated to be 0.0455, it is important to compare this value to the significance level (α) chosen for the hypothesis test. The significance level, often denoted as α, represents the threshold at which we reject the null hypothesis. Commonly used significance levels include 0.05, 0.01, and 0.10.

In this case, we are given four potential significance levels to consider: 0.025, 0.05, 0.10, and 0.05.

Let's evaluate each one individually:

At a significance level of 0.025:

Since the p-value (0.0455) is greater than the chosen significance level (0.025), we do not have sufficient evidence to reject the null hypothesis.

=> (0.0455) > (0.025)

Therefore, we would fail to reject the null hypothesis at this level of significance.

At a significance level of 0.05:

Comparing the p-value (0.0455) to the significance level (0.05), we find that the p-value is smaller.

=> (0.0455) < (0.05)

When the p-value is less than or equal to the significance level, we reject the null hypothesis. Therefore, at this significance level, we reject the null hypothesis.

At a significance level of 0.10:

Again, the p-value (0.0455) is smaller than the significance level (0.10). Hence, we have enough evidence to reject the null hypothesis at this level of significance.

=> (0.0455) < (0.10)

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

Find the volume of the following cube using the formula v = 1. w. h
2x+3
X
x+4

Answers

Answer:

V = x³ + 11x² + 12x

Step-by-step explanation:

calculate the volume (V) using the formula

V = lwh ( l is the length, w the width and h the height )

here l = 2x + 3 , w = x , h = x + 4 , then

V = (2x + 3)(x)(x + 4)

= x(2x + 3)(x + 4) ← expand the factors using FOIL

= x(2x² + 8x + 3x + 12)

= x(2x² + 11x + 12) ← distribute terms in parenthesis by x

= 2x³ + 11x² + 12x

pattern with matches is shown below. Figure 1 (i) Explain how the pattern is formed. (ii) Complete the table. Figure number 1 Number of 3 matches 2 Figure 2 5 3 7 4 (iii) What rule did you use to complete the table? 5 6 MA If you used the recursive rule to complete the table it Figure 3 7 (iv) How many matches are needed to form figure number 9 and 17? Explain. 8 (2) (5) (1) (2)

Answers

Therefore, the recursive rule for the pattern is that each pattern has two matches added to the previous pattern to form the next pattern. Completion of the table by using the rule shown in pattern .

The initial pattern has three matches, while the second pattern has five matches, indicating that two matches have been added. Similarly, the third pattern has seven matches, indicating that two matches have been added, and the fourth pattern has nine matches. The pattern continues in the same manner, with two matches added to each new pattern. The rule used to complete the table To complete the table, the recursive rule is used, which states that each pattern has two matches added to the previous pattern to form the next pattern. The number of matches needed to form figure number 9 and 17 and the explanation The ninth pattern can be determined by adding two matches to the eighth pattern, which has eight matches, for a total of ten matches. As a result, the ninth pattern has ten matches. A similar approach is used to determine that the seventeenth pattern has 30 matches, which is obtained by adding two matches to the sixteenth pattern, which has 28 matches.

For such more question on recursive

https://brainly.com/question/31313045

#SPJ8

In a publication of a renowned magazine, it is stated that cars travel an average of at least 20,000 kilometers a year, but you believe that in reality the average is less. To test this claim, a randomly selected sample of 100 car owners is asked to keep track of the miles driven. Would you agree with this statement if the random sample indicated a mean of 19,000 kilometers and a standard deviation of 3,900 kilometers? Use a significance level of 0.05 and for your engineering conclusion use:
a) The classical method.
b) The P-value method as an auxiliary

Answers

The problem is about testing a claim of a renowned magazine that cars travel an average of at least 20,000 kilometers a year.

To test this claim, a randomly selected sample of 100 car owners is asked to keep track of the miles driven. They found the mean miles driven of the sample of 100 car owners to be 19,000 km, and the standard deviation of the sample to be 3,900 km.

Classical Method: We will test the null hypothesis that the average miles driven is at least 20,000 km against the alternative hypothesis that the average miles driven is less than 20,000 km. We can express this as: H0 : μ ≥ 20,000 Ha : μ < 20,000 Where H0 is the null hypothesis, Ha is the alternative hypothesis, and μ is the population mean.
To know more about average visit:

https://brainly.com/question/29550341

#SPJ11

Gallup conducted a poll in September 2021 of parents with children under the age of 12 about whether or not they plan to get their children vaccinated. The poll compared several demographics of the parents, including political party identification. There were 305 parents who identify as Democrat, with 253 of them saying they plan to get their children vaccinated. There were 282 parents eho identified as Republican, with 59 of them saying they plan to get their children vaccinated. Test the null hypotestis of no difference between the population proportions of Democrat and Republican parents who plan to get their children under the age of 12vaccinated. What is the research hypothesis?
a. there is no difference between the population proportions of Democrat and Republican parents who plan to get their chiildren under the age of 12 vaccinated.
b. there is a difference between the population porportions of democrat and republican parents who plan to get their children under the age of 12 vaccinated.

Answers

Therefore, the research hypothesis would be that there is a difference between the population proportions of Democrat and Republican parents who plan to get their children under the age of 12 vaccinated.

The research hypothesis is that there is a difference between the population proportions of Democrat and Republican parents who plan to get their children under the age of 12 vaccinated.

When it comes to data analysis, testing hypotheses is a crucial component of statistical analysis.

A hypothesis is a claim or statement about a characteristic or feature of a population, and hypothesis testing is a statistical method for testing whether that claim is valid or not.

The null hypothesis (H0) is a hypothesis that assumes that there is no significant difference between two groups or variables, whereas the alternative hypothesis (Ha) is a hypothesis that assumes that there is a significant difference between two groups or variables.

The research hypothesis is the opposite of the null hypothesis.

Thus, in this study, the null hypothesis is that there is no difference between the population proportions of Democrat and Republican parents who plan to get their children under the age of 12 vaccinated.

To know more about null hypothesis visit:

https://brainly.com/question/32575796

#SPJ11

A line passes through points P1 = (−1, 2) and P2 = (3, −4). For
this line, find two equations in the point-slope form corresponding
to point P1 and P2.

Answers

The required two equations in point-slope form corresponding to points P1 and P2 are:

1. y - 2 = (-3/2)(x + 1)

2. y + 4 = (-3/2)(x - 3)

Given that, the line passes through points P1 = (−1, 2) and P2 = (3, −4).

To find the slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1) and the equation of a line in point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

For point P1 = (-1, 2): The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1)

Substituting the coordinates, gives,

m = (-4 - 2) / (3 - (-1)) = -6/4 = -3/2.

Using point-slope form, the equation corresponding to point P1 is:

y - 2 = (-3/2)(x - (-1))

Simplifying, gives,

y - 2 = (-3/2)(x + 1).

For point P2 = (3, -4): Similarly, the slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1)

Substituting the coordinates, gives,

m = (-4 - 2) / (3 - (-1)) = -6/4 = -3/2.

Using point-slope form, the equation corresponding to point P2 is:

y - (-4) = (-3/2)(x - 3)

Simplifying, gives,

y + 4 = (-3/2)(x - 3).

Therefore, the two equations in point-slope form corresponding to points P1 and P2 are:

1. y - 2 = (-3/2)(x + 1)

2. y + 4 = (-3/2)(x - 3)

Learn more about point-slope form and line equations, click here:

https://brainly.com/question/29045561

#SPJ4.

The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 6, 5. a. What is the point estimate of the population mean? 23. 24. 25. b. What is the point estimate of the population standard deviation (to 3 decimals)? (ci c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)? d. What is the 95% confidence interval for the population mean (to 1 decimal)? ) A Hint(s)

Answers

a. The point estimate of the population mean is 10.5.

b. The point estimate of the population standard deviation is approximately 3.26.

c. The margin of error for the estimation of the population mean with 95% confidence is approximately 2.26 (to 1 decimal place).

d. The 95% confidence interval for the population mean is (8.2, 12.8) (to 1 decimal place).

a. The point estimate of the population mean can be found by calculating the sample mean, which is the sum of the data values divided by the number of observations. In this case, the sample mean is (10 + 9 + 12 + 14 + 13 + 11 + 6 + 5) / 8 = 10.5.

b. The point estimate of the population standard deviation can be found by calculating the sample standard deviation, which is a measure of the variability in the data. The formula for the sample standard deviation is the square root of the sum of squared deviations from the sample mean divided by (n-1), where n is the number of observations. Using the given data, the sample standard deviation is approximately 3.26.

c. To calculate the margin of error for the estimation of the population mean with 95% confidence, we need to consider the standard error. The standard error is calculated by dividing the sample standard deviation by the square root of the sample size. In this case, the standard error is approximately 3.26 / sqrt(8) ≈ 1.1547. The margin of error is then obtained by multiplying the standard error by the critical value associated with the desired confidence level (in this case, 95%). The critical value for a 95% confidence interval is approximately 1.96. Therefore, the margin of error is 1.1547 * 1.96 ≈ 2.26.

d. The 95% confidence interval for the population mean can be calculated by adding and subtracting the margin of error from the point estimate of the population mean. In this case, the confidence interval is approximately 10.5 ± 2.26, which gives us the range (8.24, 12.76) with the lower bound rounded to 1 decimal place and the upper bound rounded to 1 decimal place.

To learn more about point estimate refer here:
https://brainly.com/question/30888009

#SPJ11

The value of your home over time can be found by using the equation V(t) = P(1.08)' where P represents the initial purchase price, and V represents the value of your home after t number of years. You bought your home for $420,000 and its value increases each year by 8%. Approximately, how many years will it take for the house to be worth $600,000?

Answers

it will take approximately 7.2 years for the house to be worth $600,000.To find the number of years it will take for the house to be worth $600,000, we can set up the equation as follows:

V(t) = P(1.08)^t

Where V(t) is the value of the home after t number of years, P is the initial purchase price ($420,000), and t is the number of years.

We want to find the value of t when V(t) equals $600,000. So we set up the equation:

600,000 = 420,000(1.08)^t

To solve for t, we can divide both sides by 420,000:

1.43 = (1.08)^t

Taking the logarithm of both sides, we get:

log(1.43) = log((1.08)^t)

Using logarithm properties, we can bring down the exponent:

t * log(1.08) = log(1.43)

Finally, we can solve for t by dividing both sides by log(1.08):

t = log(1.43) / log(1.08)

Using a calculator, we find that t is approximately 7.2 years.

Therefore, it will take approximately 7.2 years for the house to be worth $600,000.

To learn more about equation click here:brainly.com/question/29657983

#SPJ11

Recording sheet for Activity: Which inference method will you use? We're considering the '15-'16 regular season game data as a sample of games the Golden State Warrior (GSW) basketball team might have played against other NBA opponents in that or future seasons Most key variables for this activity have to do with free throws: number attempted (FTA) and number successfully made (FT) for GSW and those for their opponents (OppFTA and OppFT). Free throws are shots awarded to a team for certain infractions (fouls) made by its opponent (hence they are also called foul shots). Free throws are taken at a set distance (15 feet) from the basket with no opponent allowed to defend shot. Put the letter corresponding to each scenario in the appropriate box to indicate what inference procedure it is. Inference for: Hypothesis test Confidence Interval One mean, u (simulation type: BT or RND ; distribution type: z ort) One proportion, p (simulation type: BT or RND ; distribution type: z ort) Difference in proportions from two separate samples, M1-M2 (simulation type: BT or RND ; distribution type: z ort) Paired means, HD (simulation type: BT or RND; distribution type: z ort) Difference in proportions from two samples, P1-P2 (simulation type: BT or RND ; distribution type: z ort) A. What's an average number of free throws for the Warriors to attempt during a game? C. Do the Warriors make more free throws (on average) during games at home than on the road? E. What proportion of free throw attempts do the Warrior players make? G. How much better (or worse) are the Warriors at making free throw attempts compared to their opponents? I. Is the mean number of free throw attempts awarded to the Warriors during their games different from the mean number attempted by their opponents? K. (Challenge) On average, is the point spread when GSWarriors win larger than the point spread when they lose? B. Is the proportion of free throws made by the Warriors different between games they play at home and those they play on the road? D. Over the past 10 years, NBA teams have averaged close to 25 free throw attempts per game. Treating this as the population mean, is the mean number of free throw attempts by the Warriors much different? F. How many more (or fewer) free throw attempts do the Warriors take on average) for home games compared to road games? H. Players in the NBA as a whole make about 75.6% of their free throws. Is the proportion made by the Warriors different from this? J. How does the average number of free throws made (per game) by the Warriors compare to their opponents? L. (Extra) On average, what is the point spread in GS Warrior games? (where "+" means they won; "-"means they lost)

Answers

The inference procedure for each is give below-

A. The inference procedure: Confidence Interval - One mean, μ.

C. The inference procedure: Hypothesis test - Difference in proportions from two samples, P1-P2.

E. The inference procedure: Confidence Interval - One proportion, p.

G. The inference procedure: Confidence Interval - Difference in proportions from two separate samples, M1-M2

I. The Inference procedure: Hypothesis test - Difference in means from two independent samples.

K. The Inference procedure: Hypothesis test - Paired means, HD.

B. The Inference procedure: Hypothesis test - Difference in proportions from two samples, P1-P2.

D. The Inference procedure: Hypothesis test - One mean, μ.

F. Inference procedure: Confidence Interval - Paired means, HD.

H. Inference procedure: Hypothesis test - One proportion, p.

J. Inference procedure: Confidence Interval - Difference in means from two independent samples.

L. It doesn't directly involve inference.

Now we have-

A. What's the average number of free throws for the Warriors to attempt during a game?

Distribution type: z

C. Do the Warriors make more free throws (on average) during games at home than on the road?

Simulation type: BT (bootstrap)

Distribution type: z

E. What proportion of free throw attempts do the Warrior players make?