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You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 99% confident that the sample percentage is within 5.5 percentage points of the true population percentage. Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. nequals 549 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 34% of air passengers prefer an aisle seat. nequals nothing (Round up to the nearest integer.)

Answers

Answer 1

Answer:

Answer:

a) $n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

b) $n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

Step-by-step explanation:

Previous concept

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{(p(1-p))/(n)})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_(\alpha/2)=-2.58, t_(1-\alpha/2)=2.58$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_(\alpha/2)\sqrt{(\hat p (1-\hat p))/(n)}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\hat p (1-\hat p))/(((ME)/(z))^2)$ (b)

We can assume that $\hat p =0.5$ since we don't know prior info. And replacing into equation (b) the values from part a we got:

$n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

Part b

$n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

Answer 2

Answer:

Final answer:

To determine the required sample size for the survey, we can use a sample size formula based on the desired confidence level and margin of error. If nothing is known about the passenger preferences, a sample size of 549 would be needed. If a prior survey suggests a certain proportion, the sample size can be calculated using the known proportion.

Explanation:

In order to determine the number of randomly selected air passengers that must be surveyed, we need to calculate the required sample size for a desired confidence level and margin of error.

a. If nothing is known about the percentage of passengers who prefer aisle seats, we can use a sample size formula given by n = (Z^2 * p * q) / E^2, where Z is the z-score corresponding to the desired confidence level, p and q are the estimated proportions for aisle seat preference and non-aisle seat preference respectively, and E is the desired margin of error. Since a confidence level of 99% and a margin of error of 5.5% are specified, we can round up the sample size to 549.

b. If a prior survey suggests that about 34% of air passengers prefer an aisle seat, we can use the same sample size formula but with the known proportion p = 0.34. We do not have information about the non-aisle seat preference, so we cannot determine the required sample size.

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To solve this problem you must apply the proccedure shown below:

1. You have the following quadratic equation, which is given in the problem above:

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2. So, to solve it, you can use the quadratic formula, which is:

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Answers

Answer:

did you ever get the answer?

Step-by-step explanation:

Which statements are true? Select three options. ∠F corresponds to ∠F'. Segment EE' is parallel to segment FF'. The distance from point D' to the origin is One-third the distance of point D to the origin. The measure of ∠E' is One-third the measure of ∠E. △DEF △D'E'F'

Answers

Answer:

The correct options are (1), (3) and (5).

Step-by-step explanation:

The two triangles are shown below.

The measure of ∠F corresponds to ∠F'.

The distance between the points D and origin is of 9 units.

And the distance between the points D' and origin is 3 units.

Thus, the distance from point D' to the origin is One-third the distance of point D to the origin.

Check for similarity:

$(D'F')/(DF)=(D'E')/(DE)=(F'E')/(FE)=(1)/(3)$

Thus, the △DEF is similar to △D'E'F'.

Thus, the correct options are (1), (3) and (5).

Answer:

I think it's the first, third, and fifth options.

Step-by-step explanation:

I hope this helps.

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Answers

Answer:

Step-by-step explanation:

eq. of circle with (x1,y1 ) and (x2,y2) as extremities of diameter is

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x²+2x+y²-14y+42=0

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(x-(-1))²+(y-7)²=8

triangle NOP is similar to triangle QRS. Find the measure of Side SQ. Round your answer to the nearest tenth if necessary

Answers

The measure of side SQ from the given similar triangles is 40.9 units.

What are similar triangles?

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle NOP is similar to triangle QRS.

Since the triangles are similar,

NP/SQ = NQ/QR

10/SQ = 13/53.2

13SQ=532

SQ=532/13

SQ=40.9 units

Therefore, the measure of side SQ is 40.9 units.

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Answer:

Step-by-step explanation:

A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

Answers

The question is incomplete. Here is the complete question.

A differential equation is given along with the field of problem area which it arises. Classify it as an ordinary differential equation (ODE) or a partial different equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

$x(d^(2)y )/(dx^(2) ) + (dy)/(dx) + xy = 0$ (aerodynamics, stress analysis)

Answer and Step-by-step explanation: The differential equation described above is anOrdinaryDifferentialEquation, because it has a definite set of variables: x and y.

It is of SecondOrder, since the highest derivative is of order 2: $(d^(2)y )/(dx^(2) )$

The differential equation is written as derivative of a function y in terms of x, which means: IndependentVariable is X and DependentVariable is Y.

As it is an ODE, the equation is Nonlinear, because y'' or $(d^(2)y )/(dx^(2) )$ is multiplied by a variable.

Final answer:

This question pertains to classifying and understanding differential equations in mathematics, specifically identifying whether it is an ordinary differential equation, determining its order, and identifying independent and dependent variables.

Explanation:

In mathematics, a differential equation is a mathematical equation that relates a function with its derivatives. An Ordinary Differential Equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term order of a differential equation is defined as the highest power of the derivative in the equation.

As an example, if we have an equation like dy/dx = x*y, it would be an ODE since it involves only one independent variable, 'x', and the dependent variable is 'y'. The order is one since the highest order derivative is dy/dx, and the equation is nonlinear because it does not meet the criteria for a linear ODE, which stipulates that the dependent variable and its derivatives are to the first power and are not multiplied together.

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