consider the large hospital that wants to estimate the average length of stay of its patients. the hospital randomly selected 27 patients and finds that the sample mean length of stay 3.2 days and standard deviation of 1.6 days. (a) what is the 80% confidence interval for the true average length of stay of its patients? interpret the result. (b) what is the 99% confidence interval for the true average length of stay of its patients? (c) determine the number of patients that must be sampled in order to estimate the true average length of stay within 0.2 with 90% confidence.

Answers

Answer 1

(a) The 80% confidence interval for the average length of stay is [2.567, 3.833]. We are 80% confident that the true average falls within this range. (b) The 99% confidence interval is [1.860, 4.540]. We are 99% confident that the true average falls within this range. (c) To estimate the average within 0.2 with 90% confidence, a sample size of approximately 32 patients is needed.

(a) To calculate the 80% confidence interval, we use the formula

Confidence Interval = Sample Mean ± Margin of Error

The margin of error can be found using the formula:

Margin of Error = Critical Value * (Standard Deviation / sqrt(sample size))

For an 80% confidence level, the critical value (obtained from the t-distribution with 26 degrees of freedom) is approximately 1.318.

Plugging in the values

Margin of Error = 1.318 * (1.6 / √(27)) ≈ 0.633

So the 80% confidence interval is

3.2 ± 0.633 = [2.567, 3.833]

(b) For the 99% confidence interval, we use the same formula but with a different critical value. For a 99% confidence level, the critical value (from the t-distribution with 26 degrees of freedom) is approximately 2.787.

Margin of Error = 2.787 * (1.6 / √(27)) ≈ 1.340

Therefore, the 99% confidence interval is

3.2 ± 1.340 = [1.860, 4.540]

(c) To determine the required sample size to estimate the true average length of stay within 0.2 days with 90% confidence, we use the formula:

n = (Z * σ / E)²

Where Z is the critical value (1.645 for a 90% confidence level), σ is the standard deviation (1.6 days), and E is the desired margin of error (0.2 days).

Plugging in the values

n = (1.645 * 1.6 / 0.2)² ≈ 31.985

Therefore, we need a sample size of approximately 32 patients.

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Related Questions

Damon is saving for a vacation. He estimates that he’ll need about $2,500 for the trip. He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal. In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation. Review his work, and select the true statement.

Step 1: y = 500 + 400x
Step 2: y − 500 = 500 + 400x − 500
Step 3: y − 500 = 400x
Step 4:
y
−
500
400
=
400
⁢
x
400

Step 5:
y
−
500
400
= x
Step 6:
2
,
500
−
500
400
= x
Step 7: 5 = x
A.
Damon used the multiplication property of equality in step 2.
B.
Damon used the subtraction property of equality in step 3.
C.
Damon used the division property of equality property in step 4.
D.
Damon used the associative property in step 5.
E.
Damon used the addition property of equality in step 6.

Answers

The $2,500 Damon estimates he needs and the equation; y = 500 + 400·x for finding the number of months of savings required indicates that in step 4, Damon used the division property of equality. The true statement is therefore;

C. Damon used the division property of equality in step 4

What is the division property of equality?

The division property of equality states that the division of both sides of an equation by the same real number which is not zero, the quotients obtained are also equal.

The Damon's work to calculate the number of months of savings it will take to reach the goal of $2,500 for his vacation trip is presented as follows;

Step 1: y = 500 + 400·x

Step 2: y - 500 = 500 + 400·x - 500

Step 3: y - 500 = 400·x

Step 4: (y - 500)/(400) = 400·x/400

Step 5: (y - 500)/400 = x

Step 6: (2,500 - 500)/400 = x

Step 7: 5 = x

Therefore; Damon used the subtraction property of equality in step 2

Damon used the division property of equality in step 4

Damon used the substitution property of equality in step 6

The true statement is therefore; Damon used the division property of equality in step 4

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Ahaahhhahhahhahahaha help

Answers

Answer:

Im pretty sure its 8.

Step-by-step explanation:

32/1 x 1/4= 32/4 = 8

If im right please give me brainliest :)

Martine grew at an average rate of 6cm/year for the first 18 years of her life. If Martine was 50 cm long when she was born, how tall was Martine when she turned 18?

Answers

Answer:

158cm

Step-by-step explanation:

Martine had the height of 50cm when born.

Every year she grows at an average rate of 6cm

So the the first 18 years will be 6cm × 18 = 108cm

She will be 108cm + 50cm = 158cm tall by the time she turns 18 years

50cm + (6 × 18)cm

50cm + (6 × 18)cm50cm + 108cm

50cm + (6 × 18)cm50cm + 108cm158cm

Solve the exponential equation
4^x = 7(3^x)

Answers

The solution to the given exponential equation is; x = 6.48

What is the solution to the exponential equation?

We want to solve the exponential equation;

4^(x) = 7 - (3^x)

We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;

x log 4 = 7 - (x log 3)

x log 4 + x log 3 = 7

x(log 4 + log 3) = 7

1.08x = 7

x = 7/1.08

x = 6.48

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What is the slope of the line that passes through the points A(-2,3) and B(-12,6)?

Answers

Answer:

The answer is

$- \frac{3}{10} $

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} $

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(-2,3) and B(-12,6)

The slope is

$m = \frac{ 6 - 3}{ - 12 - - 2} = \frac{3}{ - 12 + 2} \\ = - \frac{3}{10} $

We have the final answer as

$- \frac{3}{10} $

Hope this helps you

Work is attached in the image below.

What is the slope of the line that passes through the points A(-2,3) and B(-12,6)?

4x3 what is 4x3 I really want to know

Answers

Answer:

The answer to 4x3 is 12

same as adding 4 thee times!

4 plus 4 plus 4 equals 12

Answer:

4X3=12

Step-by-step explanation:

It's like adding 4 3 times

Are the following word sequences statements? Justify your answer.A) I swear to tell the truthB) good ideas sleep furiouslyC) Go away, you're getting on my nerves.B- Build the truth table containing the following compound propositions:> P <=> (Q V R)

Answers

SOLUTION

Looking at the sentences presented in A, B and C,

A is not a statement because it cannot be proven to be true or false

B is a statement because it can be proven to be true or false

C is not a statement because it cannot be proven to be true or false

So we will be building a truth table for B

Now we will build a table for (Q V R) first. This means Q or R.

We have

And next is P <=> (Q V R), this means P is true or false if and only if Q or R is true/false.

We have

Are the following word sequences statements? Justify your answer.A) I swear to tell the truthB) good

What is the product? 3a(8a - 6b)

24a² - 6b

24a² - 6ab

24a² - 18b²

24a² - 18ab

Answers

The answer is the last one.

Explanation:

3a(8a - 6b)
3a x 8a - 3a x 6b
24a^2 - 3a x 6b
24a^2 - 18ab

The product of expression is 24a² - 18ab.

What is Polynomial?

A polynomial is a sort of algebraic expression in which all variable exponents are whole numbers. Variable exponents in any polynomial must be non-negative integers. A polynomial is made up of constants and variables, however we cannot divide polynomials by variables.

We have,

3a( 8a - 6b)

Now, multiplying the expression as

= 3a(8a) - 3a(6b)

= 24a² - 18ab

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Jump to level 1 Given string userInput, output "Matching" if the fourth character of userInput is 'e'. Otherwise, output "Not matching". End with a newline. Ex: If the input is: threw then the output is: Matching Note: Assume the length of string userinput is greater than or equal to 4. 1 #include 2 #include 3 using namespace std; 4 5 int main() \{ string userInput; 7 8 getline(cin, userInput); 101/ Your code goes here */ 11

Answers

The code returns 0 to indicate successful execution.

How we find the code?

We can write the code to check if the fourth character of userInput is 'e' using an if-else statement:

#include <iostream>#include <string>

using namespace std;

int main() {string userInput;getline(cin, userInput);

(userInput[3] == 'e') {cout << "Matching" << endl;}{ cout << "Not matching" << endl;}return 0;}

In this code, we use userInput[3] to access the fourth character of the string userInput.

The code reads a string userInput from the user using getline(cin, userInput). Then, it checks if the fourth character of userInput is 'e' using an if statement. If it is, the code outputs "Matching" followed by a newline character using cout << "Matching" << endl;. Otherwise, it outputs "Not matching" followed by a newline character using cout << "Not matching" << endl;.

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i need help again lol-

Answers

Answer:

1.5

Step-by-step explanation:

Okay, so let's try this again, the median is the middle number, but the funny thing is, we have 8 numbers here, so we don't have a middle number. The closest we get is the middle of 1 and 2, which is 1.5.

Hope this helps:)

Convert the following fraction into decimals by changing denominator of 7/5 a multiple of 10

Answers

Answer:

1.4

Step-by-step explanation:

= 7/5 × 2/2

= 14/10

=1.4

If the given ΔXYZ is rotated by 180 degrees around point X in a clockwise direction, what are the new coordinates of the Y and Z vertices? Select the two correct answers.

If the given XYZ is rotated by 180 degrees around point X in a clockwise direction, what are the new

Answers

Answer:

Options C and D

Step-by-step explanation:

From the graph attached,

Coordinates of the vertices,

X → (0, 0)

Y → (-1, -2)

Z → (0, -2)

Rule for the rotation of a point (h, k) by 180° about the origin is given by,

(h, k) → (-h, -k)

By this rule,

Coordinates of the image points will be,

X(0, 0) → X'(0, 0)

Y(-1, -2) → Y'(1, 2)

Z(0, -2) → Z'(0, 2)

Therefore, Option (C) and Option (D) are the correct options.

Answer

C/D

Step-by-step explanation:

MATH PROBLEM SOLVING

Answers

Answer:

Probability[Selected ball is a white ball without replacement (W)] = 5 / 22

Step-by-step explanation:

Given:

Number of white ball in jar = 5

Number of black ball in jar = 6

Find;

Probability[Selected ball is a white ball without replacement (W)]

Computation:

Probability of an event = Number of favorable outcomes / Total number of outcomes

Probability of 1st white ball = 5 / [5 + 6]

Probability of 1st white ball = 5 / 11

Probability of 2nd white ball [without replacement] = 5 / [11 - 1]

Probability of 2nd white ball [without replacement] = 5 / 10

Probability[Selected ball is a white ball without replacement (W)] = [5/11][5/10]

Probability[Selected ball is a white ball without replacement (W)] = 25 / 110

Probability[Selected ball is a white ball without replacement (W)] = 5 / 22

Can someone please help? Thanks!

Answers

Hey, I have already answered these all questions except the last question in your previous question. Make sure to see them.

For the last question, the answer would be the second choice as when times keep flowing, the distance still remains the same (not to be confused with speed.)

Basically when times keep going, the distance will stay the same without any changes.

what is the difference between descriptive statistics and inferential statistics?

Answers

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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Suppose you are given a bag with 3 blue marbles and 2 red marbles, and you are asked to find the probability of drawing 2 blue marbles by drawing one marble at a time and not replacing the first marble drawn. Why does not replacing the first marble make these events dependent

Answers

Here Is the Answer:

Not replacing the first marble makes the events dependent because the outcome of the first draw affects the probability of the second draw. After the first blue marble is drawn, there are only two blue marbles and four marbles in total remaining in the bag. Therefore, the probability of drawing a second blue marble is lower than the probability of drawing a blue marble on the first draw. The probability of drawing two blue marbles is calculated as the product of the probability of drawing a blue marble on the first draw and the probability of drawing another blue marble on the second draw, given that the first marble was not replaced.

Use the long division method to find the result when 9x^3+18x^2+20x+169x 3 +18x 2 +20x+16 is divided by 3x+43x+4.

Answers

Given:

Dividend = $9x^3+18x^2+20x+16$

Divisor = $3x+4$

To find:

The quotient and remainder by using the long division method.

Solution:

Using the long division method, divide the polynomial $9x^3+18x^2+20x+16$ by $3x+4$ as shown below:

$3x+4 |\overline{9x^3+18x^2+20x+16}|3x^2+2x+4\\$

$9x^3+12x^2\\\underline{(-)\quad (-)\quad \quad \quad}$

$0+6x^2+20x$

$6x^2+8x\\\underline{(-)\quad (-)\quad \quad \quad}$

$0+12x+16$

$12x+8\\\underline{(-)\quad (-)}$

$\underline{\quad 0\quad}$

Therefore, the quotient is $3x^2+2x+4$ and the remainder is 0.

iv. What is the statement of Fick's First law? Express also, in mathematical form. Identify and explain the parameters in your equation. What is the statement of Fick's second law, in mathematical form? Identify and explain the parameters in your equation.

Answers

Fick's First law of diffusion states that the rate of diffusion of a substance is directly proportional to the concentration gradient of the substance.Fick's Second law of diffusion states that the rate of change of concentration of a substance with time is proportional to the rate of the movement of the substance by diffusion.

Fick's First law of diffusion

Fick's First law of diffusion states that the rate of diffusion of a substance is directly proportional to the concentration gradient of the substance. The mathematical equation for Fick's First Law is given as follows:

J = - D(dC/dx),

where J represents the flux of the diffusing species, dC/dx is the concentration gradient, and D is the diffusion coefficient.

The parameter dC/dx refers to the concentration gradient that exists between two points and is the change in concentration of a substance over a distance. This parameter helps in determining the movement of a substance from higher concentration to lower concentration.

Fick's Second law of diffusion

Fick's Second law of diffusion states that the rate of change of concentration of a substance with time is proportional to the rate of the movement of the substance by diffusion.

The mathematical equation for Fick's Second Law is given as follows:

∂C/∂t = D(∂2C/∂x2),

where C is the concentration of the diffusing species, t is the time, x is the distance, and D is the diffusion coefficient.

The parameter ∂C/∂t refers to the rate of change of concentration with time, while ∂2C/∂x2 refers to the rate of change of concentration with distance. These parameters are important in determining the rate of diffusion of a substance in a given system.

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PLEASE HELP ME!!!! I really need to get a good grade on this assignment I WILL give brainly points

Answers

The answer is true. It does increase

Which transformation can NOT be used to prove that ABC is congruent to DEF?

A. Rotation
B. Dilation
C. Reflection
D. Translation

Answers

Hello!

Which transformation can NOT be used to prove that ABC is congruent to DEF?

The transformation you'd need to use would be a dilation.

According to the Pythagorean theorem

It is B. Dilation

Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions, and whole numbers.
i) 3/7 ii) 5/8 iii) 9/7 iv) 6/5 v) 12/7 vi) 1/8 vii) 1/11

Answers

The reciprocal of each of the following fractions:

i) 7/3 - improper fraction

ii) 8/5 - improper fraction

iii) 7/9 - proper fraction

iv) 5/6 - proper fraction

v) 7/12 - proper fraction

vi) 8 - whole number

vii) 11 - whole number

To find the reciprocal of a fraction, we simply invert the fraction by swapping the numerator and the denominator.

i) Reciprocal of 3/7: 7/3

- Classification: Improper fraction

ii) Reciprocal of 5/8: 8/5

- Classification: Improper fraction

iii) Reciprocal of 9/7: 7/9

- Classification: Proper fraction

iv) Reciprocal of 6/5: 5/6

- Classification: Proper fraction

v) Reciprocal of 12/7: 7/12

- Classification: Proper fraction

vi) Reciprocal of 1/8: 8/1 or simply 8

- Classification: Whole number

vii) Reciprocal of 1/11: 11/1 or simply 11

- Classification: Whole number

So, to summarize the classifications:

- Proper fractions: 7/9, 5/6, 7/12

- Improper fractions: 7/3, 8/5

- Whole numbers: 8, 11.

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he cardinality of a finite set is the number of elements in the set. What is the cardinality of set A

Answers

The cardinality of the set A is 4

How to determine the cardinality of set A

From the question, we have the following parameters that can be used in our computation:

A = {2, 4, 6, 8}

In the above, we can see that

There are 4 elements in the set

By the definition of cardinality, we have the cardinality of set A to be 4

Hence, the cardinality of set A is 4

Answers

Answer:

3.75 as a decimal

Step-by-step explanation:

I NEED SOME HELP!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Find the values of the variables and the lengths of the sides of this kite.

Answers

Answer:

x = 7, y = 16

Step-by-step explanation:

Looking at the image we can conclude the following
Sides with measurements y - 4 and x + 5 are equal

So we get the equation y - 4 = x + 5

The sides with measurements 2x + 5 and x + 12 are equal\

We get another equation 2x + 5 = x + 12

Let's take the second equation which is in terms of x only and solve for x

2x + 5 = x + 12

Subtract x from both sides

2x - x + 5 = x - x + 12

==> x + 5 = 12

Subtract 5 from both sides:
x + 5 - 5 = 12 - 5

x = 7

Now that we know the value of x, we can substitute this value into the first equation y - 4 = x + 5

==> y - 4 = 7 + 5

y - 4 = 12

Add 4 to both sides:

y - 4 + 4 = 12 + 4

y = 16

6-3x=2x-4
explain why it’s a one solution problem

Answers

Step-by-step explanation:

notice how there is a variable. that is the reason. since there is an variable and we solve for it thats why it will lead us to 1 solution.

solve the following equation for y 2x - 4y = -8

Answers

Answer:

y = (x/2) + 2

Step-by-step explanation:

Given equation,

→ 2x - 4y = -8

Solving for the value of y,

→ 2x - 4y = -8

→ -4y = -2x - 8

→ 4y = 2x + 8

→ y = (2x + 8)/4

→ [ y = (x/2) + 2 ]

Hence, the value is (x/2) + 2.

PLEASE HELP RATIONAL EQUATIONS

Answers

It’s the first one.

Find the amount accumulated after
investing a principal P for t years at an
interest rate compounded annually.
P = $15,500
r = 9.5%
t = 12
Hint: A = P (1 + ) kt
A = $[?]
Round your answer to the nearest cent (hundredth).

Answers

The amount accumulated after investing a principal P for t years at an interest rate compounded annually is $46,057.58.

How to solve compound interest ?

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

$A = p(1 + \frac{r}{n} )^{nt}$

where

P = principalr = ratet = timen = number of time

p = 15,500

r = 9.5%

t = 12

n = 1

$A = 15500(1 + \frac{0.095}{1} )^{1(12)}$

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

A medium-sized shipping box with side length s
units has volume of s^3 cubic units.
a. A large shipping box has side lengths that are 3
units longer than the medium box. Write a
binomial expression for the volume of the large box.
b. Expand the polynomial in part a to simplify the
volume of the large shipping box.
c. A small shipping box has side lengths that are 2
units shorter than the medium box. Write a
binomial expression for the volume of the small
shipping box.

Answers

Answer:

See below

Step-by-step explanation:

Medium- sized box:

Side = s, Volume = s^3

a) Large -sided box

Side = s + 3Volume = (s + 3)^3

(s + 3)^3 = s^3 + 9s^2 + 27s + 27

c) Small-sized box

Side = s - 2Volume = (s - 2)^3 =s^3 - 6s^2 + 12s - 8

1
=
Using two pieces of data from the table below, write the equation of a line in slope-intercept form.
-4
0
4
8
12
29
28
27
26
25
A. y = 4x - 28
B. y = - 4x + 28
OC. y= 3x-28
OD. y=x+28

Answers

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 4, 29) and (x₂, y₂ ) = (0, 28) ← 2 ordered pairs from the table

m = $\frac{28-29}{0+4}$ = - $\frac{1}{4}$

The line crosses the y- axis at (0, 28 ) ⇒ c = 28

y = - $\frac{1}{4}$ x + 28 ← equation of line → D

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There are TWO answers needed for this question John rode 2 kilometers on his bike. His sister Sally rode 300 meters on her bike. Who rode the farthest and how much farther did they ride (answer in km)? Describe two ways that the point (3,7) can be transformed to the point (7,3) . guys help rn whats Enter the value for x that makes the equation 1/2 (10x-4)+3x=30 If a legal monopoly owns the exclusive rights to a good for 20 years, it has a ________ for that good. PleaseeeeeeeeeeeeeeeeeeeeeeeeeJust Answer Get 50 Points. The Dawes Commission goal was to negotiate agreements with the leaders of the Cherokee, Choctaw, Chickasaw, Creek, and Seminole that would end tribal land ownership and give each member individual possession of a portion of the tribal lands.True or False? Les livres ? Nous ne les avons pas encore _____a) lusb) luesc) lud) lis Why does the US government create regulatory agencies? Check all that apply. 1.To create fair competition between producers 2.To limit the knowledge of certain consumers 3.To allow producers to have greater freedom 4.To protect consumers' health and safety 5.To prevent the formation of monopolies Stalin attended this on scholarship, but was kicked out How do we correctly store products?. 1. Harmony enhances a melodyTrueFalse Explain the Principle of operation of 3-phase induction motor to assist with searching for a missing child, the operations section chief assigns 4 teams of 3 people each to specific search areas. the operations section chief is applying what ics principle? What is the quality of the cord shown in the diagram? What is the authors overall claim in the passage? A. Efforts must be taken to conserve water. B. Water is a valuable resource for people. C. Water is often wasted on peoples yards. D. Efforts must be taken to conserve energy. Which of the following expenditures of a trust or estate is divided equally between principal and income under the provisions of the Uniform Act? A. Property taxes imposed on real property held by the trust B. Estate taxes paid by the estate C. Ordinary repairs of property held by a trust D. Investment advisory services Submit Ansirers A professor wants to estimate how many hours per week her students study. A simple random sample of 53 students had a mean of 19 hours of studying per week. Construct a 90%90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 33 hours per week. Round to two decimal places. What is the correct order that the four parts of a cover letter should appear in? a. Introduction, Heading, Argument, Closing b. Heading, Introduction, Argument, Closing c. Introduction, Argument, Heading, Closing d. Heading, Introduction, Closing, Argument Please select the best answer from the choices provided A B C D Which among the following is in the form of an atoll?A) the northern mountain. B) the peninsular plateauC)the great Indian desert. D) The Lakshadweep Between 1820 - 1840 because of power sources and trade routes, which mid-western towns grew into urban centers the fastest? (please help and explain and give the right answer) a. the communities built on waterfronts and waterways. b. the communities built on the open prairie. c. the communities built by the mountains.