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andreyandreev [35.5K]
3 years ago
14

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

imate at the 99% level of confidence. For a sample of 4657 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.7. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.
Mathematics
1 answer:
Lesechka [4]3 years ago
5 0

Answer:

The 99% confidence interval is given by (24.7;25.2)    

Step-by-step explanation:

1) Previous concepts

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".

\bar X=24.9 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=5.7 represent the population standard deviation

n=4657 represent the sample size

Confidence =0.99 or 99%  

2) Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

24.9-2.58\frac{5.7}{\sqrt{4657}}=24.685    

24.9+2.58\frac{5.7}{\sqrt{4657}}=25.115

So on this case the 99% confidence interval would be given by (24.7;25.2)    

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Please help with this question!! I need serious help!!
asambeis [7]

Answer:

<h2>The circumference is multipled by 4.</h2>

Step-by-step explanation:

The formula of an area of a circle"

A=\pi r^2

The formula of a circumference of a circle:

C=2\pi r

The area multipled by 16:

16A=16\pi r^2\\\\16A=\pi(4^2r^2)\\\\16A=\pi(4r)^2

The radius has increased fourfold, therefore:

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Calculate the radius:

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r^2=2152.96\to r=\sqrt{2152.96}\\\\r=46.4\ in

Calculate the circumference of both circles:

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th
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Answer:

The rocket hits the ground at a time of 11.59 seconds.

Step-by-step explanation:

The height of the rocket, after x seconds, is given by the following equation:

y = -16x^2 + 177x + 98

It hits the ground when y = 0, so we have to find x for which y = 0, which is a quadratic equation.

Finding the roots of a quadratic equation:

Given a second order polynomial expressed by the following equation:

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This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

y = -16x^2 + 177x + 98

-16x^2 + 177x + 98 = 0

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Write your answer in the space below.

The answer to the question Is all 5.

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Write your answer in the space below.

Group 1 is a success because none of the numbers 73 and 99 show up.

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Write your answer in the space below.

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