5. Let x represent the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean and standard deviation of the x distribution are ? = 2 minutes and ? = 0.8 minutes, respectively. (a) If x is the sample mean time for a random sample of n = 9 students, where is the sampling distribution of x centered, and what is the standard deviation of the sampling distribution of x? (Round your standard deviation to three decimal places.) ?x = ?x = (b) Repeat part (a) for a sample of size of n = 20. (Round your standard deviation to three decimal places.) ?x = ?x = Repeat part (a) again for a sample of size of n = 100. (Round your standard deviation to three decimal places.) ?x = ?x = How do the centers and variabilities of the three x sampling distributions compare to one another? The three centers are all the same, and the larger the sample size, the smaller the standard deviation of the x distribution.The three centers are all the same, and the larger the sample size, the larger the standard deviation of the x distribution. The larger the sample size, the larger the center and the standard deviation of the x distribution.The larger the sample size, the smaller the center and the standard deviation of the x distribution.The larger the sample size, the larger the center and the smaller the standard deviation of the x distribution. Which sample size would be most likely to result in an x value close to ?, and why? Since the sampling distribution of when n = (9, 20, 100) has the (SMALLEST/LARGEST) standard deviation, this sample size is most likely to result in a value of x close to ?.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5. Let x represent the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean and standard deviation of the x distribution are ? = 2 minutes and ? = 0.8 minutes, respectively.

(a)

is the sample mean time for a random sample of

n = 9 students,

where is the sampling distribution of

centered, and what is the standard deviation of the sampling distribution of

(Round your standard deviation to three decimal places.)

?_x

(b)

Repeat part (a) for a sample of size of

n = 20.

(Round your standard deviation to three decimal places.)

?_x

Repeat part (a) again for a sample of size of

n = 100.

(Round your standard deviation to three decimal places.)

?_x

How do the centers and variabilities of the three

sampling distributions compare to one another?

The three centers are all the same, and the larger the sample size, the smaller the standard deviation of the x distribution.The three centers are all the same, and the larger the sample size, the larger the standard deviation of the x distribution. The larger the sample size, the larger the center and the standard deviation of the x distribution.The larger the sample size, the smaller the center and the standard deviation of the x distribution.The larger the sample size, the larger the center and the smaller the standard deviation of the x distribution.

Which sample size would be most likely to result in an

value close to ?, and why?

Since the sampling distribution of when

n = (9, 20, 100)

has the (SMALLEST/LARGEST) standard deviation, this sample size is most likely to result in a value of x close to ?.

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