Suppose that Felisha is a librarian, and she read in a scholarly journal that the number of words in children's picture books published since 1950 is normally distributed with a mean of 802.2 words and a standard deviation of 92.0 words. She wishes to construct a confidence interval for the mean number of words in all children's picture books published after 2010, in case the number has changed in recent years. Felisha took a random sample of 20 children's picture books published after 2010 and counted the number of words in all 20 books. Her data is presented in the stem-and-leaf plot. table represents stem and leaf plot: 4 9 5 1 9 6 0 4 5 7 0 3 4 6 8 8 1 3 4 6 9 1 5 9 10 1 7 Leaf Unit=10 Felisha calculated the mean of her sample to be 773.0 words, and now she wants to calculate the margin of error of a 99% confidence interval for the mean number of words in all books published after 2010. She assumes that the number of words in children's picture books published after 2010 has the same normal distribution and same standard deviation as the general population of all books published since 1950. Compute the margin of error of a 99% confidence interval for the mean number of words in all children's picture books published after 2010. Give your answer precise to one decimal place.

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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Suppose that Felisha is a librarian, and she read in a scholarly journal that the number of words in children's picture books published since 1950 is normally distributed with a mean of 802.2 words and a standard deviation of 92.0 words. She wishes to construct a confidence interval for the mean number of words in all children's picture books published after 2010, in case the number has changed in recent years. Felisha took a random sample of 20 children's picture books published after 2010 and counted the number of words in all 20 books. Her data is presented in the stem-and-leaf plot.

table represents stem and leaf plot:

4	9
5	1	9
6	0	4	5
7	0	3	4	6	8
8	1	3	4	6
9	1	5	9
10	1	7

Leaf Unit=10

Felisha calculated the mean of her sample to be 773.0 words, and now she wants to calculate the margin of error of a 99% confidence interval for the mean number of words in all books published after 2010. She assumes that the number of words in children's picture books published after 2010 has the same normal distribution and same standard deviation as the general population of all books published since 1950.

Compute the margin of error of a 99% confidence interval for the mean number of words in all children's picture books published after 2010. Give your answer precise to one decimal place.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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