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Name: #35- A simple random sample of 10 pages from a dictionary is obtained.
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Description: #35- A simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results n=10, (bar x)=55.7 words, s=16.5 words. Given that this dictionary has 1492 pages with defined words, t

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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#35- A simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results n=10, (bar x)=55.7 words, s=16.5 words. Given that this dictionary has 1492 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 46.9 words. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 46.9 words. What does the result suggest about the claim that there are more than 70,000 defined words? Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed.

What are the null and alternative hypotheses?

A. H0: μ=46.9 words

H1: μ>46.9words

B. H0: μ>46.9words

H1: μ<46.9 words

C. H0: μ=46.9 words

H1:μ≠46.9 words

D. H0: μ=46.9 words

H1: μ<46.9 words

Determine the test statistic.

_____(Round to two decimal places as needed.)

Determine the P-value.

_____(Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

(Fail to reject/ Reject) H0. There is (sufficient/not sufficient)

evidence to support the claim that there (are/are fewer than/are more than) 70,000 defined words in the dictionary.

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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