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, x=65.9 words, s=16.4 words. Given that this dictionary has 1423 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 49.2 words. Use a 0.10 significance level to test the claim that the mean number of words per page is greater than 49.2 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>49.2 words H1: μ<49.2 words B. H0: μ=49.2 words H1: μ>49.2 words C. H0: μ=49.2 words H1: μ<49.2 words D. H0: μ=49.2 words H1: μ≠49.2 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. (Reject/Fail to reject) H0 The

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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Question

A simple random sample of

pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results

n=10,

x=65.9

words,

s=16.4

words. Given that this dictionary has

1423

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

49.2

words. Use a

0.10

significance level to test the claim that the mean number of words per page is greater than

49.2

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?

H0:

μ>49.2

words

H1:

μ<49.2

words

H0:

μ=49.2

words

H1:

μ>49.2

words

H0:

μ=49.2

words

H1:

μ<49.2

words

H0:

μ=49.2

words

H1:

μ≠49.2

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.

(Reject/Fail to reject) H0 There is (not sufficient/sufficient) evidence to conclude that the mean of the population of ratings is (greater than/Not/Less than/equal)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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