A simple random sample of

20

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

n=20,

x=53.1

words,

s=16.1

words. Given that this dictionary has

1478

pages with defined , the claim that there are more than 70,000 defined is equivalent to the claim that the mean number of words per is greater than

47.4

words. Use a

0.01

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

47.4

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.