Question

A simple random sample of 20 pages from a dictionary is obtained. The numbers of words defined on those pages are​ found, with the results nequals20​, x overbarequals54.3 ​words, sequals16.6 words. Given that this dictionary has 1477 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 47.4 words. Use a 0.10 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.

Answer 1

H₀: = 47.4

H₁: > 47.4

The test statistic t = ()/(s/)

                             = (54.3 - 47.4)/(16.6/)

                            = 1.86

P-value = P(T > 1.86)

             = 1 - P(T < 1.86)

             = 1 - 0.9608

             = 0.0392

Since the P-value is less than the significance level(0.0392 < 0.10), we should reject H₀.

So there is sufficient evidence to support the claim that the mean number of words per page is greater than 47.4 words.

Hence there is sufficient evidence to support the claim that there are more than 70,000 defined words.