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 n =20​, x overbar =57.8 ​words, s =15.9 words. Given that this dictionary has 1494 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 0.10 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?

Determine the test statistic. ____ (round to two decimals)

State the final conclusion that addresses the original claim.:

Fail or reject? There is ____(not sufficient or sufficient) evidence to support the claim that there ____ ​70,000 defined words in the dictionary.

Answer 1

Solution :

Given that,

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 46.9

Ha: 46.9

The test statistics,

t =( - )/ (s /n)

= ( 57.8 - 46.9 ) / ( 15.9 / 20 )

= 3.07

P-value = 0.0032

The p-value is p = 0.0032 < 0.10, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to support the claim that there are more than​ ​70,000 defined words in the dictionary.