Question

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=65.7 words, s=15.4 words. Given that this dictionary has 1430 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 49.0 words. Use a 0.10 significance level to test the claim that the mean number of words per page is greater than 49.0 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.

a. What are the null and alternative hypotheses?

b. Determine the test statistic. (Round to two decimal places as needed.)

c. Determine the P-value. (Round to three decimal places as needed.)

Answer 1

Claim:-  mean number of words per page is greater than 49.0 words

So, it is a right tailed hypothesis test

(A)

using TI 84 calculator

press stat then tests then Ttest

enter the data

press enter, we get

(B) test statistic = 3.43

(C) p value = 0.004

p value is less than 0.10 significance level, so we can reject the null hypothesisn

therefore, there is sufficient evidence to conclude that the mean number of words per page is greater than 49.0 words