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=52.8 words, s=16.6 words. Given that this dictionary has 1439 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 48.6 words. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.6 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

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 1.1315

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.1315 ) = 0.136
Reject null hypothesis if P value < level of significance
P - value = 0.136 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that  the mean number of words per page is greater than 48.6 words. at 1% level of significance.

Since the mean number of words per page is not greater than 48.6, we cal also conclude that  there are no more than 70,000 defined words.

I.e There are less than 70000 defined words.