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=52.8 ​words, s=15.4 words. Given that this dictionary has 1442 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 48.5 words. Use a 0.05 significance level to test the claim that the mean number of words per page is greater than 48.5 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?

A. H0​: μ>48.5 and H1​: μ<48.5 words

B. H0​: μ=48.5 and H1​: μ≠48.5 words

C. H0​: μ=48.5 and H1​: μ>48.5 words

D. H0​: μ=48.5 and H1​: μ<48.5 words

Determine the test statistic. ___ (round to two decimals places)

Reject

Fail to reject

Upper H 0H0.

There is ____ (sufficient or not sufficient evidence) to support the claim that there___ (are more than, are, are fewer than) ​70,000 defined words in the dictionary

Answer 1

Solution :

Given that,

This a right (One) tailed test.

The null and alternative hypothesis is,  

C)

Ho: 48.5

Ha: 48.5

The test statistics,

t =( - )/ (s /n)

= ( 52.8 - 48.5) / ( 15.4 / 20 )

= 1.25

P-value = 0.1132

The p-value is p = 0.1132 > 0.05, it is concluded that fail to reject the null hypothesis.

There is not sufficient evidence to support the claim that there are more than​ ​70,000 defined words in the dictionary.