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 overbarequals59.2 ​words, sequals15.1 words. Given that this dictionary has 1437 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 48.7 words. Use a 0.05 significance level to test the claim that the mean number of words per page is greater than 48.7 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. Upper H 0​: muequals48.7 words Upper H 1​: mugreater than48.7 words Your answer is correct.B. Upper H 0​: muequals48.7 words Upper H 1​: munot equals48.7 words C. Upper H 0​: muequals48.7 words Upper H 1​: muless than48.7 words D. Upper H 0​: mugreater than48.7 words Upper H 1​: muless than48.7 words

Determine the test statistic.

Answer 1

Solution :

Given that ,

= 48.7

= 59.2

s = 15.1

n = 20

The null and alternative hypothesis is ,

Upper H₀ :   = 48.7

Upper H₁ : >  48.7

This is the right tailed test .

Test statistic = t

= ( - ) / s / n

= ( 59.2 - 48.7) / 15.1 / 20

= 3.11

The test statistic = 3.11