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=53.75 ​words, s=15.21 words. Given that this dictionary has 1484 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 47.24 words. Use a 0.100 significance level to test the claim that the mean number of words per page is greater than 47.24 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 47.24
Alternative Hypothesis, Ha: μ > 47.24

Rejection Region
This is right tailed test, for α = 0.1 and df = 19
Critical value of t is 1.328.
Hence reject H0 if t > 1.328

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (53.75 - 47.24)/(15.21/sqrt(20))
t = 1.914

P-value Approach
P-value = 0.0354
As P-value < 0.1, reject the null hypothesis.

There is sufficient evidence to conclude that the mean number of words per page is greater than 47.24 words