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

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