During a infuenza epidemic, 4% of the population of a large city was affected on

Question

During a infuenza epidemic, 4% of the population of a large city was affected on a given day. The manager of a factory that employs 100 people found that 12 of his employees were absent, claiming to have influenza a. Using a 5% sigificane level, find the critical region that would enable the manager to test whether or not there is evidence that the percentage of people having influenza at his factory was greater than that of the large city. b. State the conclusion the manager came to giving a reason for your answer.

Explanation / Answer

(a) Ho: p=0.04 (i.e. null hypothesis)

Ha: p>0.04 (i.e. alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(12/100-0.04)/sqrt(0.04*(1-0.04)/100)

=4.08

Given a=0.05, the critical value is Z(0.05) = 1.645 (from standard normal table)

Since Z=4.08 is greater than 1.645, we reject Ho.

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(b) So we can conclude that there is evidence that the percentage of people having influenza at his factory was greater than that of the large city

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