Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are not business related.A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance.Fifty-four of the messages were not business related.The appropriate decision is __.
A)increase the sample size
B)gather more data
C)reject the null hypothesis
D)do not reject the null hypothesis
E)maintain status quo

Question

Quizplus · Accepted Answer

A hypothesis test is conducted to determine if there is sufficient evidence to reject the null hypothesis. In this case, the null hypothesis is that less than or equal to 25% of email messages sent by GFS employees are not business related. The alternative hypothesis is that more than 25% of email messages are not business related.
Based on the sample data, 54 out of 300 emails were not business related. We can calculate the test statistic using the formula: 
z = (p̂ - p) / √(p*(1-p)/n)
where p̂ is the sample proportion of emails that are not business related, p is the hypothesized proportion of emails that are not business related, and n is the sample size.
In this case, p̂ = 54/300 = 0.18 and p = 0.25. Plugging these values into the formula, we get:
z = (0.18 - 0.25) / √(0.25*(1-0.25)/300) = -2.572
Using a z-table or calculator, we can find that the p-value associated with this test statistic is less than 0.01. This means that there is less than a 1% chance of obtaining a sample proportion as extreme as 0.18, assuming that the true proportion is actually 0.25 or less. 
Since the p-value is less than the significance level of 0.01, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than 25% of email messages sent by GFS employees are not business related. Therefore, the appropriate decision is to reject the null hypothesis (choice C).