Elwin Osbourne,CIO at GFS,Inc.,suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail 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) fail to reject the null hypothesis
E) maintain status quo

Question

Quizplus · Accepted Answer

The null hypothesis is that no more than 25% of e-mails sent by GFS employees are not business related. The alternative hypothesis is that more than 25% of e-mails are not business related.

Using a significance level of 0.01, we can compare the observed proportion of non-business emails in the sample (54/300 = 0.18) to the expected proportion of no more than 25%.

We can use a one-sample proportion test to calculate the p-value. The test statistic is:

z = (0.18 - 0.25) / sqrt[(0.25 * 0.75) / 300] = -3.21

The corresponding p-value is less than 0.01, which means that the observed proportion of non-business emails is statistically significantly lower than the expected proportion.

Therefore, we reject the null hypothesis and conclude that more than 25% of e-mails sent by GFS employees are not business related. The company may need to take action to address this issue.