Question

A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 76% . He examines a random sample of 500 emails received at an email server, and finds that 360 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from ? use both and levels of significance and the -value method with the ti-84 plus calculator.

Answer 1

The question is about whether the true percentage of spam emails at a corporation is different from a reported 71.8% using hypothesis testing with a TI-84 Plus calculator.

Step-by-step explanation:

The student is asking whether the percentage of emails that are spam at a corporation is statistically different from a researcher-reported percentage. In this case, the researcher reports a 71.8% spam rate, while the system manager of the corporation believes their rate is 76%. Testing a sample of 500 emails, 360 are spam, constituting 72%. To answer using both α levels of significance (typically 0.05 and 0.01) and the p-value method, we would use a hypothesis test for a proportion on a TI-84 Plus calculator.

We define our null hypothesis as the proportion of spam emails being equal to 71.8% and the alternative hypothesis as the proportion being different from 71.8%. Calculating the standard error, we find the z-score and then determine the p-value. If the p-value is lower than our α level, we reject the null hypothesis, suggesting the true proportion of spam emails at the corporation is statistically different from 71.8%.