According to Secure List, 71.8% of all email sent is spam. A system manager at a large corporation believes that the percentage at his company may be 80%. He examines a random sample of 500 emails received at an email server, and finds that 382 of the messages are spam.

a. State the appropriate null and alternate hypotheses.

b. Compute the test statistic z.

c. Using α = 0.05, can you conclude that the percentage of emails that are spam differs from 80%?

d. Using α = 0.01, can you conclude that the percentage of emails that are spam differs from 80%?