3. A company’s penetration rate is the percent of the market that uses its product. A market research firm is testing the
penetration rate for ACME widgets. In a random sample of 425 widget consumers, 185 purchased the ACME brand.

(a) Do these data provide good evidence that ACME’s penetration rate for widgets is greater than 40%? Test at the
2.5% level of significance.

(b) Explain the meaning of the P-value in the context of the data.