Question: As the vice president of marketing for Sparkling Clean dishwasher detergent, you have recently become concerned by a new marketing campaign of one of your competitors. Historically, Sparkling Clean has held a 30% share of the dishwasher detergent market. In order to see if the competitors marketing campaign has reduced your market share, you charge your marketing team with taking a survey based on a random sample of 25 consumers to determine their dishwasher detergent preferences.

a) Assuming Sparkling Clean still maintains its 30% market share, what is the probability that exactly 5 respondents in the survey will say they prefer Sparkling Clean over other brands of dishwashing detergent?

b) In the actual survey of 25 consumers, only 2 consumers indicated a preference for Sparkling Clean. Is there sufficient evidence to conclude that there has been a loss of market share for Sparkling Clean? (Hint: Compute the probability of 2 or fewer consumers indicating a preference for Sparkling Clean in the sample of 25 consumers under the assumption that Sparkling Clean has a 30% market share. Work this calculated figure into your response.)