The goal of your marketing campaign is for more than 25% of supermarket shoppers to recognize your brand name. A recent survey of 150 random shoppers found that 21.3% recognized your brand name.
a. It might be argued that the burden of proof is to show that more than 25% of shoppers recognize your brand name. Identify the appropriate one-sided hypotheses in this case and perform the test at level 0.05.
b. On the other hand, it might be argued that you would be interested in knowing about all three possibilities: significantly more than 25% (indicating success), significantly less than 25% (indicating failure), and not significantly different from 25% (indicating that there is not enough information to say for sure). Identify the appropriate two-sided hypotheses in this case and perform the test at level 0.05.
c. For the two-sided test, write a brief paragraph describing the result, the error that might have been made, and its implications for your marketing strategy.