Question 2

A study of ad effectiveness found that 20% of consumers who had not yet been exposed to a new advertising campaign (the “control group”) reported having a “favorable” or “very favorable” perception of a certain brand. By contrast, out of a simple random sample of 400 consumers who were exposed to the advertising campaign, 100 (25%) reported having a “favorable” or “very favorable” perception of the brand. The advertising company claims that their ad has increased the fraction of exposed customers with “favorable” or “very favorable” perceptions of the brand by at least

10%, from the base level of 20% in the control group to a new level of at least 22% (MLE = 25%).

Question 2a. What is the probability that 100 or more out of 400 people would respond favorably (i.e., with a “favorable” or “very favorable” perception) by chance if the true probability of such a response is 0.2?

Question 2b. What is the probability that 100 or more out of 400 people would respond favorably (i.e., with a “favorable” or “very favorable” perception) by chance if the true probability of such a response is 0.22?

My incorrect answers:

#Q2

p=0.2

n=400

se=sqrt((p*(1-p))/n)

pcap=100/400

z=(pcap-p)/se

round(1-pnorm(z),4)

# Answer=0.0062

#Q3

p1=0.22

n=400

se1=sqrt((p1*(1-p1))/n)

pcap=100/400

z1=(pcap-p1)/se1

round(1-pnorm(z1),4)

# Answer=0.0738