In marketing, response modeling is a method for identifying customers most likely to respond to an advertisement. Suppose that in past campaigns 31.6% of customers identified as likely respondents did not respond to a nationwide direct marketing campaign. After making improvements to their model, a team of marketing analysts hoped that the proportion of customers identified as likely respondents who did not respond to a new campaign would decrease. The analysts selected a random sample of 1500 customers and found that 441 did not respond to the marketing campaign.

 

 

The marketing analysts want to use a one? sample z? test to see if the proportion of customers who did not respond to the advertising campaign, p, has decreased since they updated their model. They decide to use a significance level of ?=0.05.

 

Determine the p? value for this test. Give your answer precise to at least three decimal places.

 

Determine the value of the z? statistic. Give your answer precise to at least two decimal places.