The manager of a large company that sells electronic devices online wants to increase sales by encouraging repeat purchases. The manager believes that if past customers are offered 50 dollars of their next purchase, more than 40% of them will place an order. To investigate the believe, 60 customers who placed an order in the past year are selected at random. Each of the selected customers is sent an email with a coupon for 1 $50 off the next purchase if the order is placed within 30 days. Of those who receive the coupon, 25 place an order. (a) State null and alternative hypotheses relevant to determining whether there is convincing statistical evidence that the manager's belief is correct.

(b) Are the assumptions for performing the one-sample z-test for a population proportion satisfied? Explain.

(c) Perform a test of the stated hypotheses at the 5% significance level. Make sure to compute the test statistic and p-value and make a conclusion in the context of the problem.

(d) Based on your conclusion from part (c) which of the two errors, Type I or Type II could have been made? Interpret the consequence of the error in context.