A manager of a certain shop is interested in the customer satisfaction. She collects questionnaires from 77 randomly chosen customers and studies the proportion of customers who are unhappy (= not satisfied) with the service. To be able to better identify the sources of unhappiness, she splits the customers into two groups based on where they made their orders: online or in a shop. In her sample, she observes the following numbers: 15 customers who made their orders online were unhappy with the service; this corresponds to 37.5% of the customers who shopped online. Among the questioned customers who made their orders in a shop, there were 21 unhappy customers.

Note that all customers who are not unhappy are considered satisfied. Round to three digits, but only at the end, and use the critical values in the following table.

	/2
20%	1.282
10%	1.645
5%	1.960
1%	2.576

a) Find the 95% confidence interval for the proportion of unhappy customers among all customers who make their orders in a shop

b) Find the 99% confidence interval for the proportion of satisfied customers among all customers who make their orders online

c) Find the 95% confidence interval for the proportion of unhappy customers among all customers

d) Does the (individual) 80% confidence intervals for the proportion of unhappy customers for the two groups of customers intersect? How?

e) What is the natural point estimator for the proportion of unhappy customers among all customers make their orders in a shop