1. A local government official observes an increase in the number of individuals with cardiovascular and obesity problems in his barangay. In order to improve the health conditions of his constituents, he aims to promote an easy and cheap way to reduce weight. It is known that obesity results in greater risk of having illnesses like diabetes and heart problems. He encouraged his constituents to participate in his Dance for Life project every weekend for 3 months. To know if the program is effective in reducing weight, he randomly selected 12 participants from the group who completed the program. The weight loss data, in kilograms, of the 12 randomly selected participants after completing the program are: 0.5, 0.7, 0.9, 1.1, 1.2, 1.3, 1.4, 2.0, 2.3, 2.4, 2.7, and 3.0. It is known that the weight loss of those who have completed the dance program follows a normal distribution with a standard deviation of 1.8 kg.

a. Compute for themean, construct and interpret a90% confidence intervalfor the true mean weight loss of the participants who have completed the dance program.

b. How many participants must be sampled in order to be95% confidentthat the estimated mean weight loss of the participants will be within0.5 kgof the true mean?