1. A group of policy analysts offered a group of 317 students in Kenya education subsidies. They followed the students and observed their average number of years of education is 8.2 years. The researchers know that the number of years of education in the population has the standard deviation 4.5 years.

(a) (5 points) Calculate a 90% confidence interval for the mean number of years of education if the population of students were offered the same subsidy. Interpret the result.

(b) (4 points) Suppose the researchers wanted to obtain a 90% confidence interval with a margin of error of 0.2. What is the minimum sample size they have to observe to achieve their objective?

2. In an European country, the average number of children in a family is = 1.24, with standard deviation of = 1.26. Suppose you sample 120 families and calculate the mean number of children.

(a) (6 points) What percentage times you will get a mean larger than 1?

(b) (6 points) Now suppose you don't know the value of , but you still know = 1.26. You sample 63 families and you

observe the average number of children is 3.142. Calculate a 95% confidence interval for .

(c) (4 points) With the information above, calculate a 99% confidence interval for .