A teacher would like to know the average height (in inches) of the students in her school. She divided the students into 4 groups based on their ages from the youngest to the oldest. The total number of students for group 1 is 125, for group 2 is 118, for group 3 is 132, and for group 4 is 123. Random samples of heights of students are taken from each group where the sample size, sample mean, and sample standard deviation are summarized in the following table.

Group 1 Group 2 Group 3 Group 4 ni 45 34 41 30 xi 58 64 63.5 65 si 0.3 0.1 1.1 0.8

a. Using an unbiased estimation procedure, estimate the mean height of students in the school.

b. Find a 90% confidence interval for the mean height of students in group 1.

c. Find a 90% confidence interval for the mean height of students in the whole school.