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.

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.

Transcribed Image Text:

n₂ x₂ S₁ Group 1 45 58 0.3 Group 2 34 64 0.1 Group 3 41 63.5 1.1 Group 4 30 65 0.8