a) Population: Entire high school student body.
b) Sample: 50 students randomly chosen from each grade level.
c) Sampling Method: Stratified random sampling.
d) Parameter: Proportion of all students playing sports.
Statistic: Proportion of sample students playing sports (estimates parameter)
a. Population: The entire student body at the high school is the population, as it represents the group from whom the teacher wants to draw conclusions about the proportion of students playing sports.
b. Sample: The 50 students randomly chosen from each grade level make up the sample. This is a subset of the population used to estimate the proportion of students playing sports for the entire school.
c. Sampling Method: The teacher used a stratified random sampling method. He first divided the population into strata based on grade levels (e.g., 9th, 10th, 11th, 12th), ensuring each level is represented in the sample. Then, he randomly selected 50 students from each stratum, giving each student an equal chance of being chosen.
d. Parameter and Statistic (Extra credit):
Parameter: The proportion of students in the entire school population who play at least one sport is the parameter we want to estimate. It's unknown and fixed for the entire population.
Statistic: The proportion of students in the sample who play at least one sport is the statistic we calculate based on the sample data. It's an estimate of the population parameter and varies depending on the specific sample chosen.
Therefore, by studying the sample proportion, the teacher can get an idea of the true proportion of sport-playing students in the whole school population (parameter).