Final answer:
To select 20 teachers for a survey about opinions on teaching 6 out of 7 periods, Mrs. King can use a simple random sample by assigning numbers to each teacher and randomly selecting 20 numbers. Alternatively, she can use a stratified random sample by dividing teachers into groups and selecting a proportional number from each group. A systematic random sample involves assigning numbers to teachers and selecting every nth teacher. Stopping the first 20 teachers seen in the foyer is not a good idea as it introduces bias.
Step-by-step explanation:
a) Simple Random Sample
In order to select 20 teachers using a simple random sample (SRS), Mrs. King would need to assign each teacher at PWSH a unique identifier number. She could then use a random number generator or a table of random numbers to select 20 numbers corresponding to the teachers' identifiers. The teachers with those identifiers would be selected for the survey.
b) Stratified Random Sample
To select 20 teachers using a stratified random sample, Mrs. King would first divide the teachers at PWSH into different strata based on certain characteristics, such as grade level or subject area. She would then randomly select a proportional number of teachers from each stratum. For example, if there are 4 grade levels (freshman, sophomore, junior, senior), she could randomly select 5 teachers from each grade level to ensure representation from each group.
c) Systematic Random Sample
To use a systematic random sample, Mrs. King would first assign each teacher at PWSH a number. She would then determine the sampling interval by dividing the total number of teachers (200) by 20 (the desired sample size). Starting at a random point, she would select every nth teacher based on the sampling interval. For example, if the sampling interval is 10, she would select the 10th, 20th, 30th, and so on, teachers until she reaches a total of 20.
d) Not a Good Idea
Mrs. King's decision to stop the first 20 teachers she sees in the foyer would not be a good idea because it introduces bias into the sample. The teachers she sees first may not be representative of the entire population of teachers at PWSH. Additionally, the teachers in the foyer at any given time may not be a random sample of all the teachers at PWSH.